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Stefano De Marchi: publications and preprints


My H-index and citations from Google Scholar

    Works in progress


    Submitted

  1. Shape-Driven Interpolation with Discontinuous Kernels: Error Analysis, Edge Extraction and Applications in MPI
    draft (Mar. 2019) with W. Erb, F. Marchetti, E. Perracchione and M. Rossini
  2. Polynomial interpolation via mapped bases without resampling
    draft (Feb. 2019) with F. Marchetti, E. Perracchione and D. Poggiali
  3. On the Lebesgue constant of the trigonometric Floater-Hormann rational interpolant at equally spaced nodes
    draft (Feb. 2019) with C. Bandiziol
  4. A stable meshfree PDE solver for source-type flows in porous media
    draft (Dec. 2018) with R. Campagna, S. Cuomo, E. Perracchione and G. Severino
  5. Jumping with Variably Scaled Discontinuos Kernels (VSDK)
    draft (Aug. 2018), with F. Marchetti and E. Perracchione.
  6. In the footsteps of Copernicus: Padova (Italy) and Uppsala (Sweden)
    draft (May 2018) with M. Klimek.

    Accepted/In Press

  7. Analysis of a new class of rational RBF expansions
    draft (Feb. 2018) with M. Buhmann, E. Perracchione, accepted by IMA J. Numer. Analysis

    2019

  8. Mathematics and Oenology: exploring an unlikely pairing. (Mathematics and wine)
    with L. Cadeddu and A. Cauli.
    in Handbook of the Mathematics of the Arts and Sciences", pp. 1-31, doi:10.1007/978-3-319-70658-0_67-1, Springer 2019. Ed. B. Sriraman.
  9. Fast and stable rational RBF-based Partition of Unity interpolation
    draft with A. Martinez, E. Perracchione. J. Comput. Appl. Math. 349 (2019), pp. 331-343
    online version.

    2018

  10. RBF-based partition of unity method for elliptic PDEs: Adaptivity and stability issues via VSKs
    draft (June 2017) with A. Martinez, E. Perracchione and M. Rossini. J. Sci. Comput. DOI:10.1007/s10915-018-0851-2 online first
  11. Image Reconstruction from Scattered Radon Data with Weighted Positive Definite Kernel Functions
    draft, with A. Iske and G. Santin, Calcolo 55(2) (2018), https://doi.org/10.1007/s10092-018-0247-6.
  12. Quasi-Monte Carlo integration on manifolds with mapped low-discrepancy points and greedy minimal Riesz $s$-energy points,
    draft, with G. Elefante, Appl. Num. Math. 127(5), pp. 110-124 (2018), online version
  13. On multivariate Marcinkiewicz--Zygmund type inequalities
    draft (August 2017), with A. Kroó Acta Math. Hungar. 151(1), pp.69--89 (2018), online version .

    2017

  14. Ricci tensors and wine in Lugo di Romagna and Padova, Italy
    draft (Apr. 2017) with G. Andreatta, Math. Intelligencer 39 (3), pp. 56--60. online version .
  15. Lissajous sampling and spectral filtering in MPI applications: the reconstruction algorithm for reducing the Gibbs phenomenon
    draft (Feb. 2017) with W. Erb and F. Marchetti, Proceedings of SampTA 2017. , pp. 580--584.
    IEEE Xplore Digital Library DOI: 10.1109/SAMPTA.2017.8024375
  16. A rescaled method for RBF approximation
    draft (Nov. 2016) with A. Idda and G. Santin, Proceedings of "Approximation Theory XV",
    Springer Proceedings on Mathematics and Statistics, Vol. 201 (2017), pp.39--59.
  17. Spectral filtering for the reduction of the Gibbs phenomenon of polynomial approximation methods on Lissajous curves with applications in MPI
    with W. Erb and F. Marchetti, Dolomites Res. Notes Approx. 10 (2017), pp. 128--137.
  18. Partition of unity interpolation using stable kernel-based techniques
    (draft), with R. Cavoretto et al., Appl. Numer. Math. 116 (2017), pp. 95--107, online.
  19. Polynomial approximation on Lissajous curves in the d-cube ,
    proceeding conference honoring prof. F. Costabile, with L. Bos and M. Vianello.
    Appl. Numer. Math., available online 26 January 2017 here
  20. Trivariate polynomial approximation on Lissajous curves
    with L. Bos and M. Vianello. IMA J. Numer. Analysis (2017) 37, pp. 519--541.

