Marco Vianello: work on Meshless Approximation

online publications and preprints (downloadable pdf)

1. Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers
   arXiv: 2410.03279, with M. Mohammadi and A. Sommariva
   
   
2. Unisolvence of unsymmetric random Kansa collocation by Gaussians and other analytic RBF vanishing at infinity
   arXiv: 2405.18550, with A. Sommariva
   
   
3. Nonsingularity of unsymmetric Kansa matrices: random collocation by MultiQuadrics and Inverse MultiQuadrics
   arXiv: 2403.18017, with R. Cavoretto, A. De Rossi, F. Dell'Accio and A. Sommariva
   Math. Comput. Simul., minor revision
   
   
4. Random sampling and polynomial-free interpolation by Generalized MultiQuadrics
   preprint, with A. Sommariva
   J. Approx. Theory 306 (2025), 106119
   
   
5. Polynomial-free unisolvence of polyharmonic splines with odd exponent by random sampling
   with A. Sommariva
   Dolomites Res. Notes Approx. (DRNA) 17 (2024), 45--47
   
   
6. Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation
   preprint, with F. Dell'Accio and A. Sommariva
   Eng. Anal. Bound. Elem. 165 (2024), 105773
   
   
7. A note on polynomial-free unisolvence of polyharmonic splines at random points
   preprint, with L. Bos and A. Sommariva
   Appl. Math. Lett. 157 (2024), 109161
   
   
8. 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), 115793
   
   
9. Random sampling and unisolvent interpolation by almost everywhere analytic functions
   preprint, with F. Dell'Accio and A. Sommariva
   Appl. Math. Lett. 145 (2023)
   
   
10. 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)
    
    
11. RBFCUB: a numerical package for near-optimal meshless cubature on general polygons
    preprint, with R. Cavoretto, A. De Rossi and A. Sommariva
    Appl. Math. Lett. 125 (2022)
    
    
12. 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
    
    
13. RBF moment computation and meshless cubature on general polygonal regions
    preprint, with A. Sommariva
    Appl. Math. Comput. 409 (2021)
    
    
14. Meshless cubature over the disk by Thin-Plate Splines
    preprint, with A. Punzi and A. Sommariva
    J. Comput. Appl. Math. 221 (2008), 430--436
    
    
15. Meshless cubature by Green's formula
    preprint, with A. Sommariva
    Appl. Math. Comput. 183 (2006), 1098--1107
    
    
16. Numerical cubature on scattered data by radial basis functions
    preprint, with A. Sommariva
    Computing 76 (2006), 295--310