Marco Vianello: work on Polynomial Interpolation and Regression

online publications and preprints (downloadable pdf), with some conference posters
see also the software section

1. CPOLYMESH: Matlab and Python codes for complex polynomial approximation by Chebyshev admissible meshes
   preprint, with D. Kenne and A. Sommariva
   JAS - J. Approx. Software 1, 2 (2024)
   
   
2. Evaluating Lebesgue constants by Chebyshev polynomial meshes on cube, simplex and ball
   arXiv:2311.18656, with L. Bialas-Ciez, D. Kenne and A. Sommariva
   Electron. Trans. Numer. Anal. 60 (2024), 428--445
   
   
3. Numerical cubature on scattered data by adaptive interpolation
   preprint, with R. Cavoretto, A. De Rossi, F. Dell'Accio, F. Di Tommaso, N. Siar and A. Sommariva
   J. Comput. Appl. Math. 444 (2024)
   
   
4. Chebyshev admissible meshes and Lebesgue constants of complex polynomial projections
   preprint, with L. Bialas-Ciez, D. Kenne and A. Sommariva
   J. Comput. Appl. Math. 443 (2024)
   
   
5. Random sampling and unisolvent interpolation by almost everywhere analytic functions
   preprint, with F. Dell'Accio and A. Sommariva
   Appl. Math. Lett. 145 (2023)
   
   
6. DISC: an adaptive numerical Differentiator by local polynomial Interpolation on SCattered data
   preprint, with F. Dell'Accio, F. Di Tommaso and N. Siar
   Dolomites Res. Notes Approx. DRNA 15 (2022) (Special Issue "Software for Approximation 2022", 92--100)
   
   
7. Numerical differentiation on scattered data through multivariate polynomial interpolation
   arXiv preprint 2105.09262, with F. Dell'Accio, F. Di Tommaso and N. Siar
   BIT Numer. Math. 62 (2022), 773--801
   
   
8. Near-optimal polynomial interpolation on spherical triangles
   preprint, with A. Sommariva
   Mediterr. J. Math. 19 (2022)
   
   
9. Numerical hyperinterpolation over spherical triangles
   preprint, with A. Sommariva
   Math. Comput. Simul. 190 (2021), 15--22
   
   
10. dCATCH: a numerical package for d-variate near G-optimal Tchakaloff regression via fast NNLS
    with M. Dessole and F. Marcuzzi
    MDPI-Mathematics 8(7) (2020) - Special Issue "Numerical Methods"
    
    
11. Near G-optimal Tchakaloff designs
    preprint, with L. Bos and F. Piazzon
    Comput. Statistics 35 (2020), 803--819
    
    
12. Accelerating the Lawson-Hanson NNLS solver for large-scale Tchakaloff regression designs
    preprint, with M. Dessole and F. Marcuzzi
    Dolomites Res. Notes Approx. DRNA 13 (2020), 20--29
    
    
13. CaTchDes: Matlab codes for Caratheodory-Tchakaloff Near-Optimal Regression Designs
    with L. Bos
    SoftwareX 10 (2019)
    
    
14. Near optimal polynomial regression on norming meshes
    preprint, with L. Bos and F. Piazzon
    Sampling Theory and Applications 2019, IEEE Xplore Digital Library, DOI: 10.1109/SampTA45681.2019.9030910
    
    
15. Dubiner distance and stability of Lebesgue constants
    preprint
    J. Inequal. Spec. Funct. 10-2 (2019), 49--60
    
    
16. Stability inequalities for Lebesgue constants via Markov-like inequalities
    preprint, with F. Piazzon
    Dolomites Res. Notes Approx. DRNA 11 (2018), 1--9
    
    
17. Subperiodic Trigonometric Hyperinterpolation
    preprint, with G. Da Fies and A. Sommariva
    "Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan" (invited paper)
    J. Dick, F.Y. Kuo, H. Wozniakowski Eds., Springer, 2018
    
    
18. Caratheodory-Tchakaloff Least Squares
    preprint, with F. Piazzon and A. Sommariva
    2017 International Conference on Sampling Theory and Applications (SampTA)
    IEEE Xplore Digital Library DOI: 10.1109/SAMPTA.2017.8024337
    poster presented at SampTA 2017, Tallinn (Estonia)
    
    
19. Numerical hyperinterpolation over nonstandard planar regions
    preprint, with A. Sommariva
    Math. Comput. Simulation 141 (2017), 110--120
    
    
20. Polynomial approximation on Lissajous curves in the d-cube
    preprint, with L. Bos and S. De Marchi
    Appl. Numer. Math. 116 (2017), 47--56
    
    
21. Polynomial approximation and quadrature on geographic rectangles
    preprint, with M. Gentile and A. Sommariva
    Appl. Math. Comput. 297 (2017), 159--179
    poster presented at SIAM GeoSciences 2013, Padova (Italy)
    
    
22. Trivariate polynomial approximation on Lissajous curves
    preprint, with L. Bos and S. De Marchi
    IMA J. Numer. Anal. 37 (2017), 519--541
    
    
23. Polynomial fitting and interpolation on circular sections
    preprint, with A. Sommariva
    Appl. Math. Comput. 258 (2015), 410--424
    
    
24. Compression of multivariate discrete measures and applications
    preprint, with A. Sommariva
    Numer. Funct. Anal. Optim. 36 (2015), 1198--1223
    
    
25. Multivariate Christoffel functions and hyperinterpolation
    with S. De Marchi and A. Sommariva
    Dolomites Res. Notes Approx. DRNA 7 (2014), 26--33
    
