Back to "Padova-Verona research group on Constructive Approximation and Applications" (CAA) Home Page

Publications and preprints of the CAA group 2005-present
(downloadable pdf)


    submitted

  1. RBFCUB: a numerical package for near-optimal meshless cubature on general polygons
    draft - R. Cavoretto, A. De Rossi, A. Sommariva and M. Vianello
  2. A shape preserving quasi-interpolation operator based on a new transcendental RBF
    draft - S. De Marchi, M. Heidari and M. Mohammadi
  3. Stable discontinuous mapped bases: the Gibbs-Runge-Avoiding Stable Polynomial Approximation (GRASPA) method
    draft - S. De Marchi, G. Elefante and F. Marchetti
  4. Numerical differentiation on scattered data through multivariate polynomial interpolation
    arXiv preprint 2105.09262 - F. Dell'Accio, F. Di Tommaso, N. Siar and M. Vianello
  5. Kernel-Based Models for Influence Maximization on Graphs based on Gaussian Process Variance Minimization
    arXiv preprint 2103.01575 - S. Cuomo, W. Erb and G. Santin
  6. Partition of Unity Methods for Signal Processing on Graphs
    arXiv preprint 2012.10636 - R. Cavoretto, A. De Rossi and W. Erb
  7. Semi-Supervised Learning on Graphs with Feature-Augmented Graph Basis Functions
    arXiv preprint 2003.07646 - W. Erb
  8. Graph Signal Interpolation with Positive Definite Graph Basis Functions
    arXiv preprint 1912.02069 - W. Erb
  9. Anisotropic Gaussian approximation in L^2(R^2)
    arXiv preprint 1910.10319 - W. Erb, T. Hangelbroek and A. Ron

    to appear

  10. On (beta,gamma)-Chebyshev functions and points of the interval
    preprint - S. De Marchi, G. Elefante and F. Marchetti
    accepted by J. Approx. Theory
  11. Mapped polynomials and discontinuous kernels for Runge and Gibbs phenomena
    preprint - S. De Marchi
    to appear in SEMA SIMAI Springer Series

    published

    2022

  12. Near-optimal polynomial interpolation on spherical triangles
    draft - A. Sommariva and M. Vianello
    Mediterr. J. Math., to appear in April 2022

    2021

  13. Oversampling errors in multimodal medical imaging are due to the Gibbs effect
    preprint - S. De Marchi, D. Poggiali, C. Campi and D. Cecchin
    MDPI-Mathematics 9(12) (2021)
  14. RBF moment computation and meshless cubature on general polygonal regions
    preprint - A. Sommariva and M. Vianello
    Appl. Math. Comput. 409 (2021)
  15. Numerical hyperinterpolation over spherical triangles
    preprint - A. Sommariva and M. Vianello
    Math. Comput. Simul. 190 (2021), 15--22
  16. Quadrature at fake nodes
    S. De Marchi, G. Elefante, E. Perracchione and D. Poggiali
    Dolomites Res. Notes Approx. DRNA 14 (2021), 39--45
    (Special Issue "Multivariate Approximation: Theory and Applications 2020")
  17. Near-algebraic Tchakaloff-like quadrature on spherical triangles
    preprint - A. Sommariva and M. Vianello
    Appl. Math. Lett. 120 (2021)
  18. The extension of Rippa's algorithm beyond LOOCV
    preprint - F. Marchetti
    Appl. Math. Lett. 120 (2021)
  19. Optimal Polynomial Prediction Measures and Extremal Polynomial Growth
    arXiv preprint 1912.12462 - L. Bos, N. Levenberg and J. Ortega-Cerdà
    Constr. Approx., published online 2 November 2020
  20. Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk
    arXiv preprint 1812.00437 - W. Erb
    Constr. Approx. 53 (2021), 281--318
  21. Numerical implementation of the mathematical model describing the prostate tumor growth:
    Radial basis function-generated finite difference (RBF-FD) scheme combined with a semi-implicit time discretization

    preprint - V. Mohammadi, M. Dehghan and S. De Marchi
    J. Comput. Appl. Math. 388 (2021)
  22. Convergence rate in terms of the continuous ssim (Cssim) index in RBF interpolation
    F. Marchetti
    Dolomites Res. Notes Approx. DRNA 14 (2021), 27--32
  23. Shapes of Uncertainty in Spectral Graph Theory
    arXiv preprint 1909.10865 - W. Erb
    IEEE Trans. Inform. Theory 67 (2021), 1291--1307
  24. Computing Tchakaloff-like cubature rules on spline curvilinear polygons
    preprint - A. Sommariva and M. Vianello
    Dolomites Res. Notes Approx. DRNA 14 (2021), 1--11
  25. Multivariate approximation at fake nodes
    preprint - S. De Marchi, F. Marchetti, E. Perracchione and D. Poggiali
    Appl. Math. Comput. 391 (2021)

