Marco Vianello:
list of 20 selected publications in Numerical
Analysis
- 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
- G. Da Fies, M. Vianello, On the Lebesgue constant of
subperiodic trigonometric
interpolation,
J. Approx. Theory 167 (2013), 59--64.
- G. Da Fies,
A. Sommariva, M. Vianello, Algebraic cubature by linear blending of
elliptical arcs,
Appl. Numer. Math. 74 (2013), 49--61.
- G. Da Fies, M. Vianello, Trigonometric Gaussian quadrature on
subintervals of
the period, Electron. Trans. Numer. Anal. 39 (2012), 102--112.
- L. Bos, M. Vianello, Subperiodic trigonometric interpolation and
quadrature,
Appl. Math. Comput. 218 (2012), 10630--10638.
- 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.
- 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.
- 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
- 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)
- 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)
- 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)
- A. Sommariva, M. Vianello, Product Gauss cubature over polygons
based on Green's
integration formula,
BIT Numerical Mathematics 47 (2007), 441--453.
- 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
- 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)
- 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)
- 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.
- 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)
- 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
- 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
- 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