    2016

  21. A new quasi-Monte Carlo technique based on nonnegative least-squares and approximate Fekete points
    (draft) with C. Bittante and G. Elefante. Numer. Math. TMA. 9(4) (2016), pp. 640--663;
    doi: 10.4208/nmtma.2016.m1516 .
  22. Kernel-based Image Reconstruction from Scattered Radon Data
    (draft) with A. Iske, A. Sironi. Dolomites Res. Notes on Approx. Vol 9,
    special issue for the workshop "Kernel-based methods and function approximation", pp. 19--31.
  23. Approximating basins of attraction for dynamical systems via stable radial bases
    R. Cavoretto, S. De Marchi, A. De Rossi, E. Perracchione and G. Santin
    AIP Conference Proceedings, 1738, 390003 (2016); doi:10.1063/1.4952177 online

    2015

  24. Fast computation of orthonormal bases for RBF spaces through Krylov spaces methods
    (draft, Nov. 2014), with G. Santin, BIT Numerical Math. 55(4) (2015), pp. 949--966.
  25. RBF approximation of large datasets by partition of unity and local stabilization
    (draft, May 2015) with R. Cavoretto et al., Proceedings of CMMSE 2015, Vol. I-II-III-IV, pp. 317--326.
  26. Polynomial Meshes: Computation and Approximation
    (draft, May 2015) with F. Piazzon, A. Sommariva and M. Vianello Proceedings of CMMSE 2015, Vol. I-II-III-IV, pp. 414--425.
  27. A few remarks on "On certain Vandermonde determinants whose variables separate"
    (draft, May 2015) with A. P. de Camargo, Dolomites Res. Notes Approx. 8 (2015), pp. 1--11.
  28. Analytical and experimental FWHM of a gamma camera: theoretical and practical issues ,
    (reviewed version, 2015), with D. Cecchin, D, Poggiali, L. Riccardi, P. Turco, F. Bui, PeerJ 3:e722; DOI 10.7717/peerj.722 (2015).
  29. On the constrained Mock-Chebyshev least squares,
    (draft Nov. 2014) with F. Dell'Accio and M. Mazza, J. Comput. Appl. Math. 280 (2015), pp. 94--109.
    Online version here

    2014

  30. Multivariate Christoffel functions and hyperinterpolation
    draft, with A. Sommariva and M. Vianello, Dolomites Res. Notes Approx. Vol. 7 (2014), pp. 26--33.
  31. Fekete Type Points for Ridge Function Interpolation and Hyperbolic Potential Theory
    with L. Bos and N. Levenberg, Publ. Math. Inst. (Beograd), Vol. 110 (2014), pp. 41-48.
  32. Proceedings of the workshop Multivariate Approximation 2013 .
    Guest editor of the Special issue of Dolomites Res. Notes Approx. Vol. 7 (2014).
  33. On certain multivariate Vandermonde determinants whose variables separate
    draft, with K. Usevich, Linear Alg. Appl., Vol. 449 (2014), pp. 17--27.

    2013

  34. Polynomial approximation on pyramids, cones and solids of rotation
    draft, with M. Vianello, Dolomites Res. Notes Approx, Proceedings DWCAA12, Vol. 6 (2013), pp. 20--26
    Matlab package for 3-dimensional WAMs: 3dWAM
  35. A new stable basis for radial basis function interpolation
    draft, with G. Santin, J. Comp. Appl. Math., Vol. 253 (2013), pp. 1--13. online
  36. Bounding the Lebesgue constant of Berrut's rational interpolant at general nodes
    draft, with L. Bos, K. Hormann and J. Sidon, J. Approx. Theory Vol. 169 (2013), pp. 7--22. most cited of JAT 2018