    2020

  26. Accurate numerical determination of a self-preserving quantum vortex ring
    M. Caliari and S. Zuccher
    J. Phys. A: Math. Theor. 54 (2020)
  27. Correction/Addendum to: "The Extremal Function for the Complex Ball for Generalized
    Notions of Degree and Multivariate Polynomial Approximation"

    arXiv preprint 2005.02518 - T. Bloom, L. Bos, N. Levenberg, S. Ma'u and F. Piazzon
    Ann. Polon. Math. 125 (2020), 193--202
  28. On the Probability that the Maximum of a Polynomial is at an Endpoint of an Interval
    L. Bos and T. Ware
    Analysis Mathematica 46 (2020), 195--224
  29. Approximation of the matrix exponential for matrices with skinny fields of values
    preprint - M. Caliari, F. Cassini and F. Zivcovich
    BIT Numer. Math. 60 (2020), 1113--1131
  30. A new 3D model for magnetic particle imaging using realistic magnetic field topologies for algebraic reconstruction
    arXiv preprint 2004.13357 - G. Bringout, W. Erb and J. Frikel
    Inverse Problems 36 (2020)
  31. An RBF approach for oil futures pricing under the jump-diffusion model
    preprint - S. De Marchi, M.K. Esfahani and A. Neisy
    J. Math. Modelling 9 (2020), 81--92
  32. Extremal growth of polynomials
    preprint - L. Bos, S. Ma'u and S. Waldron
    Analysis Mathematica 46 (2020), 195--224
  33. Fake Nodes approximation for Magnetic Particle Imaging
    preprint - S. De Marchi, W. Erb, E. Francomano, F. Marchetti, E. Perracchione and D. Poggiali
    2020 IEEE 20th Mediterranean Electrotechnical Conference (MELECON), Palermo, 434-438, doi: 10.1109/MELECON48756.2020.9140583
  34. Variably Scaled Kernels Improve Classification of Hormonally-Treated Patient-Derived Xenografts
    preprint - F. Marchetti, F. De Martino, M. Shamseddin, S. De Marchi and C. Brisken
    2020 IEEE Conference on Evolving and Adaptive Intelligent Systems (EAIS), Bari, 1-6, doi: 10.1109/EAIS48028.2020.9122767
  35. Analysis of a new class of rational RBF expansions
    preprint - M. Buhmann, S. De Marchi and E. Perracchione
    IMA J. Numer. Anal. 40 (2020), 1972--1993
  36. dCATCH: a numerical package for d-variate near G-optimal Tchakaloff regression via fast NNLS
    M. Dessole, F. Marcuzzi and M. Vianello
    MDPI-Mathematics 8(7) (2020) - Special Issue "Numerical Methods"
  37. Quadrature-based polynomial optimization
    preprint - A. Martinez, F. Piazzon, A. Sommariva and M. Vianello
    Optim. Lett. 14 (2020), 1027--1036
  38. Jumping with Variably Scaled Discontinuos Kernels (VSDK)
    preprint - S. De Marchi, F. Marchetti and E. Perracchione
    BIT Numer. Math. 60 (2020), 441--463
  39. Treating the Gibbs phenomenon in barycentric rational interpolation and approximation via the S-Gibbs algorithm
    preprint - J.-P. Berrut, S. De Marchi, G. Elefante and F. Marchetti
    Appl. Math. Letters 103 (2020)
  40. Near G-optimal Tchakaloff designs
    preprint - L. Bos, F. Piazzon and M. Vianello
    Comput. Statistics 35 (2020), 803--819
  41. Shape-Driven Interpolation with Discontinuous Kernels: Error Analysis, Edge Extraction and Applications in MPI
    arXiv preprint 1903.03095 - S. De Marchi, W. Erb, F. Marchetti, E. Perracchione and M. Rossini
    SIAM J. Sci. Comput. 42(2) (2020), B472--B491
  42. Accelerating the Lawson-Hanson NNLS solver for large-scale Tchakaloff regression designs
    preprint - F. Marcuzzi, M. Dessole and M. Vianello
    Dolomites Res. Notes Approx. DRNA 13 (2020), 20--29
  43. Compressed cubature over polygons with applications to optical design
    preprint - B. Bauman, A. Sommariva and M. Vianello
    J. Comput. Appl. Math. 370 (2020)
  44. On the Convergence of the Rescaled Localized Radial Basis Function Method
    preprint - S. De Marchi and H. Wendland
    Appl. Math. Letters 99 (2020)
  45. Polynomial interpolation via mapped bases without resampling
    preprint - S. De Marchi, F. Marchetti, E. Perracchione and D. Poggiali
    J. Comput. Appl. Math. 364 (2020)
  46. Algebraic cubature on polygonal elements with a circular edge
    preprint - E. Artioli, A. Sommariva and M. Vianello
    Comput. Math. Appl. 79 (2020), 2057--2066
  47. A stable meshfree PDE solver for source-type flows in porous media
    preprint - R. Campagna, S. Cuomo, S. De Marchi, E. Perracchione and G. Severino
    Appl. Numer. Math. 149 (2020), 30--42

