A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations

Beibei Li; Jingjing Cui; Zhengge Huang; Xiaofeng Xie

Applications of Mathematics (2024)

  • Volume: 69, Issue: 3, page 311-337
  • ISSN: 0862-7940

Abstract

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We multiply both sides of the complex symmetric linear system A x = b by 1 - i ω to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed method.

How to cite

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Li, Beibei, et al. "A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations." Applications of Mathematics 69.3 (2024): 311-337. <http://eudml.org/doc/299394>.

@article{Li2024,
abstract = {We multiply both sides of the complex symmetric linear system $Ax=b$ by $1-\{\rm i\}\omega $ to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed method.},
author = {Li, Beibei, Cui, Jingjing, Huang, Zhengge, Xie, Xiaofeng},
journal = {Applications of Mathematics},
keywords = {DDSS iteration method; linear equations; SPD matrix; SPSD matrix; convergence property},
language = {eng},
number = {3},
pages = {311-337},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations},
url = {http://eudml.org/doc/299394},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Li, Beibei
AU - Cui, Jingjing
AU - Huang, Zhengge
AU - Xie, Xiaofeng
TI - A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 3
SP - 311
EP - 337
AB - We multiply both sides of the complex symmetric linear system $Ax=b$ by $1-{\rm i}\omega $ to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed method.
LA - eng
KW - DDSS iteration method; linear equations; SPD matrix; SPSD matrix; convergence property
UR - http://eudml.org/doc/299394
ER -

References

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