# Finite-difference preconditioners for superconsistent pseudospectral approximations

Lorella Fatone; Daniele Funaro; Valentina Scannavini

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 6, page 1021-1039
- ISSN: 0764-583X

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topFatone, Lorella, Funaro, Daniele, and Scannavini, Valentina. "Finite-difference preconditioners for superconsistent pseudospectral approximations." ESAIM: Mathematical Modelling and Numerical Analysis 41.6 (2007): 1021-1039. <http://eudml.org/doc/250039>.

@article{Fatone2007,

abstract = {
The superconsistent collocation method, which is based on a
collocation grid different from the one used to represent the
solution, has proven to be very accurate in the resolution of
various functional equations. Excellent results can be also
obtained for what concerns preconditioning. Some analysis and
numerous experiments, regarding the use of finite-differences
preconditioners, for matrices arising from pseudospectral
approximations of advection-diffusion boundary value problems, are
presented and discussed, both in the case of Legendre and
Chebyshev representation nodes.
},

author = {Fatone, Lorella, Funaro, Daniele, Scannavini, Valentina},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Spectral collocation method; preconditioning;
superconsistency; Lebesgue constant.; spectral collocation; superconsistency; Lebesgue constant; numerical results; finite differences; advection-diffusion boundary value problems},

language = {eng},

month = {12},

number = {6},

pages = {1021-1039},

publisher = {EDP Sciences},

title = {Finite-difference preconditioners for superconsistent pseudospectral approximations},

url = {http://eudml.org/doc/250039},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Fatone, Lorella

AU - Funaro, Daniele

AU - Scannavini, Valentina

TI - Finite-difference preconditioners for superconsistent pseudospectral approximations

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/12//

PB - EDP Sciences

VL - 41

IS - 6

SP - 1021

EP - 1039

AB -
The superconsistent collocation method, which is based on a
collocation grid different from the one used to represent the
solution, has proven to be very accurate in the resolution of
various functional equations. Excellent results can be also
obtained for what concerns preconditioning. Some analysis and
numerous experiments, regarding the use of finite-differences
preconditioners, for matrices arising from pseudospectral
approximations of advection-diffusion boundary value problems, are
presented and discussed, both in the case of Legendre and
Chebyshev representation nodes.

LA - eng

KW - Spectral collocation method; preconditioning;
superconsistency; Lebesgue constant.; spectral collocation; superconsistency; Lebesgue constant; numerical results; finite differences; advection-diffusion boundary value problems

UR - http://eudml.org/doc/250039

ER -

## References

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