Marco Vianello:
list of 20 selected publications in Numerical Analysis



  1. L. Bos, S. De Marchi, M. Vianello, Trivariate polynomial approximation on Lissajous curves, IMA J. Numer. Anal. 37 (2017), 519--541.
    Cited in the state of the art survey: L.N. Trefethen, Cubature, approximation, and isotropy in the hypercube, SIAM Rev., to appear

  2. G. Da Fies, M. Vianello, On the Lebesgue constant of subperiodic trigonometric interpolation, J. Approx. Theory 167 (2013), 59--64.

  3. G. Da Fies, A. Sommariva, M. Vianello, Algebraic cubature by linear blending of elliptical arcs, Appl. Numer. Math. 74 (2013), 49--61.

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

  5. L. Bos, M. Vianello, Subperiodic trigonometric interpolation and quadrature, Appl. Math. Comput. 218 (2012), 10630--10638.

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

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

  8. A. Sommariva, M. Vianello, Gauss-Green cubature and moment computation over arbitrary geometries, J. Comput. Appl. Math. 231 (2009), 886--896.
    Cited in the state of the art survey: Q. Zhang, On donating regions: Lagrangian flux through a fixed curve, SIAM Review 55, 2013

  9. A. Sommariva, M. Vianello, Computing approximate Fekete points by QR factorizations of Vandermonde matrices, Comput. Math. Appl. 57 (2009), 1324--1336.
    Cited in the state of the art survey: T. Bloom, L. Bos, J.-P. Calvi and N. Levenberg, Polynomial Interpolation and Approximation in C^d, Ann. Polon. Math. 106 (2012)

  10. M. Caliari, S. De Marchi, M. Vianello, Algorithm 886: Padua2D: Lagrange Interpolation at Padua Points on Bivariate Domains, ACM Trans. Math. Software 35-3 (2008).
    Cited in the state of the art survey: T. Bloom, L. Bos, J.-P. Calvi and N. Levenberg, Polynomial Interpolation and Approximation in C^d, Ann. Polon. Math. 106 (2012)

  11. L. Bos, S. De Marchi, M. Vianello, Y. Xu, Bivariate Lagrange interpolation at the Padua points: the ideal theory approach, Numer. Math. 108 (2007), 43--57.
    Cited in the state of the art survey: T. Bloom, L. Bos, J.-P. Calvi and N. Levenberg, Polynomial Interpolation and Approximation in C^d, Ann. Polon. Math. 106 (2012)

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

  13. L. Bos, M. Caliari, S. De Marchi, M. Vianello, Y. Xu, Bivariate Lagrange interpolation at the Padua points: the generating curve approach, J. Approx. Theory 143 (2006), 15--25.
    Cited in the state of the art surveys:
    N. Levenberg, Approximation in C^n, Surveys in Approximation Theory 2 (2006)
    T. Bloom, L. Bos, J.-P. Calvi and N. Levenberg, Polynomial Interpolation and Approximation in C^d, Ann. Polon. Math. 106 (2012)
    L.N. Trefethen, Cubature, approximation, and isotropy in the hypercube, SIAM Rev., to appear

  14. M. Caliari, S. De Marchi, M. Vianello, Bivariate polynomial interpolation on the square at new nodal sets, Appl. Math. Comput. 165/2 (2005), 261--274.
    Cited in the state of the art survey: T. Bloom, L. Bos, J.-P. Calvi and N. Levenberg, Polynomial Interpolation and Approximation in C^d, Ann. Polon. Math. 106 (2012)

  15. M. Caliari, M. Vianello, L. Bergamaschi, Interpolating discrete advection-diffusion propagators at Leja sequences, J. Comput. Appl. Math. 172 (2004), 79--99.
    M. Hochbruck and A. Ostermann, Exponential Integrators, Acta Numerica 19 (2010)

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

  17. L. Bergamaschi, M. Vianello, Efficient computation of the exponential operator for large, sparse, symmetric matrices, Numer. Linear Algebra Appl. 7 (2000), 27--45.
    Cited in the state of the art survey: M. Hochbruck and A. Ostermann, Exponential Integrators, Acta Numerica 19 (2010)

  18. R. Spigler, M. Vianello, F. Locatelli, Liouville-Green-Olver approximations for complex difference equations, J. Approx. Theory 96 (1999), 301--322.
    Cited in the books:
    NIST Handbook and Digital Library of Math. Functions, Ch. 2: Asymptotic Approximations (F.W.J. Olver and R. Wong), 2.9: Difference Equations
    S. Bodine and D.A. Lutz, Asymptotic Integration of Differential and Difference Equations, Springer Lecture Notes in Mathematics 2129, 2015

  19. S. Dassie`, M. Vianello, R. Zanovello, Asymptotic summation of power series, Numer. Math. 80 (1998), 61--73.
    Cited in the book: G. Mastroianni and G. Milovanovic, Interpolation processes: Basic theory and applications, Springer Monographs in Mathematics, 2008

  20. R. Spigler, M. Vianello, Liouville-Green approximations for a class of linear oscillatory difference equations of the second order, J. Comput. Appl. Math. 41 (1992), 105--116.
    Cited in the books:
    NIST Handbook and Digital Library of Math. Functions, Ch. 2: Asymptotic Approximations (F.W.J. Olver and R. Wong), 2.9: Difference Equations
    S. Bodine and D.A. Lutz, Asymptotic Integration of Differential and Difference Equations, Springer Lecture Notes in Mathematics 2129, 2015