    2019

  48. A Kinetic Neural Network Approach for Absolute Quantification and Change Detection in Positron Emission Tomography
    preprint - D. Poggiali, D. Cecchin and S. De Marchi
    Proceedings of MASCOT2018-IMACS Workshop, IMACS Series in Computational and Applied Mathematics, ISSN: 1098-870X, vol. 22, 2019, 91--100
  49. Anisotropic osmosis filtering for shadow removal in images
    preprint - S. Parisotto, L. Calatroni, M. Caliari, C.-B. Schoenlieb and J. Weickert
    Inverse Probl. 35 (2019)
  50. Laplace-Beltrami operator in the Baran metric and pluripotential equilibrium measure: the ball, the simplex and the sphere
    preprint - F. Piazzon
    Comput. Methods Funct. Theory 19 (2019), 547--582
  51. The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation
    arXiv preprint 1801.02401 - T. Bloom, L. Bos, N. Levenberg, S. Ma'u and F. Piazzon
    Ann. Polon. Math. 123 (2019), 171--195
  52. CaTchDes: Matlab codes for Caratheodory-Tchakaloff Near-Optimal Regression Designs
    preprint - L. Bos and M. Vianello
    SoftwareX 10 (2019)
  53. Learning with subsampled kernel-based methods: Environmental and financial applications
    M. Aminian Shahrokhabadi, A. Neisy, E. Perracchione and M. Polato
    Dolomites Res. Notes Approx. DRNA 12 (2019), 17--27
  54. Near optimal polynomial regression on norming meshes
    preprint - L. Bos, F. Piazzon and M. Vianello
    Sampling Theory and Applications 2019, IEEE Xplore Digital Library, DOI: 10.1109/SampTA45681.2019.9030910
  55. Chebyshev-Dubiner norming webs on starlike polygons
    preprint - M. Vianello
    J. Inequal. Spec. Funct. 10-3 (2019), 26--32
  56. Tchakaloff polynomial meshes
    preprint - L. Bos and M. Vianello
    Ann. Polon. Math. 122 (2019), 221--231
  57. Dubiner distance and stability of Lebesgue constants
    preprint - M. Vianello
    J. Inequal. Spec. Funct. 10-2 (2019), 49--60
  58. On the Lebesgue constant of the trigonometric Floater-Hormann rational interpolant at equally spaced nodes
    C. Bandiziol and S. De Marchi
    Dolomites Res. Notes Approx. DRNA 12 (2019), 51--67
  59. Markov inequalities, Dubiner distance, norming meshes and polynomial optimization on convex bodies
    preprint - F. Piazzon and M. Vianello
    Optim. Lett. 13 (2019), 1325--1343
  60. Markov factors on average: An L^infty case
    L. Bos
    J. Approx. Theory 247 (2019), 20--31
  61. Fast and accurate computation of divided differences for analytic functions, with an application to the exponential function
    F. Zivcovich
    Dolomites Res. Notes Approx. DRNA 12 (2019), 28--42
  62. RBF-based partition of unity method for elliptic PDEs: Adaptivity and stability issues via VSKs
    preprint - S. De Marchi, A. Martinez Calomardo, E. Perracchione and M. Rossini
    J. Sci. Comput. 79(1) (2019), 321--344
  63. Pluripotential Numerics
    preprint - F. Piazzon
    Constr. Approx. 49 (2019), 227--263
  64. Fast and stable rational RBF-based Partition of Unity interpolation
    preprint - S. De Marchi, A. Martinez Calomardo and E. Perracchione
    J. Comput. Appl. Math. 349 (2019), 331--343
  65. Markov factors on average: An L^2 case
    L. Bos
    J. Approx. Theory 241 (2019), 1--10
  66. On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm
    preprint - M. Caliari and F. Zivcovich
    J. Comput. Appl. Math. 346 (2019), 532--548
  67. On the computation of sets of points with low Lebesgue constant on the unit disk
    preprint - G. Meurant and A. Sommariva
    J. Comput. Appl. Math. 345 (2019), 388--404

    2018

  68. The extremal plurisubharmonic function of the torus
    F. Piazzon
    Dolomites Res. Notes Approx. DRNA 11 (2018), 75--85
    (Special Issue on Norm Levenberg's 60th birthday)
  69. Fekete Points as Norming Sets
    L. Bos
    Dolomites Res. Notes Approx. DRNA 11 (2018), 20--25
    (Special Issue on Norm Levenberg's 60th birthday)
  70. Near optimal Tchakaloff meshes for compact sets with Markov exponent 2
    M. Vianello
    Dolomites Res. Notes Approx. DRNA 11 (2018), 92--96
    (Special Issue on Norm Levenberg's 60th birthday)
  71. Statistical and Numerical Considerations of Backus-Average Product Approximation
    L. Bos, T. Danek, M. Slawinski and T. Stanoev
    J. Elasticity 132 (2018), 141--159
  72. Backward error analysis of polynomial approximations for computing the action of the matrix exponential
    preprint - M. Caliari, P. Kandolf and F. Zivcovich
    BIT Numerical Math. 58 (2018), 907--935
  73. Rational RBF-based partition of unity method for efficiently and accurately approximating 3D objects
    preprint - E. Perracchione
    Comput. Appl. Math. 37 (2018), 4633--4648
  74. Subperiodic Dubiner distance, norming meshes and trigonometric polynomial optimization
    preprint - M. Vianello
    Optim. Lett. 12 (2018), 1659--1667
  75. Discrete norming inequalities on sections of sphere, ball and torus
    preprint - A. Sommariva and M. Vianello
    J. Inequal. Spec. Funct. 9-4 (2018), 113--121
  76. Nearly optimal nested sensors location for polynomial regression on complex geometries
    preprint - A. Sommariva and M. Vianello
    Sampl. Theory Signal Image Process. 17 (2018), 95--101
  77. On the Uniqueness of an Orthogonality Property of the Legendre Polynomials
    L. Bos and A.F. Ware
    Dolomites Res. Notes Approx. DRNA 11 (2018), 37--42
  78. Global polynomial optimization by norming sets on sphere and torus
    preprint - M. Vianello
    Dolomites Res. Notes Approx. DRNA 11 (2018), 10--14
  79. Stability inequalities for Lebesgue constants via Markov-like inequalities
    preprint - F. Piazzon and M. Vianello
    Dolomites Res. Notes Approx. DRNA 11 (2018), 1--9
  80. Image Reconstruction from Scattered Radon Data by Weighted Positive Definite Kernel Functions
    preprint - S. De Marchi, A. Iske and G. Santin
    Calcolo 55 (2), 2018
  81. Subperiodic Trigonometric Hyperinterpolation
    preprint - G. Da Fies, A. Sommariva and M. Vianello
    in: "Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan" (invited paper)
    J. Dick, F.Y. Kuo, H. Wozniakowski Eds., Springer, 2018, 283--304
  82. Bernstein-Walsh Theory Associated to Convex Bodies and Applications to Multivariate Approximation Theory
    preprint - L. Bos and N. Levenberg
    Comput. Methods Funct. Theory 18 (2018), 361--388
  83. On multivariate Marcinkiewicz-Zygmund type inequalities
    preprint - S. De Marchi and A. Kroó
    Acta Math. Hungarica 154 (2018), 69--89
  84. Optimal selection of local approximants in RBF-PU interpolation using bivariate LOOCV
    preprint - R. Cavoretto, A. De Rossi and E. Perracchione
    J. Sci. Comput. 74 (2018), 1--22
  85. An elementary approach to polynomial optimization on polynomial meshes
    preprint - M. Vianello
    J. Math. Fund. Sci. 50 (2018), 84--91
  86. Meshless partition of unity method for attraction basins of periodic orbits: Fast detection of separatrix points
    Alessandra De Rossi, Emma Perracchione, Ezio Venturino
    Dolomites Res. Notes Approx. DRNA 11 (2018)
    Special Issue on Multivariate Approximation: Theory, Algorithms & Applications (MATAA17), 15--22
  87. Quasi-Monte Carlo integration on manifolds with mapped low-discrepancy points and greedy minimal Riesz s-energy points
    preprint - S. De Marchi and G. Elefante
    Appl. Numer. Math. 127 (2018), 110--124
  88. How often is the max of a quadratic at an endpoint?
    L. Bos
    MatematicaMente 232 (2018)
  89. A note on total degree polynomial optimization by Chebyshev grids
    preprint - F. Piazzon and M. Vianello
    Optim. Lett. 12 (2018), 63--71