    2012

  37. Polynomial approximation and cubature at approximate Fekete and Leja points of the cylinder
    draft, with M. Marchioro and A. Sommariva, Appl. Math. Comput. Vol. 218(21), pp. 10617-10629
  38. On the Lebesgue constant of barycentric rational interpolation at equidistant nodes
    draft, with L. Bos, K. Hormann and G. Klein, Numer. Math. 121(3) 2012, 461-471
  39. A mathematical view of matching food and wine
    draft, Int. J. Contemp. Math. Sciences (7) 2012, no. 33, 1639 - 1652
    Matlab files.
  40. Barycentric rational interpolation at quasi-equidistant nodes
    draft, with K. Hormann and G. Klein, Dolomites Research Notes Approx, Vol 5, 2012, pp. 1--6

    2011

  41. On the Whittaker--Shannon sampling by means of Berrut's rational interpolant and its extension by Floater and Hormann
    draft, with L. Bos, East J. Approx. 17(3) (2011), pp. 267--284
  42. On optimal points for interpolation by univariate exponential functions
    draft, with L. Bos, Dolomites Research Notes on Approx. (DRNA), Vol. 4 (2011), pp. 8--12.
  43. Dolomites Research Notes on Approximation (DRNA), Vol. 4, Special Issue for the Proceedings of Robert Schaback's 65th birthday, pp. 63,
    Guest editors: M. Buhmann, S. De Marchi and G. Plonka-Hock.
  44. On Multivariate Newton Interpolation at Discrete Leja Points
    draft, with L. Bos, A. Sommariva and M. Vianello, Dolomites Res. Notes Approx, Vol. 4 (Proceedings of Robert Schaback's 65th birthday), pp. 15--20.
  45. On the Lebesgue constant of Berrut's rational interpolant at equidistant nodes
    draft, with L. Bos and K. Hormann, J. Comput. Appl. Math. 236 (2011), pp. 504--510.
  46. Preface
    with C. Brezinki, J. M. Carnicer, A. Iske, M. Redivo-Zaglia, S. Seatzu, E. Venturino and M. Vianello
    Calcolo 48 (2011), pp. 1-3
  47. Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave
    draft, with M. Caliari, A. Sommariva and M. Vianello, Numer. Algorithms Vol. 56(1), 2011, pp. 45--60,
    on-line
  48. Weakly Admissible Meshes and Discrete Extremal Sets
    draft, with L. Bos, A. Sommariva and M. Vianello
    Numer. Math. Theor. Meth. Appl. Vol. 4(1), 2011, pp. 1--12

    2010

  49. Computing multivariate Fekete and Leja points by numerical linear algebra
    draft, with L. Bos, A. Sommariva and M. Vianello
    SIAM J. Num. Anal. Vol. 48(5), 2010, pp. 1984-1999.
    Available on line: here
  50. Special Issue of Numer. Algorithms Vol 55, 2-3, Preface pp. 141-143 (2010)
    with J. M. Carnicer, M. Redivo Zaglia, E. Venturino and M. Vianello
    "Second Dolomites Workshop on Constructive Approximation and Applications (DWCAA09)".
  51. Stability of Kernel-Based Interpolation
    draft, with R. Schaback
    Adv. Comput. Math. Vol. 32(2), 2010, p. 155-161 available on line.
    Examples and more
    These are the examples and the figures illustrating the results of the paper Stability of Kernel-Based Interpolation.

    2009

  52. Nonstandard kernels and their Applications
    draft, with R. Schaback.
    DRNA (Dolomites Research Notes on Approximations) Vol. 2, 2009, pp. 16-43.
    Matlab and Maple files.
  53. On the Vandermonde Determinant of Padua-like Points
    draft, with L. Bos and S. Waldron
    an Open Problem for DRNA (Dolomites Research Notes on Approximation), Vol. 2, 2009, pp. 1-15.
  54. Geometric greedy and greedy points for RBF interpolation
    Draft. Proceedings of the 9th CMMSE (Gijon, Spain, July 2009), Vol. II, pp. 381--392
    Editors: P. Alonso, S. Oharu, E. Venturino and B. A. Wade.
  55. A numerical code for fast interpolation and cubature at the Padua points
    draft, with M. Caliari, A. Sommariva and M. Vianello.
    Proceedings of the 9th CMMSE (Gijon, Spain, July 2009), Vol. I, p. 218-228.
    Editors: P. Alonso, S. Oharu, E. Venturino and B. A. Wade.
  56. New cubature formulae and hyperinterpolation in three variables
    draft, with M. Vianello and Y. Xu.
    BIT Numerical Mathematics, Vol. 49(1) 2009, 55-73. on line

