A Conditionality Criterion for Systems of Linear Algebraic Equations

被引：3

作者：

Kalitkin, N. N. ^{[1
]}

Yukhno, L. F. ^{[1
]}

Kuz'mina, L. V. ^{[1
]}

机构：

[1] Russian Acad Sci, MV Keldysh Appl Math Inst, Moscow 125047, Russia

来源：

DOKLADY MATHEMATICS | 2010年 / 82卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Diagonal Matrix; Iteration Method; DOKLADY Mathematic; Linear Algebraic Equation; Decimal Digit;

D O I：

10.1134/S1064562410050376

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A conditionality criterion for systems of linear algebraic equations is proposed. Direct Gauss method and an iteration method of the type of conjugate gradients is applied to solve the matrices. The system of equations is considered that depends n nonsingular square matrix of order N. Ortega has proposed a conditionality criterion known as volume criterion based on geometric considerations to perform computations with floating point for systems. A criterion based on other geometric considerations is also proposed and a practical criterion for termination of the iteration process is used. In solving the three-diagonal system arising in the difference approximation of boundary value problems for second-order differential equations by the matching method, the round-off errors do not accumulate.

引用

页码：820 / 823

页数：4