    2017

  90. An Explicit Example of Leave-One-Out Cross-Validation Parameter Estimation for a Univariate Radial Basis Function
    L. Bos and F. Polato
    Dolomites Res. Notes Approx. DRNA 10 (2017), 43--50
  91. A weighted extremal function and equilibrium measure
    preprint - L. Bos, N. Levenberg, S. Ma`u and F. Piazzon
    Math. Scand. 121 (2017), 243--262
  92. Numerical quadrature on the intersection of planar disks
    preprint - A. Sommariva and M. Vianello
    FILOMAT 31:13 (2017), 4105--4115
  93. Subperiodic trigonometric subsampling: a numerical approach
    preprint - A. Sommariva and M. Vianello
    Appl. Anal. Discrete Math. 11 (2017), 470--483
  94. A rescaled method for RBF approximation
    preprint - S. De Marchi, A. Idda and G. Santin
    Springer Proceedings on Mathematics and Statistics, Vol. 201 (2017), 39--59
  95. Lissajous sampling and spectral filtering in MPI applications: the reconstruction algorithm for reducing the Gibbs phenomenon
    preprint - S. De Marchi, W. Erb and F. Marchetti
    Sampling Theory and Applications 2017, IEEE Xplore Digital Library, DOI: 10.1109/SAMPTA.2017.8024375
  96. Caratheodory-Tchakaloff Least Squares
    preprint - F. Piazzon, A. Sommariva and M. Vianello
    Sampling Theory and Applications 2017, IEEE Xplore Digital Library, DOI: 10.1109/SAMPTA.2017.8024337
  97. Some results on the rational Bernstein-Markov property in the complex plane
    preprint - F. Piazzon
    Comput. Methods Funct. Theory 17 (2017), 405--443
  98. Numerical hyperinterpolation over nonstandard planar regions
    preprint - A. Sommariva and M. Vianello
    Math. Comput. Simulation 141 (2017), 110--120
  99. Spectral filtering for the reduction of the Gibbs phenomenon for polynomial approximation methods on Lissajous curves with applications in MPI
    S. De Marchi, W. Erb and F. Marchetti
    Dolomites Res. Notes Approx. DRNA 10(2017), 128--137
  100. On the use of compressed polyhedral quadrature formulas in embedded interface methods
    preprint - Y. Sudhakar, A. Sommariva, M. Vianello and W.A. Wall
    SIAM J. Sci. Comput. 39 (2017), B571-B587
  101. Optimal polynomial meshes and Caratheodory-Tchakaloff submeshes on the sphere
    preprint - P. Leopardi, A. Sommariva and M. Vianello
    Dolomites Res. Notes Approx. DRNA 10 (2017), 18--24
  102. Caratheodory-Tchakaloff Subsampling
    F. Piazzon, A. Sommariva and M. Vianello
    Dolomites Res. Notes Approx. DRNA 10 (2017), 5--14
  103. Polynomial approximation on Lissajous curves in the d-cube
    preprint - L. Bos, S. De Marchi and M. Vianello
    Appl. Numer. Math. 116 (2017), 47--56
  104. Partition of unity interpolation using stable kernel-based techniques
    preprint - R. Cavoretto, S. De Marchi, A. De Rossi, E. Perracchione and G. Santin
    Appl. Numer. Math. 116 (2017), 95--107
  105. A Simple Recipe for Modelling a d-cube by Lissajous curves
    L. Bos
    Dolomites Res. Notes Approx. DRNA 10 (2017), 1--4
  106. Trivariate polynomial approximation on Lissajous curves
    preprint - L. Bos, S. De Marchi and M. Vianello
    IMA J. Numer. Anal. 37 (2017), 519--541
  107. INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections
    preprint - M. Caliari and S. Zuccher
    Comput. Phys. Commun. 213 (2017), 197--207
  108. An Orthogonality Property of Legendre Polynomials
    preprint - L. Bos, A. Narayan, N. Levenberg and F. Piazzon
    Constr. Approx. 45 (2017), 65--81
  109. Polynomial approximation and quadrature on geographic rectangles
    preprint - M. Gentile, A. Sommariva and M. Vianello
    Appl. Math. Comput. 297 (2017), 159--179

