Back to Publications and preprints

Marco Vianello:
list of publications in Numerical Analysis


    2012

  1. Subperiodic trigonometric interpolation and quadrature, Appl. Math. Comput., published online 16 May 2012 (with L. Bos).

  2. Small perturbations of polynomial meshes, Appl. Anal., published online 18 January 2012 (with F. Piazzon).

  3. Trigonometric Gaussian quadrature on subintervals of the period, Electron. Trans. Numer. Anal. 39 (2012), 102--112 (with G. Da Fies).

  4. Algebraic cubature on planar lenses and bubbles, Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12 (with G. Da Fies).

  5. Computing Fekete and Lebesgue points: simplex, square, disk, J. Comput. Appl. Math. 236 (2012), 2477--2486 (with M. Briani and A. Sommariva).

  6. Low cardinality admissible meshes on quadrangles, triangles and disks, Math. Inequal. Appl. 15 (2012), 229--235 (with L. Bos).

    2011

  7. The "phase function" method to solve second-order asymptotically polynomial differential equations, Numer. Math., published online 27 December 2011 (with R. Spigler).

  8. On the generation of symmetric Lebesgue-like points in the triangle, J. Comput. Appl. Math., published online 28 November 2011 (with F. Rapetti and A. Sommariva).

  9. On Multivariate Newton Interpolation at Discrete Leja Points, Dolomites Res. Notes Approx. DRNA 4 (2011), 15--20 (with L. Bos, S. De Marchi and A. Sommariva).

  10. Polynomial interpolation and cubature over polygons, J. Comput. Appl. Math. 235 (2011), 5232--5239 (with M. Gentile and A. Sommariva).

  11. An algebraic cubature formula on curvilinear polygons, Appl. Math. Comput. 217 (2011), 10003--10015 (with G. Santin and A. Sommariva).

  12. Geometric Weakly Admissible Meshes, Discrete Least Squares Approximations and Approximate Fekete Points, Math. Comp. 80 (2011), 1601--1621 (with L. Bos, J.P. Calvi, N. Levenberg and A. Sommariva).

  13. Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave, Numer. Algorithms 56 (2011), 45--60 (with M. Caliari, S. De Marchi and A. Sommariva).

  14. Weakly Admissible Meshes and Discrete Extremal Sets, Numer. Math. Theory Methods Appl. 4 (2011), 1--12 (with L. Bos, S. De Marchi and A. Sommariva).

    2010

  15. Analytic transformations of admissible meshes, East J. Approx., 16 (2010), 313--322 (with F. Piazzon).

  16. Computing multivariate Fekete and Leja points by numerical linear algebra, SIAM J. Numer. Anal. 48 (2010), 1984--1999 (with L. Bos, S. De Marchi and A. Sommariva).

  17. Least-squares polynomial approximation on weakly admissible meshes: disk and triangle, J. Comput. Appl. Math. 235 (2010), 660--668 (with L. Bos and A. Sommariva).

  18. On simple approximations to simple curves, Dolomites Res. Notes Approx. DRNA 3 (2010), 1--6 (with L. Bos).

  19. Approximate Fekete points for weighted polynomial interpolation, Electron. Trans. Numer. Anal. 37 (2010), 1--22 (with A. Sommariva).

    2009

  20. Gauss-Green cubature and moment computation over arbitrary geometries, J. Comput. Appl. Math. 231 (2009), 886--896 (with A. Sommariva).

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

  22. Computing approximate Fekete points by QR factorizations of Vandermonde matrices, Comput. Math. Appl. 57 (2009), 1324--1336 (with A. Sommariva).

  23. New cubature formulae and hyperinterpolation in three variables, BIT Numerical Mathematics 49 (2009), 55--73 (with S. De Marchi and Y. Xu).

