Marco Vianello: publications and preprints

• complete list of publications in Numerical Analysis
  
  
• complete list of publications in Mathematical Analysis
  
  
• some bibliometrics

online publications and preprints (downloadable pdf)

Multivariate approximation

• Trigonometric Gaussian quadrature on subintervals of the period
  draft, with G. Da Fies
  

Published or to appear

2012

1. Subperiodic trigonometric interpolation and quadrature
   draft, with L. Bos
   Appl. Math. Comput., revision required
2. Algebraic cubature on circular lenses and bubbles
   draft, with G. Da Fies
   Dolomites Res. Notes Approx. DRNA, minor revision required
   
3. Small perturbations of polynomial meshes
   preprint, with F. Piazzon
   Appl. Anal., published online 18 January 2012
4. Computing Fekete and Lebesgue points: simplex, square, disk
   preprint, with M. Briani and A. Sommariva
   J. Comput. Appl. Math. 236 (2012), 2477--2486
   
5. Low cardinality admissible meshes on quadrangles, triangles and disks
   preprint, with L. Bos
   Math. Inequal. Appl. 15 (2012), 229--235
   
   

   2011

6. On the generation of symmetric Lebesgue-like points in the triangle
   preprint, with F. Rapetti and A. Sommariva
   J. Comput. Appl. Math., published online 28 November 2011
   
7. On Multivariate Newton Interpolation at Discrete Leja Points
   preprint, with L. Bos, S. De Marchi and A. Sommariva
   Dolomites Res. Notes Approx. DRNA 4 (2011), 15--20
   
8. Polynomial interpolation and cubature over polygons
   preprint, with M. Gentile and A. Sommariva
   J. Comput. Appl. Math. 235 (2011), 5232--5239
9. An algebraic cubature formula on curvilinear polygons
   preprint, with G. Santin and A. Sommariva
   Appl. Math. Comput. 217 (2011), 10003--10015
10. 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
11. 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
12. 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
    
    

    2010

13. Analytic transformations of admissible meshes
    preprint, with F. Piazzon
    East J. Approx. 16 (2010), 313--322
14. 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
    
15. 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
    
16. Approximate Fekete points for weighted polynomial interpolation
    preprint, with A. Sommariva
    Electron. Trans. Numer. Anal. 37 (2010), 1--22
    
17. On simple approximations to simple curves
    preprint, with L. Bos
    Dolomites Res. Notes on Approx. DRNA 3 (2010), 1--6
    
    

    2009

18. Gauss-Green cubature and moment computation over arbitrary geometries
    preprint, with A. Sommariva
    J. Comput. Appl. Math. 231 (2009), 886--896
    
19. Computing approximate Fekete points by QR factorizations of Vandermonde matrices
    preprint, with A. Sommariva
    Comput. Math. Appl. 57 (2009), 1324--1336
20. New cubature formulae and hyperinterpolation in three variables
    preprint, with S. De Marchi and Y. Xu
    BIT Numerical Mathematics 49 (2009), 55--73
    
    

    2008

21. 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)
    a variant has been used in Fun2D of the CP2K simulation package for molecular dynamics (see paper)
22. Nontensorial Clenshaw-Curtis cubature
    preprint, with A. Sommariva and R. Zanovello
    Numer. Algorithms 49 (2008), 409--427
23. Hyperinterpolation in the cube
    preprint, with M. Caliari and S. De Marchi
    Comput. Math. Appl. 55 (2008), 2490--2497
24. 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
25. Meshless cubature over the disk by Thin-Plate Splines
    preprint, with A. Punzi and A. Sommariva
    J. Comput. Appl. Math. 221 (2008), 430--436
    
    

    2007

26. Product Gauss cubature over polygons based on Green's integration formula
    preprint, with A. Sommariva
    BIT Numerical Mathematics 47 (2007), 441--453
27. 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
28. Hyperinterpolation on the square
    preprint, with M. Caliari and S. De Marchi
    J. Comput. Appl. Math. 210 (2007), 78--83
    
    

    2006

29. 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
30. 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
    classified in the TOP 25 Hottest Articles of JAT, Oct.-Dec. 2006
31. 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
32. On the Lebesgue constant for the Xu interpolation formula
    preprint, with L. Bos and S. De Marchi
    J. Approx. Theory 141 (2006), 134--141
    classified in the TOP 25 Hottest Articles of JAT, July-Sept. 2006
33. Meshless cubature by Green's formula
    preprint, with A. Sommariva
    Appl. Math. Comput. 183 (2006), 1098--1107
34. Numerical cubature on scattered data by radial basis functions
    preprint, with A. Sommariva
    Computing 76 (2006), 295--310
35. 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
    
    

    2005

36. 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
37. Adaptive bivariate Chebyshev approximation
    preprint, with A. Sommariva and R. Zanovello
    Numer. Algorithms 38 (2005), no. 1-3, 79--94

Exponential integrators

Published or to appear

2009

1. Efficient massively parallel implementation of the ReLPM exponential integrator for advection-diffusion models
   preprint, with L. Bergamaschi, M. Caliari and A. Martinez
   J. Comput. Appl. Math. 231 (2009), 82--91
   
   

   2007

2. The LEM exponential integrator for advection-diffusion-reaction equations
   preprint, with L. Bergamaschi and M. Caliari
   J. Comput. Appl. Math. 210 (2007), 56--63
   
   

   2006

3. Comparing Leja and Krylov approximations of large scale matrix exponentials
   preprint, with L. Bergamaschi, M. Caliari and A. Martinez
   Springer LNCS vol. 3994, 2006 (Proc. of ICCS 2006, Reading, UK), 685--692
   quoted in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 19 (2010), 209-286
   
   

   2005

4. A parallel exponential integrator for large-scale discretizations of advection-diffusion models
   preprint, with L. Bergamaschi, M. Caliari and A. Martinez
   Springer LNCS vol. 3666, 2005 (Proc. of Euro PVM MPI 2005, Sorrento, Italy), 483--492
   quoted in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 19 (2010), 209-286
   
   

   2004

5. The ReLPM exponential integrator for FE discretizations of advection-diffusion equations
   preprint, with L. Bergamaschi and M. Caliari
   Springer LNCS vol. 3039, part IV, 2004 (Proc. of ICCS 2004, Krakow, Poland), 434--442
   quoted in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 19 (2010), 209-286
6. Interpolating discrete advection-diffusion propagators at Leja sequences
   preprint, with L. Bergamaschi and M. Caliari
   J. Comput. Appl. Math. 172 (2004), no. 1, 79--99
   quoted in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 19 (2010), 209-286
   
   

   2003

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

   2000

8. Efficient computation of the exponential operator for large, sparse, symmetric matrices
   preprint, with L. Bergamaschi
   Numer. Linear Algebra Appl. 7 (2000), 27--45
   quoted in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 19 (2010), 209-286