Storage algorithm for wavelet Galerkin method

Author

Feng, X.C. ; Zhang, X.S. ; Tang, X.M. ; Tang, Yuan Y.

Author_Institution

Xidian Univ., Xi´´an, China

Volume

4

fYear

2003

fDate

2-5 Nov. 2003

Firstpage

2365

Abstract

The representation of an integral operator in wavelet bases is a large numerical sparse matrix. Thus, a suitable approach is needed that converts the matrix from full storage mode into sparse storage mode, which not only saves the storage, but also saves the execution time. In this paper, the storage of this kind of matrix is discussed in the symmetric case. First, we present a standard storage approach. Then, a modified one is proposed, which is based on a special decomposition of the symmetric matrix. When iterative solvers are used to solve the corresponding linear system, the main cost is the multiplication of the symmetric sparse matrix and a given vector. The modified sparse storage mode is optimized for this purpose and reduces nearly half of the number of multiplications.

Keywords

Galerkin method; integral equations; iterative methods; optimisation; sparse matrices; wavelet transforms; integral operator; iterative solvers; linear system; numerical sparse matrix; sparse storage; storage algorithm; symmetric matrix decomposition; wavelet Galerkin method; Computer science; Costs; Linear systems; Mathematics; Matrix converters; Matrix decomposition; Moment methods; Sparse matrices; Symmetric matrices; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Machine Learning and Cybernetics, 2003 International Conference on

Print_ISBN

0-7803-8131-9

Type

conf

DOI

10.1109/ICMLC.2003.1259905

Filename

1259905