    2008

  24. Algorithm 886: Padua2D: Lagrange Interpolation at Padua Points on Bivariate Domains, ACM Trans. Math. Software 35-3 (2008) (with M. Caliari and S. De Marchi).
    a variant has been used in the Fun2D tool of the CP2K simulation package for molecular dynamics
    (see M. Guidon, J. Hutter and J. VandeVondele, "Robust Periodic Hartree-Fock Exchange for Large-Scale Simulations Using Gaussian Basis Sets", J. Chem. Theory Comput. 5 (2009), 3010--3021)

  25. Nontensorial Clenshaw-Curtis cubature, Numer. Algorithms 49 (2008), 409--427 (with A. Sommariva and R. Zanovello).

  26. Hyperinterpolation in the cube, Comput. Math. Appl. 55 (2008), 2490--2497 (with M. Caliari and S. De Marchi).

  27. Bivariate Lagrange interpolation at the Padua points: computational aspects, J. Comput. Appl. Math. 221 (2008), 284--292 (with M. Caliari and S. De Marchi).

  28. Meshless cubature over the disk by Thin-Plate Splines, J. Comput. Appl. Math. 221 (2008) 430--436 (with A. Punzi, A. Sommariva).

    2007

  29. Bivariate Lagrange interpolation at the Padua points: the ideal theory approach, Numer. Math. 108 (2007), 43--57 (with L. Bos, S. De Marchi and Y. Xu).

  30. Product Gauss cubature over polygons based on Green's integration formula, BIT Numerical Mathematics 47 (2007), 441--453 (with A. Sommariva).

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

  32. Hyperinterpolation on the square, J. Comput. Appl. Math. 210 (2007), 78--83 (with M. Caliari, S. De Marchi).

    2006

  33. Meshless cubature by Green's formula, Appl. Math. Comput. 183 (2006), 1098--1107 (with A. Sommariva).

  34. Hyper2d: a numerical code for hyperinterpolation on rectangles, Appl. Math. Comput. 183 (2006), 1138--1147 (with M. Caliari, S. De Marchi, R. Montagna).

  35. Bivariate Lagrange interpolation at the Padua points: the generating curve approach, J. Approx. Theory 143 (2006), 15--25 (with L. Bos, M. Caliari, S. De Marchi, Y. Xu).
    Classified in the TOP 25 Hottest Articles of JAT, Oct.-Dec. 2006.

  36. Bivariate interpolation at Xu points: results, extensions and applications, Electron. Trans. Numer. Anal. 25 (2006), 1--16 (with L. Bos, M. Caliari, S. De Marchi).

  37. On the Lebesgue constant for the Xu interpolation formula, J. Approx. Theory 141 (2006), 134--141 (with L. Bos, S. De Marchi).
    Classified in the TOP 25 Hottest Articles of JAT, July-Sept. 2006.

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

  39. A numerical study of the Xu polynomial interpolation formula in two variables, Computing 76 (2006), 311--324 (with L. Bos, M. Caliari, S. De Marchi).

  40. Numerical cubature on scattered data by radial basis functions, Computing 76 (2006), 295--310 (with A. Sommariva).

    2005

  41. Bivariate polynomial interpolation on the square at new nodal sets, Appl. Math. Comput. 165 (2005), 261--274 (with M. Caliari, S. De Marchi).

  42. Adaptive bivariate Chebyshev approximation, Numer. Algorithms 38 (2005), 79--94 (with A. Sommariva, R. Zanovello).

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

    2004

  44. The ReLPM exponential integrator for FE discretizations of advection-diffusion equations, Springer LNCS vol. 3039, part IV, 2004 (Proc. of ICCS 2004, Krakow, Poland), 434--442 (with L. Bergamaschi, M. Caliari).
    quoted in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 19 (2010), 209-286

  45. Adaptive bivariate Chebyshev approximation and efficient evaluation of integral operators, Appl. Numer. Anal. Comput. Math. 1 (2004), 115--121 (with A. Mardegan, A. Sommariva, R. Zanovello).

  46. Interpolating discrete advection-diffusion propagators at Leja sequences, J. Comput. Appl. Math. 172 (2004), 79--99 (with L. Bergamaschi, M. Caliari).
    quoted in M. Hochbruck, A. Ostermann, Exponential Integrators, Acta Numerica 19 (2010), 209-286

    2003

  47. Fast evaluation of discrete integral transforms by Chebyshev and Leja polynomial approximation, Constructive theory of functions, 347--353, DARBA, Sofia, 2003 (with S. De Marchi).