    2016

  110. A new quasi-Monte Carlo technique based on nonnegative least-squares and approximate Fekete points
    preprint - L. Bittante, S. De Marchi and G. Elefante
    Numer. Math. TMA. 9 (2016), 609--632
  111. Kernel-based Image Reconstruction from Scattered Radon Data
    S. De Marchi, A. Iske and A. Sironi
    Dolomites Res. Notes Approx. DRNA 9 (2016), 19--31
  112. Approximation of eigenfunctions in kernel-based spaces
    preprint - G. Santin and R. Schaback
    Adv. Comput. Math. 42 (2016), 973--993
  113. Jacobi norming meshes
    preprint - F. Piazzon and M. Vianello
    Math. Inequal. Appl. 19 (2016), 1089--1095
  114. Approximating basins of attraction for dynamical systems via stable radial bases
    preprint - R. Cavoretto, S. De Marchi, A. De Rossi, E. Perracchione and G. Santin
    AIP Conference Proceedings 1738 (2016), doi:10.1063/1.4952177
  115. The Leja method revisited: backward error analysis for the matrix exponential
    preprint - M. Caliari, P. Kandolf, A. Ostermann and S. Rainer
    SIAM J. Sci. Comput. 38 (2016), A1639--A1661
  116. Optimal Polynomial Admissible Meshes on Some Classes of Compact Subsets of R^d
    preprint - F. Piazzon
    J. Approx. Theory 207 (2016), 241--264
  117. Compressed sampling inequalities by Tchakaloff's theorem
    preprint - M. Vianello
    Math. Inequal. Appl. 19 (2016), 395--400

    2015

  118. Transfinite diameter on curves, Hankel determinants and the moment problem
    preprint - L. Bos and S. Ma`u
    Banach Center Publications 107 (2015), 79--100
  119. Fast computation of orthonormal bases for RBF spaces through Krylov spaces methods
    preprint - S. De Marchi and G. Santin
    BIT Numerical Math. 55 (2015), 949--966
  120. Bernstein-Markov: a survey
    T. Bloom, N. Levenberg, F. Piazzon and F. Wielonsky
    Dolomites Res. Notes Approx. DRNA 8 (2015), 75--91
  121. Application of modified Leja sequences to polynomial interpolation
    L. Bos and M. Caliari
    Dolomites Res. Notes Approx. DRNA 8 (2015), 66--74
  122. A few remarks on "On certain Vandermonde determinants whose variables separate"
    A. Perro de Camargo and S. De Marchi
    Dolomites Res. Notes Approx. DRNA 8 (2015), 1--11
  123. RBF approximation of large datasets by partition of unity and local stabilization
    preprint - R. Cavoretto, S. De Marchi, A. De Rossi, E. Perracchione and G. Santin
    Proceedings of CMMSE 2015, 317--326, ISBN 978-84-617-2230-3, ISSN 2312-0177
  124. Polynomial Meshes: Computation and Approximation
    preprint - S. De Marchi, F. Piazzon, A. Sommariva and M. Vianello
    Proceedings of CMMSE 2015, 414--425, ISBN 978-84-617-2230-3, ISSN 2312-0177
  125. Analytical and experimental FWHM of a gamma camera: theoretical and practical issues
    preprint - D. Cecchin, D, Poggiali, L. Riccardi, P. Turco, F. Bui and S. De Marchi
    PeerJ 3e:722, https://dx.doi.org/10.7717/peerj.722
  126. Compression of multivariate discrete measures and applications
    preprint - A. Sommariva and M. Vianello
    Numer. Funct. Anal. Optim. 36 (2015), 1198--1223
  127. Polynomial fitting and interpolation on circular sections
    preprint - A. Sommariva and M. Vianello
    Appl. Math. Comput. 258 (2015), 410--424
  128. On the constrained Mock-Chebyshev least squares
    preprint - S. De Marchi, F. Dell'Accio and M. Mazza
    J. Comput. Appl. Math. 280 (2015), 94--109

