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Publications and preprints of the CAA group
(downloadable pdf)

Multivariate Approximation:
Polynomials, RBF, Numerical Cubature


    2014

  1. Product Gaussian quadrature on circular lunes
    draft - G. Da Fies and M. Vianello
    Numer. Math. Theory Methods Appl., to appear
  2. Sub-optimal polynomial meshes on planar Lipschitz domains
    draft, F. Piazzon and M. Vianello
    Numer. Funct. Anal. Optim., revision required

    2013

  3. Constructing optimal polynomial meshes on planar starlike domains
    draft, F. Piazzon and M. Vianello
    Dolomites Res. Notes Approx. DRNA, to appear
  4. Algebraic cubature by linear blending of elliptical arcs
    preprint - G. Da Fies, A. Sommariva and M. Vianello
    Appl. Numer. Math., published online 21 August 2013
  5. Norming meshes by Bernstein-like inequalities
    preprint - M. Vianello
    Math. Inequal. Appl., to appear
  6. Polynomial approximation on pyramids, cones and solids of rotation
    preprint - S. De Marchi and M. Vianello
    Dolomites Res. Notes Approx. DRNA 6 (2013), 20--26
  7. A new stable basis for radial basis function interpolation
    preprint - S. De Marchi and G. Santin
    J. Comp. Appl. Math. 253 (2013), 1--13
  8. Small perturbations of polynomial meshes
    preprint - F. Piazzon and M. Vianello
    Appl. Anal. 92 (2013), 1063--1073
  9. 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
  10. Fast construction of Fejer and Clenshaw-Curtis rules for general weight functions
    preprint - A. Sommariva
    Comput. Math. Appl. 65 (2013), 682--693
  11. On the Lebesgue constant of subperiodic trigonometric interpolation
    preprint - G. Da Fies and M. Vianello
    J. Approx. Theory 167 (2013), 59--64

    2012

  12. The transfinite diameter of a real ball and simplex
    preprint - T. Bloom, L. Bos and N. Levenberg
    Ann. Polon. Math. 106 (2012), 83--96
  13. 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
  14. Computing almost minimal formulas on the square
    draft - M. Festa and A. Sommariva
    J. Comput. Appl. Math. 236 (2012), 4296--4302
  15. 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
  16. Algebraic cubature on planar lenses and bubbles
    preprint - G. Da Fies and M. Vianello
    Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12
  17. 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
  18. Subperiodic trigonometric interpolation and quadrature
    preprint - L. Bos and M. Vianello
    Appl. Math. Comput. 218 (2012), 10630--10638
  19. 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
  20. Trigonometric Gaussian quadrature on subintervals of the period
    preprint - G. Da Fies and M. Vianello
    Electron. Trans. Numer. Anal. 39 (2012), 102--112
  21. Computing Fekete and Lebesgue points: simplex, square, disk
    preprint - M. Briani, A. Sommariva and M. Vianello
    J. Comput. Appl. Math. 236 (2012), 2477--2486
  22. Barycentric rational interpolation at quasi-equidistant nodes
    preprint - S. De Marchi, K. Hormann and G. Klein
    Dolomites Res. Notes Approx. DRNA 5 (2012), 1--6
  23. Low cardinality admissible meshes on quadrangles, triangles and disks
    preprint - L. Bos and M. Vianello
    Math. Inequal. Appl. 15 (2012), 229--235

    2011

  24. 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
  25. On optimal points for interpolation by univariate exponential functions
    preprint - L. Bos and S. De Marchi
    Dolomites Res. Notes Approx. DRNA 4 (2011), 8--12
  26. 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
  27. On Multivariate Newton Interpolation at Discrete Leja Points
    draft - L. Bos, S. De Marchi, A. Sommariva and M. Vianello
    Dolomites Res. Notes Approx. DRNA 4 (2011), 15--20
  28. Polynomial interpolation and cubature over polygons
    preprint - M. Gentile, A. Sommariva and M. Vianello
    J. Comput. Appl. Math. 235 (2011), 5232--5239
  29. An algebraic cubature formula on curvilinear polygons
    preprint - G. Santin, A. Sommariva and M. Vianello
    Appl. Math. Comput. 217 (2011), 10003--10015
  30. 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
  31. 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
  32. 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

  33. Analytic transformations of admissible meshes
    preprint - F. Piazzon and M. Vianello
    East J. Approx. 16 (2010), 313--322
  34. 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
  35. 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
  36. Approximate Fekete points for weighted polynomial interpolation
    preprint - A. Sommariva and M. Vianello
    Electron. Trans. Numer. Anal. 37 (2010), 1--22
  37. On simple approximations to simple curves
    preprint - L. Bos and M. Vianello
    Dolomites Res. Notes Approx. DRNA 3 (2010), 1--6
  38. Stability of Kernel-Based Interpolation
    preprint - S. De Marchi and R. Schaback
    Adv. Comput. Math. 32 (2010), 155--161