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

    2001

  49. Approximating the approximant: a numerical code for polynomial compression of discrete integral operators, In memory of W. Gross. Numer. Algorithms 28 (2001), 101--116 (with S. De Marchi).

  50. Positive multiplication preserves dissipativity in commutative C*-algebras, J. Inequal. Appl. 6 (2001), 247--251 (with A. Sommariva).

  51. Fast summation of power series with coefficients analytic at infinity, Numer. Algorithms 27 (2001), 77--87 (with A. Sommariva, R. Zanovello).

    2000

  52. Chebyshev-like compression of linear and nonlinear discretized integral operators, Neural Parallel Sci. Comput. 8 (2000), 327--353.

  53. Computing positive fixed-points of decreasing Hammerstein operators by relaxed iterations, J. Integral Equations Appl. 12 (2000), 95--112 (with A. Sommariva).

  54. Relaxed Picard-like methods for nonlinear integral equations arising in transport theory, Applied and industrial mathematics, Venice--2, 1998, 273--285, Kluwer Acad. Publ., Dordrecht, 2000 (with E. Facchinello, A. Sommariva).

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

  56. A new summation method for power series with rational coefficients, Math. Comp. 69 (2000), 749--756 (with S. Dassie`, R. Zanovello).

    1999

  57. Liouville-Green-Olver approximations for complex difference equations, J. Approx. Theory 96 (1999), 301--322 (with F. Locatelli, R. Spigler).

    1998

  58. Asymptotic summation of power series, Numer. Math. 80 (1998), 61--73 (with S. Dassie`, R. Zanovello).

  59. Approximating fixed-points of decreasing operators in spaces of continuous functions, Numer. Funct. Anal. Optim. 19 (1998), 635--646 (with A. Sommariva).

    1997

  60. Peano's kernel theorem for vector-valued functions: a weak version in normed spaces, Numer. Funct. Anal. Optim. 18 (1997), 65--74 (with S. De Marchi).

    1996

  61. Peano's kernel theorem for vector-valued functions and some applications, Numer. Funct. Anal. Optim. 17 (1996), 57--64 (with S. De Marchi).

    1995

  62. Convergence analysis of the semi-implicit Euler method for abstract evolution equations, Numer. Funct. Anal. Optim. 16 (1995), 785--803 (with R. Spigler).

  63. On some connections between well-posedness and general properties of numerical methods, Z. Angew. Math. Mech. 75 (1995), 237--241 (with R. Zanovello).

  64. On regularity at t=0 for semilinear ADEs and its numerical applications, Semigroup Forum 50 (1995), 97--104.

    1994

  65. Splitting functions and numerical analysis of WR-type methods for evolutionary and stationary problems, Mathematics of Computation 1943--1993: a half-century of computational mathematics (Vancouver, BC, 1993), 281--285, Proc. Sympos. Appl. Math., 48, Amer. Math. Soc., Providence, RI, 1994 (with S. De Marchi, R. Zanovello).

  66. Semi-implicit discretization of abstract evolution equations, Equadiff 8 (Bratislava, 1993), Tatra Mt. Math. Publ. 4 (1994), 207--212 (with R. Spigler).

    1992

  67. On the superlinear convergence of the secant method, Amer. Math. Monthly 99 (1992), 758--761 (with R. Zanovello).

  68. Liouville-Green approximations for a class of linear oscillatory difference equations of the second order, Asymptotic methods in analysis and combinatorics, J. Comput. Appl. Math. 41 (1992), 105--116 (with R. Spigler).

  69. Improved estimates for the derivatives of the O-symbols in view of numerical applications, J. Math. Anal. Appl. 164 (1992), 480--488 (with R. Spigler).

    1990

  70. A numerical method for evaluating zeros of solutions of second-order linear differential equations, Math. Comp. 55 (1990), 591--612 (with R. Spigler).