    2014

  129. Fast variants of the Golub and Welsch algorithm for symmetric weight functions in Matlab
    preprint - G. Meurant and A. Sommariva
    Numer. Algorithms 67 (2014), 491--506
  130. Fekete Type Points for Ridge Function Interpolation and Hyperbolic Potential Theory
    preprint - L. Bos S. De Marchi and N. Levenberg
    Publ. Math. Inst. (Beograd) 110 (2014), 41--48
  131. Multivariate Christoffel functions and hyperinterpolation
    S. De Marchi, A. Sommariva and M. Vianello
    Dolomites Res. Notes Approx. DRNA 7 (2014), 26--33
  132. Blossoms - a Flowery Approach to Polynomials
    L. Bos
    MatematicaMente 195 (2014)
  133. Product Gaussian quadrature on circular lunes
    preprint - G. Da Fies and M. Vianello
    Numer. Math. Theory Methods Appl. 7 (2014), 251--264
  134. On certain multivariate Vandermonde determinants whose variables separate
    preprint - S. De Marchi and K. Usevich
    Linear Algebra Appl. 449 (2014), 17--27
  135. Constructing optimal polynomial meshes on planar starlike domains
    F. Piazzon and M. Vianello
    Dolomites Res. Notes Approx. DRNA 7 (2014), 22--25
  136. Comparison of software for computing the action of the matrix exponential
    preprint - M. Caliari, P. Kandolf, A. Ostermann and S. Rainer
    BIT Numerical Math. 54 (2014), 113--128
  137. Norming meshes by Bernstein-like inequalities
    preprint - M. Vianello
    Math. Inequal. Appl. 17 (2014), 929--936
  138. Sub-optimal polynomial meshes on planar Lipschitz domains
    preprint - F. Piazzon and M. Vianello
    Numer. Funct. Anal. Optim. 35 (2014), 1467--1475

    2013

  139. Interpolation on real algebraic curves to polynomial data
    L. Bos and I. Lagu
    Dolomites Res. Notes Approx. DRNA 6 (2013), 1--25
  140. Algebraic cubature by linear blending of elliptical arcs
    preprint - G. Da Fies, A. Sommariva and M. Vianello
    Appl. Numer. Math. 74 (2013), 49--61
  141. Polynomial approximation on pyramids, cones and solids of rotation
    S. De Marchi and M. Vianello
    Dolomites Res. Notes Approx. DRNA 6 (2013), 20--26
  142. A new stable basis for radial basis function interpolation
    preprint - S. De Marchi and G. Santin
    J. Comp. Appl. Math. 253 (2013), 1--13
  143. Small perturbations of polynomial meshes
    preprint - F. Piazzon and M. Vianello
    Appl. Anal. 92 (2013), 1063--1073
  144. Meshfree Exponential Integrators
    preprint - M. Caliari, A. Ostermann and S. Rainer
    SIAM J. Sci. Comput. 35 (2013), A431--A452
  145. A Meshfree splitting method for soliton dynamics in nonlinear Schroedinger equations
    preprint- M. Caliari, A. Ostermann and S. Rainer
    Lect. Notes Comput. Sci. Eng. 89 (2013)
  146. Bounding the Lebesgue constant of Berrut's rational interpolant at general nodes
    preprint - L. Bos, S. De Marchi, K. Hormann and J. Sidon
    J. Approx. Theory 169 (2013), 7--22
    among the most cited articles of JAT 2013-2017
  147. Fast construction of Fejer and Clenshaw-Curtis rules for general weight functions
    preprint - A. Sommariva
    Comput. Math. Appl. 65 (2013), 682--693
    cited in S. Olver, M. Slevinsky, A. Townsend, Fast algorithms using orthogonal polynomials, Acta Numerica 2020
  148. On the Lebesgue constant of subperiodic trigonometric interpolation
    preprint - G. Da Fies and M. Vianello
    J. Approx. Theory 167 (2013), 59--64

    2012

  149. The transfinite diameter of a real ball and simplex
    preprint - T. Bloom, L. Bos and N. Levenberg
    Ann. Polon. Math. 106 (2012), 83--96
  150. Polynomial Interpolation and Approximation in C^d
    preprint - T. Bloom, L. Bos, J.-P. Calvi and N. Levenberg
    Ann. Polon. Math. 106 (2012), 53--81
  151. Computing almost minimal formulas on the square
    preprint - M. Festa and A. Sommariva
    J. Comput. Appl. Math. 236 (2012), 4296--4302
  152. On the Lebesgue constant of barycentric rational interpolation at equidistant nodes
    preprint - L. Bos, S. De Marchi, K. Hormann and G. Klein
    Numer. Math. 121 (2012), 461--471
  153. On Bezier and Subdivision Curves
    L. Bos
    MatematicaMente 172 (2012)
  154. Algebraic cubature on planar lenses and bubbles
    G. Da Fies and M. Vianello
    Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12
  155. On the generation of symmetric Lebesgue-like points in the triangle
    preprint - F. Rapetti, A. Sommariva and M. Vianello
    J. Comput. Appl. Math. 236 (2012), 4925--4932
  156. Subperiodic trigonometric interpolation and quadrature
    preprint - L. Bos and M. Vianello
    Appl. Math. Comput. 218 (2012), 10630--10638
  157. Polynomial approximation and cubature at approximate Fekete and Leja points of the cylinder
    preprint - S. De Marchi, M. Marchioro and A. Sommariva
    Appl. Math. Comput. 218 (2012), 10617--10629
  158. Trigonometric Gaussian quadrature on subintervals of the period
    preprint - G. Da Fies and M. Vianello
    Electron. Trans. Numer. Anal. 39 (2012), 102--112
  159. Computing Fekete and Lebesgue points: simplex, square, disk
    preprint - M. Briani, A. Sommariva and M. Vianello
    J. Comput. Appl. Math. 236 (2012), 2477--2486
  160. Barycentric rational interpolation at quasi-equidistant nodes
    S. De Marchi, K. Hormann and G. Klein
    Dolomites Res. Notes Approx. DRNA 5 (2012), 1--6
  161. Low cardinality admissible meshes on quadrangles, triangles and disks
    preprint - L. Bos and M. Vianello
    Math. Inequal. Appl. 15 (2012), 229--235

