Representation of differential operators in wavelet basis

M. A. Hajji; S. Melkonian; R. Vaillancourt

doi:10.1016/s0898-1221(04)90083-1

Representation of differential operators in wavelet basis

M. A. Hajji
, S. Melkonian
, R. Vaillancourt

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

Existing work on the representation of operators in one-dimensional, compactly-supported, orthonormal wavelet bases is extended to two dimensions. The nonstandard form of the representation of operators is given in separable two-dimensional, periodic, orthonormal wavelet bases. The matrix representation of the partial-differential operators ∂_x and ∂_y are constructed and a closed form formula for the matrix representation of a general partial-differential operator g(∂_x, ∂_y) is derived, where g is an analytic function.

Original language	English
Pages (from-to)	1011-1033
Number of pages	23
Journal	Computers and Mathematics with Applications
Volume	47
Issue number	6-7
DOIs	https://doi.org/10.1016/s0898-1221(04)90083-1
Publication status	Published - 2004
Externally published	Yes

Keywords

Block circulant
Circulant
Partial-differential operator
Wavelet

ASJC Scopus subject areas

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/s0898-1221(04)90083-1

Cite this

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title = "Representation of differential operators in wavelet basis",

abstract = "Existing work on the representation of operators in one-dimensional, compactly-supported, orthonormal wavelet bases is extended to two dimensions. The nonstandard form of the representation of operators is given in separable two-dimensional, periodic, orthonormal wavelet bases. The matrix representation of the partial-differential operators ∂x and ∂y are constructed and a closed form formula for the matrix representation of a general partial-differential operator g(∂x, ∂y) is derived, where g is an analytic function.",

keywords = "Block circulant, Circulant, Partial-differential operator, Wavelet",

author = "Hajji, \{M. A.\} and S. Melkonian and R. Vaillancourt",

note = "Funding Information: This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.",

year = "2004",

doi = "10.1016/s0898-1221(04)90083-1",

language = "English",

volume = "47",

pages = "1011--1033",

journal = "Computers and Mathematics with Applications",

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TY - JOUR

T1 - Representation of differential operators in wavelet basis

AU - Hajji, M. A.

AU - Melkonian, S.

AU - Vaillancourt, R.

N1 - Funding Information: This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.

PY - 2004

Y1 - 2004

N2 - Existing work on the representation of operators in one-dimensional, compactly-supported, orthonormal wavelet bases is extended to two dimensions. The nonstandard form of the representation of operators is given in separable two-dimensional, periodic, orthonormal wavelet bases. The matrix representation of the partial-differential operators ∂x and ∂y are constructed and a closed form formula for the matrix representation of a general partial-differential operator g(∂x, ∂y) is derived, where g is an analytic function.

AB - Existing work on the representation of operators in one-dimensional, compactly-supported, orthonormal wavelet bases is extended to two dimensions. The nonstandard form of the representation of operators is given in separable two-dimensional, periodic, orthonormal wavelet bases. The matrix representation of the partial-differential operators ∂x and ∂y are constructed and a closed form formula for the matrix representation of a general partial-differential operator g(∂x, ∂y) is derived, where g is an analytic function.

KW - Block circulant

KW - Circulant

KW - Partial-differential operator

KW - Wavelet

UR - https://www.scopus.com/pages/publications/2542470477

UR - https://www.scopus.com/pages/publications/2542470477#tab=citedBy

U2 - 10.1016/s0898-1221(04)90083-1

DO - 10.1016/s0898-1221(04)90083-1

M3 - Article

AN - SCOPUS:2542470477

SN - 0898-1221

VL - 47

SP - 1011

EP - 1033

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 6-7

ER -

Representation of differential operators in wavelet basis

Abstract

Keywords

ASJC Scopus subject areas

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