A Review of Preconditioners for the Interval Gauss-Seidel Method

A Review of Preconditioners for the Interval Gauss-Seidel Method (1991)

Cached

Download Links

[interval.louisiana.edu]

by R. Baker Kearfott , Chenyi Hu , Manuel Novoa III

Citations:

45 - 15 self

Versions

Version History

Metadata Version 2

User correction supplied by SystemCorrections

Datum	Value	Source
TITLE	A Review of Preconditioners for the Interval Gauss-Seidel Method	user correction - Legacy Corrections
AUTHOR NAME	R. Baker Kearfott	user correction - Legacy Corrections
AUTHOR AFFIL	and	user correction - Legacy Corrections
AUTHOR NAME	Chenyi Hu	user correction - Legacy Corrections
AUTHOR AFFIL	and	user correction - Legacy Corrections
AUTHOR NAME	Manuel Novoa III	user correction - Legacy Corrections
AUTHOR AFFIL	Department of Mathematics; University of Southwestern Louisiana	user correction - Legacy Corrections
ABSTRACT	. Interval Newton methods in conjunction with generalized bisection can form the basis of algorithms that find all real roots within a specified box X ae R n of a system of nonlinear equations F (X) = 0 with mathematical certainty, even in finite-precision arithmetic. In such methods, the system F (X) = 0 is transformed into a linear interval system 0 = F (M) +F 0 (X)( ~ X \Gamma M); if interval arithmetic is then used to bound the solutions of this system, the resulting box ~ X contains all roots of the nonlinear system. We may use the interval Gauss--Seidel method to find these solution bounds. In order to increase the overall efficiency of the interval Newton / generalized bisection algorithm, the linear interval system is multiplied by a preconditioner matrix Y before the interval Gauss--Seidel method is applied. Here, we review results we have obtained over the past few years concerning computation of such preconditioners. We emphasize importance and connecting relationships,...	user correction - Legacy Corrections
YEAR	1991	user correction - Legacy Corrections
CITATIONS	24 found	ParsCit 1.0