An approximate algorithm to solve linear systems by matrix with off-diagonal exponential decay entries

Qiangshun Chang; Yanping Lin; Shuzhan Xu

An approximate algorithm to solve linear systems by matrix with off-diagonal exponential decay entries

Qiangshun Chang, Yanping Lin, Shuzhan Xu

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

We present an approximate algorithm to solve only one variable out of a linear system defined by a matrix with off-diagonal exponential decay entries (including the practically most important class of band limited matrices) via a sub-linear system. This approach thus enables us to solve any subset of solution variables. Parallel implementation of such approximate schemes for every variable enables us to solve the linear system with computational time independent of the matrix size.

Original language	English
Pages (from-to)	340-352
Number of pages	13
Journal	International Journal of Numerical Analysis and Modeling
Volume	15
Issue number	3
Publication status	Published - 1 Jan 2018

Keywords

Decomposition
Linear equation
Numerical solution
Sub-linear system

ASJC Scopus subject areas

Numerical Analysis

Cite this

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abstract = "We present an approximate algorithm to solve only one variable out of a linear system defined by a matrix with off-diagonal exponential decay entries (including the practically most important class of band limited matrices) via a sub-linear system. This approach thus enables us to solve any subset of solution variables. Parallel implementation of such approximate schemes for every variable enables us to solve the linear system with computational time independent of the matrix size.",

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AU - Chang, Qiangshun

AU - Lin, Yanping

AU - Xu, Shuzhan

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N2 - We present an approximate algorithm to solve only one variable out of a linear system defined by a matrix with off-diagonal exponential decay entries (including the practically most important class of band limited matrices) via a sub-linear system. This approach thus enables us to solve any subset of solution variables. Parallel implementation of such approximate schemes for every variable enables us to solve the linear system with computational time independent of the matrix size.

AB - We present an approximate algorithm to solve only one variable out of a linear system defined by a matrix with off-diagonal exponential decay entries (including the practically most important class of band limited matrices) via a sub-linear system. This approach thus enables us to solve any subset of solution variables. Parallel implementation of such approximate schemes for every variable enables us to solve the linear system with computational time independent of the matrix size.

KW - Decomposition

KW - Linear equation

KW - Numerical solution

KW - Sub-linear system

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M3 - Journal article

SN - 1705-5105

VL - 15

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JO - International Journal of Numerical Analysis and Modeling

JF - International Journal of Numerical Analysis and Modeling

IS - 3

ER -

An approximate algorithm to solve linear systems by matrix with off-diagonal exponential decay entries

Abstract

Keywords

ASJC Scopus subject areas

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