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High-Performance Computation of the Exponential of a Large Sparse Matrix

Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large sparse matrix exponential as it requires more memory and has a higher computational cost than is actually needed. By introducing two novel concepts, i.e., real bandwidth and ε-bandwidth, to measure the sparsity of the matrix, the sparsity of the matrix exponential is analyzed. It is found that for every matrix computed in the squaring phase of the SSA, a corresponding sparse approximate matrix exists. To obtain the sparse approximate matrix, a new filtering technique based on forward error analysis is proposed. Combining the filtering technique with the idea of keeping track of the incremental part, a competitive algorithm is developed for the large sparse matrix exponential. Due to the filtering technique, the proposed method can greatly alleviate the overscaling problem. Three sets of numerical experiments, including one large matrix with a dimension larger than 2×106, are conducted. The numerical experiments show that, compared with the expm function in MATLAB, the proposed algorithm can provide higher accuracy at lower computational cost and with less memory.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.42 No.4 October-December 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1636-1655

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

SPARSE MATRIX
MATRIX EXPONENTIAL
TAYLOR SERIES
PRECISE INTEGRATION METHOD
SCALING AND SQUARING ALGORITHM
FILTERING TECHNIQUE
REAL BANDWIDTH
Ε-BANDWIDTH

Info Detail Spesifik

https://doi.org/10.1137/20M1342987

Pernyataan Tanggungjawab

Feng Wu, Kailing Zhang, Li Zhu, Jiayao Hu

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