    
26. Polynomial approximation on pyramids, cones and solids of rotation
    with S. De Marchi
    Dolomites Res. Notes Approx. DRNA 6 (2013), 20--26
    
    
27. On the Lebesgue constant of subperiodic trigonometric interpolation
    preprint, with G. Da Fies
    J. Approx. Theory 167 (2013), 59--64
    
    
28. On the generation of symmetric Lebesgue-like points in the triangle
    preprint, with F. Rapetti and A. Sommariva
    J. Comput. Appl. Math. 236 (2012), 4925--4932
    
    
29. Subperiodic trigonometric interpolation and quadrature
    preprint, with L. Bos
    Appl. Math. Comput. 218 (2012), 10630--10638
    
    
30. Computing Fekete and Lebesgue points: simplex, square, disk
    preprint, with M. Briani and A. Sommariva
    J. Comput. Appl. Math. 236 (2012), 2477--2486
    
    
31. On Multivariate Newton Interpolation at Discrete Leja Points
    with L. Bos, S. De Marchi and A. Sommariva
    Dolomites Res. Notes Approx. DRNA 4 (2011), 15--20
    
    
32. Polynomial interpolation and cubature over polygons
    preprint, with M. Gentile and A. Sommariva
    J. Comput. Appl. Math. 235 (2011), 5232--5239
    
    
33. Geometric Weakly Admissible Meshes, Discrete Least Squares Approximations and Approximate Fekete Points
    preprint, with L. Bos, J.P. Calvi, N. Levenberg and A. Sommariva
    Math. Comp. 80 (2011), 1601--1621
    
    
34. Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave
    preprint, with M. Caliari, S. De Marchi and A. Sommariva
    Numer. Algorithms 56 (2011), 45--60
    
    
35. Weakly Admissible Meshes and Discrete Extremal Sets
    preprint, with L. Bos, S. De Marchi and A. Sommariva
    Numer. Math. Theory Methods Appl. 4 (2011), 1--12
    
    
36. Least-squares polynomial approximation on weakly admissible meshes: disk and triangle
    preprint, with L. Bos and A. Sommariva
    J. Comput. Appl. Math. 235 (2010), 660--668
    
    
37. Computing multivariate Fekete and Leja points by numerical linear algebra
    preprint, with L. Bos, S. De Marchi and A. Sommariva
    SIAM J. Numer. Anal. 48 (2010), 1984--1999
    poster presented at ICIAM 2011, Vancouver
    
    
38. Approximate Fekete points for weighted polynomial interpolation
    preprint, with A. Sommariva
    Electron. Trans. Numer. Anal. 37 (2010), 1--22
    
    
39. A numerical code for fast interpolation and cubature at the Padua points
    preprint, with M. Caliari, S. De Marchi and A. Sommariva
    Proceedings of the 9th CMMSE (2009), Vol. I, 218--228
    
    
40. Computing approximate Fekete points by QR factorizations of Vandermonde matrices
    preprint, with A. Sommariva
    Comput. Math. Appl. 57 (2009), 1324--1336
    
    
41. New cubature formulae and hyperinterpolation in three variables
    preprint, with S. De Marchi and Y. Xu
    BIT Numerical Mathematics 49 (2009), 55--73
    
    
42. Algorithm 886: Padua2D: Lagrange Interpolation at Padua Points on Bivariate Domains
    preprint, with M. Caliari and S. De Marchi
    ACM Trans. Math. Software 35-3 (2008)
    
    
43. Hyperinterpolation in the cube
    preprint, with M. Caliari and S. De Marchi
    Comput. Math. Appl. 55 (2008), 2490--2497
    
    
44. Bivariate Lagrange interpolation at the Padua points: computational aspects
    preprint, with M. Caliari and S. De Marchi
    J. Comput. Appl. Math. 221 (2008), 284--292
    
    
45. Bivariate Lagrange interpolation at the Padua points: the ideal theory approach
    preprint, with L. Bos, S. De Marchi and Y. Xu
    Numer. Math. 108 (2007), 43--57
    
    
46. Hyperinterpolation on the square
    preprint, with M. Caliari and S. De Marchi
    J. Comput. Appl. Math. 210 (2007), 78--83
    
    
47. Hyper2d: a numerical code for hyperinterpolation on rectangles
    preprint, with M. Caliari, S. De Marchi and R. Montagna
    Appl. Math. Comput. 183 (2006), 1138--1147
    
    
48. Bivariate Lagrange interpolation at the Padua points: the generating curve approach
    preprint, with L. Bos, M. Caliari, S. De Marchi and Y. Xu
    J. Approx. Theory 143 (2006), 15--25
    poster presented at 5ECM, Amsterdam, 2008
    
    
49. Bivariate interpolation at Xu points: results, extensions and applications
    preprint, with L. Bos, M. Caliari and S. De Marchi
    Electron. Trans. Numer. Anal. 25 (2006), 1--16
    
    
50. On the Lebesgue constant for the Xu interpolation formula
    preprint, with L. Bos and S. De Marchi
    J. Approx. Theory 141 (2006), 134--141
    
    
51. A numerical study of the Xu polynomial interpolation formula in two variables
    preprint, with L. Bos, M. Caliari and S. De Marchi
    Computing 76 (2006), 311--324
    
    
52. Adaptive bivariate Chebyshev approximation
    preprint, with A. Sommariva and R. Zanovello
    Numer. Algorithms 38 (2005), no. 1-3, 79--94
    
    
53. Bivariate polynomial interpolation on the square at new nodal sets
    preprint, with M. Caliari and S. De Marchi
    Appl. Math. Comput. 165/2 (2005), 261--274