    2008

  57. Bivariate Lagrange interpolation at the Padua points: computational aspects
    draft, with M. Caliari and M. Vianello
    J. Comput. Appl. Math., Vol. 221 2008, 284-292.
  58. Algorithm 886: Padua2D: Lagrange Interpolation at Padua Points on Bivariate Domains
    draft, with M. Caliari and M. Vianello
    ACM Trans. Math. Software, Vol. 35(3), Article 21, 11 pages, 2008.
  59. Hyperinterpolation in the cube
    draft, with M. Caliari and M. Vianello
    Comput. Math. Appl., Vol. 55(11) 2008, 2490-2497.
  60. Univariate Radial Basis Functions with Compact Support Cardinal Functions
    draft, with L. Bos
    East J. Approx., Vol. 14(1) 2008, 69-80.

    2007

  61. Bivariate Lagrange interpolation at the Padua points: the ideal theory approach
    preprint, with L. Bos, M. Vianello and Y. Xu
    Numer. Math., 108(1) (2007), 43-57.
  62. Hyperinterpolation on the square
    preprint, with M. Caliari and M. Vianello
    J. Comput. Appl. Math. 210(1-2) (2007), 78-83
  63. Guest-Editor Preface
    with M. Redivo-Zaglia and M. Vianello
    Numer. Algorithms 45 (1-4) (2007), 1--9,
    "1st Dolomites Workshop on Constructive Approximation and Applications (DWCAA06)"
  64. Mathematics and wine
    preprint
    Appl. Math. Comput. 192 (2007), 180-190
    Some comments to the paper bt written by Nicoló Regazzoni in bargiornale.it, 22 October 2007

    2006

  65. Polynomials arising in factoring generalized Vandermonde determinants III :computation of their roots
    preprint, with M. Morandi Cecchi
    Neural, Parallel and Scientific Computations 14 (2006), 25--38
  66. Parametric method for global optimization in Hilbert Spaces
    preprint, with I. Raykov
    J. of Optim. Theory and Applications (JOTA) 130(3) (2006), 411--430
  67. Hyper2d: a numerical code for hyperinterpolation on rectangles
    preprint, with M. Caliari, R. Montagna and M. Vianello
    Appl. Math. Comput. 183 (2006), 1138--1147
  68. Bivariate Lagrange interpolation at the Padua points: the generating curve approach
    preprint, with L. Bos, M. Caliari, M. Vianello and Y. Xu
    J. Approx. Theory 143 (2006), 15--25
    classified in the TOP 25 Hottest Articles of JAT, Oct.-Dec. 2006
  69. Bivariate interpolation at Xu points: results, extensions and applications
    preprint, with L. Bos, M. Caliari and M. Vianello
    Electron. Trans. Numer. Anal. 25 (2006), 1--16
  70. On the Lebesgue constant for the Xu interpolation formula
    preprint, with L. Bos and M. Vianello
    J. Approx. Theory 141 (2006), 134--141
    classified in the TOP 25 Hottest Articles of JAT, July-Sept. 2006
  71. A numerical study of the Xu polynomial interpolation formula in two variables
    preprint, with L. Bos, M. Caliari and M. Vianello
    Computing 76(3-4)(2006), 311--324

    2005

  72. Bivariate polynomial interpolation on the square at new nodal sets
    preprint, with M. Caliari and M. Vianello
    Appl. Math. Comput. 165(2) (2005), 261--274
  73. Near-Optimal Data-independent Point Locations for Radial Basis Function Interpolation
    preprint, with R. Schaback and H. Wendland
    Adv. Comput. Math. 23(3) (2005), 317--330
  74. Sets of Near-Optimal Points for Interpolation on the Square
    preprint
    APPLIED AND INDUSTRIAL MATHEMATICS IN ITALY
    Proceedings of the 7th Conference, Venice (Italy), 20 - 24 September 2004
    Ed. M. Primicerio et al., pp. 45-55 (2005)

