Marco Vianello: publications and preprints

• complete list of mathematical publications
  
  
• list of publications in Numerical Analysis and Approximation Theory
  
  
• list of publications in Mathematical Analysis

online publications and preprints (downloadable pdf); see also the software section

Multivariate approximation

Submitted or in progress

• Implementing hyperinterpolation over nonstandard regions
  in preparation, with A. Sommariva and M. Van Barel
  
  
• Approximating equilibrium measures and Siciak extremal functions by polynomial meshes
  in preparation, with F. Piazzon
  
  
• Quadrature, hyperinterpolation and interpolation on subregions of the sphere
  in preparation, with M. Gentile and A. Sommariva
  
  
• Polynomial meshes on planar compacts with mildly regular boundary
  in preparation, with F. Piazzon
  
  
• Computing optimal polynomial meshes on planar starlike domains
  draft, with F. Piazzon
  
  
• Product Gaussian quadrature on circular lunes
  draft, with G. Da Fies
  
  

Published or to appear

2013

1. Algebraic cubature by linear blending of elliptical arcs
   preprint, with G. Da Fies and A. Sommariva
   Appl. Numer. Math., minor revision required
   
2. Polynomial approximation on pyramids, cones and solids of rotation
   preprint, with S. De Marchi
   Dolomites Res. Notes Approx. DRNA, to appear
   
3. Norming meshes by Bernstein-like inequalities
   preprint
   Math. Inequal. Appl., to appear
   
4. Small perturbations of polynomial meshes
   preprint, with F. Piazzon
   Appl. Anal. 92 (2013), 1063--1073
   
5. On the Lebesgue constant of subperiodic trigonometric interpolation
   preprint, with G. Da Fies
   J. Approx. Theory 167 (2013), 59--64
   
   

   2012

6. 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
   
7. Subperiodic trigonometric interpolation and quadrature
   preprint, with L. Bos
   Appl. Math. Comput. 218 (2012), 10630--10638
8. Trigonometric Gaussian quadrature on subintervals of the period
   preprint, with G. Da Fies
   Electron. Trans. Numer. Anal. 39 (2012), 102--112
9. Algebraic cubature on planar lenses and bubbles
   preprint, with G. Da Fies
   Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12
   
10. Computing Fekete and Lebesgue points: simplex, square, disk
    preprint, with M. Briani and A. Sommariva
    J. Comput. Appl. Math. 236 (2012), 2477--2486
    
11. Low cardinality admissible meshes on quadrangles, triangles and disks
    preprint, with L. Bos
    Math. Inequal. Appl. 15 (2012), 229--235
    
    

    2011

12. 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
    
13. Polynomial interpolation and cubature over polygons
    preprint, with M. Gentile and A. Sommariva
    J. Comput. Appl. Math. 235 (2011), 5232--5239
14. An algebraic cubature formula on curvilinear polygons
    preprint, with G. Santin and A. Sommariva
    Appl. Math. Comput. 217 (2011), 10003--10015
15. 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
    
16. 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
17. 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

18. Analytic transformations of admissible meshes
    preprint, with F. Piazzon
    East J. Approx. 16 (2010), 313--322
19. 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
    
20. 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
    
21. Approximate Fekete points for weighted polynomial interpolation
    preprint, with A. Sommariva
    Electron. Trans. Numer. Anal. 37 (2010), 1--22
    
22. On simple approximations to simple curves
    preprint, with L. Bos
    Dolomites Res. Notes on Approx. DRNA 3 (2010), 1--6
    
    

    2009

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

    2008

26. 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)
27. Nontensorial Clenshaw-Curtis cubature
    preprint, with A. Sommariva and R. Zanovello
    Numer. Algorithms 49 (2008), 409--427
28. Hyperinterpolation in the cube
    preprint, with M. Caliari and S. De Marchi
    Comput. Math. Appl. 55 (2008), 2490--2497
29. 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
30. 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

31. Product Gauss cubature over polygons based on Green's integration formula
    preprint, with A. Sommariva
    BIT Numerical Mathematics 47 (2007), 441--453
32. 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
    
33. Hyperinterpolation on the square
    preprint, with M. Caliari and S. De Marchi
    J. Comput. Appl. Math. 210 (2007), 78--83
    
    

    2006

34. 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
35. 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
36. 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
37. On the Lebesgue constant for the Xu interpolation formula
    preprint, with L. Bos and S. De Marchi
    J. Approx. Theory 141 (2006), 134--141
38. Meshless cubature by Green's formula
    preprint, with A. Sommariva
    Appl. Math. Comput. 183 (2006), 1098--1107
39. Numerical cubature on scattered data by radial basis functions
    preprint, with A. Sommariva
    Computing 76 (2006), 295--310
40. 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

41. 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
42. 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. A massively parallel 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
   
   

   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
   
   

   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
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
   
   

   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