    2009

  39. On the Vandermonde Determinant of Padua-like Points
    preprint - L. Bos, S. De Marchi and S. Waldron
    Dolomites Res. Notes Approx. DRNA 2 (2009), 1--15
  40. Nonstandard Kernels and their Applications
    preprint - R. Schaback and S. De Marchi
    Dolomites Res. Notes Approx. DRNA 2 (2009), 16--43
  41. Gauss-Green cubature and moment computation over arbitrary geometries
    preprint - A. Sommariva and M. Vianello
    J. Comput. Appl. Math. 231 (2009), 886--896
  42. Computing approximate Fekete points by QR factorizations of Vandermonde matrices
    preprint - A. Sommariva and M. Vianello
    Comput. Math. Appl. 57 (2009), 1324--1336
  43. New cubature formulae and hyperinterpolation in three variables
    preprint - S. De Marchi, M. Vianello and Y. Xu
    BIT Numerical Mathematics 49 (2009), 55--73

    2008

  44. 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)
  45. Approximation on the sphere using radial basis functions plus polynomials
    preprint - A. Sommariva and I.H. Sloan
    Adv. Comput. Math. 29 (2008), 147--177
  46. Nontensorial Clenshaw-Curtis cubature
    preprint - A. Sommariva, M. Vianello and R. Zanovello
    Numer. Algorithms 49 (2008), 409--427
  47. Hyperinterpolation in the cube
    preprint - M. Caliari, S. De Marchi and M. Vianello
    Comput. Math. Appl. 55 (2008), 2490--2497
  48. Univariate Radial Basis Functions with Compact Support Cardinal Functions
    preprint - L. Bos and S. De Marchi
    East J. Approx. 14 (2008), 69--80
  49. 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
  50. 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

  51. 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
  52. Product Gauss cubature over polygons based on Green's integration formula
    preprint - A. Sommariva and M. Vianello
    BIT Numerical Mathematics 47 (2007), 441--453
  53. Hyperinterpolation on the square
    preprint - M. Caliari, S. De Marchi and M. Vianello
    J. Comput. Appl. Math. 210 (2007), 78--83

    2006

  54. Meshless cubature by Green's formula
    preprint - A. Sommariva and M. Vianello
    Appl. Math. Comput. 183 (2006), 1098--1107
  55. 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
  56. 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
  57. 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
  58. 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
  59. 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
  60. Numerical cubature on scattered data by radial basis functions
    preprint - A. Sommariva and M. Vianello
    Computing 76 (2006), 295--310

    2005

  61. 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
  62. On the Numerical Solution of Some Semilinear Elliptic Problems - II
    preprint - K. Atkinson and A. Sommariva
    Computing 74 (2005), 159--175
  63. Quadrature over the sphere
    preprint - K. Atkinson and A. Sommariva
    Electron. Trans. Numer. Anal. 20 (2005), 104--118
  64. 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
  65. Adaptive bivariate Chebyshev approximation
    preprint - A. Sommariva, M. Vianello and R. Zanovello
    Numer. Algorithms 38 (2005), no. 1-3, 79--94

    2002

  66. On the limit under scaling of polynomial Lagrange interpolation on analytic manifolds
    preprint - L. Bos and S. De Marchi
    Rend. Circolo Matematico Palermo, Serie II, Suppl. 68 (2002), 303--314

Approximation of Matrix Exponentials and Exponential Integrators

Submitted or in progress

Published or to appear


    2013

  1. 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)

    2012

  2. Meshfree Exponential Integrators
    preprint - M. Caliari, A. Ostermann and S. Rainer
    SIAM J. Sci. Comput., to appear

    2011

  3. Meshfree integrators
    preprint - M. Caliari, A. Ostermann, and S. Rainer
    Oberwolfach Reports (2011)

    2009

  4. 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
  5. High-order time-splitting Hermite and Fourier spectral methods for the Gross-Pitaevskii equation
    preprint - M. Caliari, Ch. Neuhauser and M. Thalhammer
    J. Comput. Phys. 228 (2009), 349--360
  6. Implementation of exponential Rosenbrock-type integrators
    preprint - M. Caliari and A. Ostermann
    Appl. Numer. Math. 59 (2009), 568--581

    2007

  7. 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

    2006

  8. 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

    2005

  9. 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

    2004

  10. The ReLPM exponential integrator for FE discretizations of advection-diffusion equations
    preprint - L. Bergamaschi, M. Caliari and M. Vianello
    Springer LNCS vol. 3039, part IV, 2004 (Proc. of ICCS 2004, Krakow, Poland), 434--442
  11. Interpolating discrete advection-diffusion propagators at Leja sequences
    preprint - L. Bergamaschi, M. Caliari and M. Vianello
    J. Comput. Appl. Math. 172 (2004), no. 1, 79--99

    2003

  12. Efficient approximation of the exponential operator for discrete 2D advection-diffusion problems
    preprint - L. Bergamaschi, M. Caliari and M. Vianello
    Numer. Linear Algebra Appl. 10 (2003), 271--289

    2000

  13. Efficient computation of the exponential operator for large, sparse, symmetric matrices
    preprint - L. Bergamaschi and M. Vianello
    Numer. Linear Algebra Appl. 7 (2000), 27--45