    2004

  75. On Leja sequences: some results and applications
    preprint
    Appl. Math. Comput. 152(3) (2004), 621-647
  76. On blossoming in integer Müntz spaces
    preprint, with C. Roveredo
    Int. Math. J. 5(1) (2004), 61-66

    2003

  77. On optimal center locations for radial basis interpolation: computational aspects
    preprint
    Rend. Sem. Mat. Torino, 61(3) (2003), 343-358
  78. Fast evaluation of discrete integral operators by Chebyshev and Leja polynomial approximation
    preprint, with M. Vianello
    "Constructive Function Theory", Varna 2002 (B. Bojanov, Ed.),pp. 347-353, DARBA Sofia 2003.

    2002

  79. On the limit under scaling of polynomial Lagrange interpolation on analytic manifolds
    preprint, with L. Bos
    Rend. Circolo Matematico Palermo, Serie II, Suppl. 68 (2002), 303-314
  80. An interpolant defined by subdivision and the analysis of the error
    preprint, with A. Ligun, A. Schumeiko and S. Timchenko
    J. Comput. Appl. Math. 145(1) (2002), 71-88
  81. Polynomials arising in factoring generalized Vandermonde determinants II: a condition for monicity
    preprint
    Appl. Math. Lett. 15(5) (2002), 627-632

    2001

  82. Approximating the approximant : a numerical code for the polynomial compression of discrete integral operators
    preprint, with M. Vianello
    Numer. Algorithms 28 (2001), 101-116
  83. Polynomials arising in factoring generalized Vandermonde determinants: an algorithm for computing their coefficients
    preprint
    Math. Comput. Modelling 34 (2001), 271-281

    1993-2000

  84. Fekete points for bivariate polynomials restricted to y=xm
    preprint, with L. Bos
    East J. Approx. 6(2) (2000), 189-200
  85. On computing the factors of generalized Vandermonde determinants
    In Recent Advances in Applied and Theoretical Mathematics
    Math. Comput. Sci. Eng., World Sci. Eng. Soc. Press, (2000), 140-144
  86. Limiting values under scaling of the Lebesgue function for polynomial interpolation on spheres.
    preprint, with L. Bos
    J. Approx. Theory 96(2) (1999), 366-377
  87. A Package for Representing C1Interpolating Surfaces: Application to the Lagoon of Venice's Bed
    preprint, with D. Fasoli and M. Morandi Cecchi
    Numer. Algorithms 20(2-3) (1999), 197-215
  88. On computing derivatives for C1 interpolating schemes: an optimization
    preprint
    Computing 60 (1)(1998), 29--53
  89. Peano's kernel theorem for vector-valued functions: a weak version in normed spaces
    preprint, with M. Vianello
    Numer. Func. Anal. Optim. 18 (1&2)(1997), 65--74
  90. Peano's kernel theorem for vector-valued functions and some applications
    preprint, with M. Vianello
    Numer. Func. Anal. Optim. 17 (1&2)(1996), 57--64
  91. Reference Functional and Characteristic Space for Lagrange and Bernstein Operators
    Abstract, with M. Morandi Cecchi
    Approx. Theory Appl. (N.S.) 11(4) (1995), 6-14
  92. The polynomial approximation in the finite element method
    preprint, with M. Morandi Cecchi
    J. Comput. Appl. Math. 57 (1-2) (1995), 99-114
  93. Can Irregular Subdvisions Preserve Convexity ?
    abstract, with Morandi Cecchi
    Approximation Theory, wavelets and applications,
    NATO Adv. Sci. Inst. Ser. C Math. Phys.Sci. 454
    Kluwer Acad. Publi. (1995), 325-334
  94. Splitting functions and numerical analysis of WR-type methods for evolutionary and stationary problems
    with M. Vianello and R. Zanovello
    In Mathematics of Computation 1943-1993: a half century of computational mathematics
    Proc. Sympos. Appl. Math. (48) (1994), 281--285
  95. Fractal interpolation functions for a class of finite elements
    with M. Morandi Cecchi
    In Wavelets, images and suface fitting
    A. K. Peters, Wellesley (1994), 189--196
  96. Inverse kinematics robot calibration by spline functions.
    with F. Agrilli and A. Doria
    Appl. Math. Modelling 17(9) (1993)