    2011

  162. On the Whittaker--Shannon sampling by means of Berrut's rational interpolant and its extension by Floater and Hormann
    preprint - L. Bos and S. De Marchi
    East J. Approx. 17 (2011), 267--284
  163. On optimal points for interpolation by univariate exponential functions
    L. Bos and S. De Marchi
    Dolomites Res. Notes Approx. DRNA 4 (2011), 8--12
  164. On the Lebesgue constant of Berrut's rational interpolant at equidistant nodes
    preprint - L. Bos, S. De Marchi and K. Hormann
    J. Comput. Appl. Math. 236 (2011), 504--510
  165. Meshfree integrators
    preprint - M. Caliari, A. Ostermann, and S. Rainer
    Oberwolfach Reports (2011)
  166. On Multivariate Newton Interpolation at Discrete Leja Points
    L. Bos, S. De Marchi, A. Sommariva and M. Vianello
    Dolomites Res. Notes Approx. DRNA 4 (2011), 15--20
  167. Polynomial interpolation and cubature over polygons
    preprint - M. Gentile, A. Sommariva and M. Vianello
    J. Comput. Appl. Math. 235 (2011), 5232--5239
  168. An algebraic cubature formula on curvilinear polygons
    preprint - G. Santin, A. Sommariva and M. Vianello
    Appl. Math. Comput. 217 (2011), 10003--10015
  169. Geometric Weakly Admissible Meshes, Discrete Least Squares Approximations and Approximate Fekete Points
    preprint - L. Bos, J.P. Calvi, N. Levenberg, A. Sommariva and M. Vianello
    Math. Comp. 80 (2011), 1601--1621
  170. Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave
    preprint - M. Caliari, S. De Marchi, A. Sommariva and M. Vianello
    Numer. Algorithms 56 (2011), 45--60
  171. Weakly Admissible Meshes and Discrete Extremal Sets
    preprint - L. Bos, S. De Marchi, A. Sommariva and M. Vianello
    Numer. Math. Theory Methods Appl. 4 (2011), 1--12

    2010

  172. Analytic transformations of admissible meshes
    preprint - F. Piazzon and M. Vianello
    East J. Approx. 16 (2010), 313--322
  173. Computing multivariate Fekete and Leja points by numerical linear algebra
    preprint - L. Bos, S. De Marchi, A. Sommariva and M. Vianello
    SIAM J. Numer. Anal. 48 (2010), 1984--1999
  174. On the convergence of optimal measures
    preprint - T. Bloom, L. Bos, N. Levenberg and S. Waldron
    Constr. Approx. 32 (2010), 159--179
  175. On polynomial inequalities on exponential curves in C^n
    preprint - L. Bos, A. Brudnyi and N. Levenberg
    Constr. Approx. 31 (2010), 139--147
  176. Least-squares polynomial approximation on weakly admissible meshes: disk and triangle
    preprint - L. Bos, A. Sommariva and M. Vianello
    J. Comput. Appl. Math. 235 (2010), 660--668
  177. Approximate Fekete points for weighted polynomial interpolation
    preprint - A. Sommariva and M. Vianello
    Electron. Trans. Numer. Anal. 37 (2010), 1--22
  178. On simple approximations to simple curves
    L. Bos and M. Vianello
    Dolomites Res. Notes Approx. DRNA 3 (2010), 1--6
  179. Stability of Kernel-Based Interpolation
    preprint - S. De Marchi and R. Schaback
    Adv. Comput. Math. 32 (2010), 155--161

    2009

  180. On the Vandermonde Determinant of Padua-like Points
    L. Bos, S. De Marchi and S. Waldron
    Dolomites Res. Notes Approx. DRNA 2 (2009), 1--15
  181. Nonstandard Kernels and their Applications
    R. Schaback and S. De Marchi
    Dolomites Res. Notes Approx. DRNA 2 (2009), 16--43
  182. Efficient massively parallel implementation of the ReLPM exponential integrator for advection-diffusion models
    preprint - L. Bergamaschi, M. Caliari, A. Martinez and M. Vianello
    J. Comput. Appl. Math. 231 (2009), 82--91
    cited in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 2010
  183. Implementation of exponential Rosenbrock-type integrators
    preprint - M. Caliari and A. Ostermann
    Appl. Numer. Math. 59 (2009), 568--581
    cited in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 2010
  184. Gauss-Green cubature and moment computation over arbitrary geometries
    preprint - A. Sommariva and M. Vianello
    J. Comput. Appl. Math. 231 (2009), 886--896
  185. Geometric greedy and greedy points for RBF interpolation
    preprint - S. De Marchi
    Proceedings of the 9th CMMSE (2009), Vol. II, 381--392
  186. A numerical code for fast interpolation and cubature at the Padua points
    preprint - M. Caliari, S. De Marchi, A. Sommariva and M. Vianello
    Proceedings of the 9th CMMSE (2009), Vol. I, 218--228
  187. Computing approximate Fekete points by QR factorizations of Vandermonde matrices
    preprint - A. Sommariva and M. Vianello
    Comput. Math. Appl. 57 (2009), 1324--1336
  188. New cubature formulae and hyperinterpolation in three variables
    preprint - S. De Marchi, M. Vianello and Y. Xu
    BIT Numerical Math. 49 (2009), 55--73

