On a Sparse Representation of an n-Dimensional Laplacian in Wavelet Coordinates

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F16%3A00003742" target="_blank" >RIV/46747885:24510/16:00003742 - isvavai.cz</a>

Result on the web

<a href="http://link.springer.com/article/10.1007/s00025-015-0488-5" target="_blank" >http://link.springer.com/article/10.1007/s00025-015-0488-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00025-015-0488-5" target="_blank" >10.1007/s00025-015-0488-5</a>

Result language

angličtina

Original language name

On a Sparse Representation of an n-Dimensional Laplacian in Wavelet Coordinates

Original language description

Important parts of adaptive wavelet methods are well-conditioned wavelet stiffness matrices and an efficient approximate multiplication of quasi-sparse stiffness matrices with vectors in wavelet coordinates. Therefore it is useful to develop a well-conditioned wavelet basis with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzero elements in each column is bounded by a constant. Consequently, the stiffness matrix corresponding to the n-dimensional Laplacian in the tensor product wavelet basis is also sparse. Then a matrix-vector multiplication can be performed exactly with linear complexity. In this paper, we construct a wavelet basis based on Hermite cubic splines with respect to which both the mass matrix and the stiffness matrix corresponding to a one-dimensional Poisson equation are sparse. Moreover, a proposed basis is well-conditioned on low decomposition levels. Small condition numbers for low decomposition levels and a sparse structure of stiffness matrices are kept for any well-conditioned second order partial differential equations with constant coefficients; furthermore, they are independent of the space dimension.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Results in Mathematics

ISSN

1422-6383

e-ISSN

—

Volume of the periodical

69

Issue of the periodical within the volume

1-2

Country of publishing house

CH - SWITZERLAND

Number of pages

19

Pages from-to

225-243

UT code for WoS article

000376102900012

EID of the result in the Scopus database

2-s2.0-84955634906