On the convergence of subproper (multi)-splitting methods for solving rectangular linear systems

Lijing Lin; Yimin Wei

doi:10.1007/s10092-008-0141-8

On the convergence of subproper (multi)-splitting methods for solving rectangular linear systems

Lijing Lin^*, Yimin Wei

^*Corresponding author for this work

Department of Mathematics

Key Laboratory of Nonlinear Science (Fudan University)

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

Abstract

We give a convergence criterion for stationary iterative schemes based on subproper splittings for solving rectangular systems and show that, for special splittings, convergence and quotient convergence are equivalent. We also analyze the convergence of multisplitting algorithms for the solution of rectangular systems when the coefficient matrices have special properties and the linear systems are consistent.

Original language	English
Pages (from-to)	17-33
Number of pages	17
Journal	Calcolo
Volume	45
Issue number	1
DOIs	https://doi.org/10.1007/s10092-008-0141-8
Publication status	Published - Mar 2008

Keywords

Hermitian positive semi-definite matrix
iterative method
multisplitting
proper splitting
quotient convergence
rectangular linear system
regularity
subproper splitting

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10.1007/s10092-008-0141-8

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abstract = "We give a convergence criterion for stationary iterative schemes based on subproper splittings for solving rectangular systems and show that, for special splittings, convergence and quotient convergence are equivalent. We also analyze the convergence of multisplitting algorithms for the solution of rectangular systems when the coefficient matrices have special properties and the linear systems are consistent.",

keywords = "Hermitian positive semi-definite matrix, iterative method, multisplitting, proper splitting, quotient convergence, rectangular linear system, regularity, subproper splitting",

author = "Lijing Lin and Yimin Wei",

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AU - Wei, Yimin

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AB - We give a convergence criterion for stationary iterative schemes based on subproper splittings for solving rectangular systems and show that, for special splittings, convergence and quotient convergence are equivalent. We also analyze the convergence of multisplitting algorithms for the solution of rectangular systems when the coefficient matrices have special properties and the linear systems are consistent.

KW - Hermitian positive semi-definite matrix

KW - iterative method

KW - multisplitting

KW - proper splitting

KW - quotient convergence

KW - rectangular linear system

KW - regularity

KW - subproper splitting

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SP - 17

EP - 33

JO - Calcolo

JF - Calcolo

IS - 1

ER -

On the convergence of subproper (multi)-splitting methods for solving rectangular linear systems

Abstract

Keywords

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