    2008

  189. Algorithm 886: Padua2D: Lagrange Interpolation at Padua Points on Bivariate Domains
    preprint - M. Caliari, S. De Marchi and M. Vianello
    ACM Trans. Math. Software 35-3 (2008)
  190. Approximation on the sphere using radial basis functions plus polynomials
    preprint - A. Sommariva and I.H. Sloan
    Adv. Comput. Math. 29 (2008), 147--177
  191. Nontensorial Clenshaw-Curtis cubature
    preprint - A. Sommariva, M. Vianello and R. Zanovello
    Numer. Algorithms 49 (2008), 409--427
  192. Hyperinterpolation in the cube
    preprint - M. Caliari, S. De Marchi and M. Vianello
    Comput. Math. Appl. 55 (2008), 2490--2497
  193. Univariate Radial Basis Functions with Compact Support Cardinal Functions
    preprint - L. Bos and S. De Marchi
    East J. Approx. 14 (2008), 69--80
  194. Bivariate Lagrange interpolation at the Padua points: computational aspects
    preprint - M. Caliari, S. De Marchi and M. Vianello
    J. Comput. Appl. Math. 221 (2008), 284--292
  195. Meshless cubature over the disk by Thin-Plate Splines
    preprint - A. Punzi, A. Sommariva and M. Vianello
    J. Comput. Appl. Math. 221 (2008), 430--436

    2007

  196. Bivariate Lagrange interpolation at the Padua points: the ideal theory approach
    preprint - L. Bos, S. De Marchi, M. Vianello and Y. Xu
    Numer. Math. 108 (2007), 43--57
  197. Accurate evaluation of divided differences for polynomial interpolation of exponential propagators
    preprint - M. Caliari
    Computing 80 (2007), 189--201
    cited in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 2010
  198. The LEM exponential integrator for advection-diffusion-reaction equations
    preprint - L. Bergamaschi, M. Caliari and M. Vianello
    J. Comput. Appl. Math. 210 (2007), 56--63
  199. Product Gauss cubature over polygons based on Green's integration formula
    preprint - A. Sommariva and M. Vianello
    BIT Numerical Math. 47 (2007), 441--453
  200. Hyperinterpolation on the square
    preprint - M. Caliari, S. De Marchi and M. Vianello
    J. Comput. Appl. Math. 210 (2007), 78--83

    2006

  201. Meshless cubature by Green's formula
    preprint - A. Sommariva and M. Vianello
    Appl. Math. Comput. 183 (2006), 1098--1107
  202. Hyper2d: a numerical code for hyperinterpolation on rectangles
    preprint - M. Caliari, S. De Marchi, R. Montagna and M. Vianello
    Appl. Math. Comput. 183 (2006), 1138--1147
  203. Comparing Leja and Krylov approximations of large scale matrix exponentials
    preprint - L. Bergamaschi, M. Caliari, A. Martinez and M. Vianello
    Springer LNCS vol. 3994, 2006 (Proc. of ICCS 2006, Reading, UK), 685--692
    cited in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 2010
  204. Bivariate interpolation at Xu points: results, extensions and applications
    preprint - L. Bos, M. Caliari, S. De Marchi and M. Vianello
    Electron. Trans. Numer. Anal. 25 (2006), 1--16
  205. On the Lebesgue constant for the Xu interpolation formula
    preprint - L. Bos, S. De Marchi and M. Vianello
    J. Approx. Theory 141 (2006), 134--141
  206. A numerical study of the Xu polynomial interpolation formula in two variables
    preprint - L. Bos, M. Caliari, S. De Marchi and M. Vianello
    Computing 76 (2006), 311--324
  207. Numerical cubature on scattered data by radial basis functions
    preprint - A. Sommariva and M. Vianello
    Computing 76 (2006), 295--310
  208. Bivariate Lagrange interpolation at the Padua points: the generating curve approach
    preprint - L. Bos, M. Caliari, S. De Marchi, M. Vianello and Y. Xu
    J. Approx. Theory 143 (2006), 15--25

    2005

  209. Near-Optimal Data-Independent Point Locations for Radial Basis Functions Interpolation
    preprint - S. De Marchi, R. Schaback and H. Wendland
    Adv. Comput. Math. 23 (2005), 317--330
    cited in R. Schaback, H. Wendland, Kernel techniques: From machine learning to meshless methods, Acta Numerica 2006
  210. Sets of Near-Optimal Points for Interpolation on the Square
    preprint - S. De Marchi
    APPLIED AND INDUSTRIAL MATHEMATICS IN ITALY
    Proceedings of the 7th Conference, Venice (Italy), 20 - 24 September 2004, Ed. M. Primicerio et al., 45--55
  211. On the Numerical Solution of Some Semilinear Elliptic Problems - II
    preprint - K. Atkinson and A. Sommariva
    Computing 74 (2005), 159--175
  212. Quadrature over the sphere
    preprint - K. Atkinson and A. Sommariva
    Electron. Trans. Numer. Anal. 20 (2005), 104--118
  213. A parallel exponential integrator for large-scale discretizations of advection-diffusion models
    preprint - L. Bergamaschi, M. Caliari, A. Martinez and M. Vianello
    Springer LNCS vol. 3666, 2005 (Proc. of Euro PVM MPI 2005, Sorrento, Italy), 483--492
    cited in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 2010
  214. Adaptive bivariate Chebyshev approximation
    preprint - A. Sommariva, M. Vianello and R. Zanovello
    Numer. Algorithms 38 (2005), no. 1-3, 79--94
  215. Bivariate polynomial interpolation on the square at new nodal sets
    preprint - M. Caliari, S. De Marchi and M. Vianello
    Appl. Math. Comput. 165/2 (2005), 261--274