    Relevant technical reports

  97. Stability constants for kernel-based interpolation processes
    with R. Schaback
    University of Verona, RR 59/2008.
  98. A study on Premixed Laminar Flames
    with G. Argentini, M. Caliari and S. Zuccher
    University of Verona, RR 46/2006.
  99. Generalized Vandermonde determinants, Toeplitz matrices and Schur functions
    Universitaet Dortmund, Ergebnisberichte Angewandte Mathematik, 176/1999.
  100. LABSUP: a LAboratory for Bivariate C1 SUrfaces and Patches
    with Damiano Fasoli and Maria Morandi Cecchi
    University of Padova, RI 9/1996.
  101. The Dyadic Iterative Interpolation Method and Some Extensions
    with M. Morandi Cecchi
    University of Padova, RI 10/1994

    Translation

  102. On the systems of Fekete-points of an arc of circumference
    preprint, by B. Germanski. Tranlation done with L. Brutman.
    East J. Approx. 8(4), 2002, 511-524

    Books



  103. Exercises of Numerical Calculus

    I Edizione 2017, pp. 122, ISBN: 978-88-986485-3-5 Editrice La Dotta-Bologna


  104. Meshfree Approximation for Multi-Asset European and American Option Problems

    I Edizione 2012, pp. 92, ISBN: 978-88-548515-1-1 Editrice Aracne-Roma


  105. Appunti di Calcolo Numerico
    (in Italian)
    II Edizione 2016, pp. 260, ISBN: 978-88-748893-9-6 Editrice Esculapio-Bologna


  106. Funzioni splines univariate

    Editrice Universitaria Udinese FORUM (2001)
    For copies you must contact the publisher at the following address: Via Larga, 38 - 33100 Udine, tel. 0432 26001.


  107. Approssimazione e Interpolazione su "Simplices": Caratterizzazioni, Metodi ed Estensioni

    Ph.D. thesis (in Italian, 1994).
    The thesis is available at the Florence national library here

    Software

  1. The LABSUP package at the Netlib
  2. Bivariate polynomial interpolation software and miscellanea

    Miscellanea Mathematics

  1. Il paradosso francese in MaddMaths, MAtematica Divulgazione Didattica, 21 Dec. 2011.
  2. Simai per la divulgazione, l'angolo arguto: Il paradosso francese
  3. From Matematicamente of Mathesis - Verona:
    nr. 113

    nr. 118

    Miscellanea: articles in local magazines, weekly, blogs, e-journals (in Italian)

  4. La Difesa del Popolo (Oct. 2012): AC: la scelta reliogiosa é restrittiva? Intervista.
  5. Toniolo Ricerca (Nov. 2011): Multiculturalitè e patto costituzionale nei 150 anni dell'unità d'Italia .
  6. Lettera Diocesana 2011/17: Openfield 2011: Editoriale
  7. La Difesa del Popolo (Ago. 2011): Openfield 2011: Multiculturalit?? e patto costituzionale. Intervista.
  8. La Difesa del Popolo (Mag. 2011): Laici e impegno sociopolitico
  9. Toniolo Ricerca (Mag. 2011): Univeneto, si parte!.
  10. La Difesa del Popolo (Apr. 2011): Quando le ferite non minano la dignità
  11. Toniolo Ricerca (Dic. 2010): Universo Università.
  12. Blog della Strada del Vino dei Colli Euganei Gocce di matematica??serata con i vini Severi
  13. La Difesa del Popolo (Mar. 2011): 17 marzo: una festa poco sentita
  14. La Difesa del Popolo (Feb. 2010): Cristiani in politica
  15. La Difesa del Popolo (Nov. 2009): Riforma Università
  16. From Blog Andrea Scanzi - Feb. 2008
  17. La Piazza del Conselvano - Feb. 2008
  18. From the Sommelier Veneto 1/08
  19. From the Sommelier Veneto 1/07