Iterative Solution of Large Linear Systems by David M. Young

By David M. Young

Self-contained remedy incorporates a evaluation of matrix conception and common homes of iterative equipment; successive overrelaxation (SOR) process and desk bound transformed SOR technique for regularly ordered matrices; nonstationary tools; generalizations of SOR conception and variations of technique; 2nd-degree tools, alternating direction-implicit equipment, and a comparability of tools. 1971 edition.

Show description

Read or Download Iterative Solution of Large Linear Systems PDF

Similar linear books

A first course in linear algebra

A primary path in Linear Algebra is an creation to the elemental innovations of linear algebra, besides an advent to the innovations of formal arithmetic. It starts off with platforms of equations and matrix algebra earlier than stepping into the speculation of summary vector areas, eigenvalues, linear differences and matrix representations.

Measure theory/ 3, Measure algebras

Fremlin D. H. degree thought, vol. three (2002)(ISBN 0953812936)(672s)-o

Elliptic Partial Differential Equations

Elliptic partial differential equations is among the major and so much lively parts in arithmetic. In our booklet we examine linear and nonlinear elliptic difficulties in divergence shape, with the purpose of supplying classical effects, in addition to more moderen advancements approximately distributional ideas. for that reason the ebook is addressed to master's scholars, PhD scholars and an individual who desires to start learn during this mathematical box.

Extra resources for Iterative Solution of Large Linear Systems

Sample text

6 there exists a nonsingular matrix L such that || A \\L < 1. Since || An \\L < || A \\nL it follows that || An \\L -> 0. 1 it follows that An —>0. , converges to A. If convergence holds, then we write A = A{1) + A™ + A™ + . . 4. The matrix I — B is nonsingular and the series I + B + B2 + . . converges if and only if S(B) < 1. 6) 36 2 / MATRIX PRELIMINARIES Proof. Let S{n) = I + B + B2 + · · + Bn. 2 it follows that || Bn+1 || -> 0. 6) holds. If on the other hand the series I + B + B2 + · · · converges, then one can easily show that Bn —► 0.

Evidently P can be joined to Q by a path consisting of line segments connecting properly adjacent mesh points. Somewhere along this path there must be a seg­ ment joining a point P' of S to a point P" of T. 17). Hence aitj φ 0 where i e S and y e T. This contradiction shows that T is empty and that A is irreducible. Next we show that A has weak diagonal dominance. 11). Moreover, since R is bounded, there exists points of Rh which are properly adjacent to one or more points of Sh. 13). Thus some of the di do not appear in the matrix A.

3. If A is an irreducible matrix with weak diagonal dom­ inance, then det A φ 0 and none of the diagonal elements of A vanishes. Proof. If i V = l , then αλ1 > 0 by weak diagonal dominance and det A φ 0. Suppose that N > 1 and aiti = 0 for some /. By the weak diagonal dominance we have aifj = 0 for all j . But this contradicts the irreducibility. For if S = {i} and T = W — {i}> we have aitj = 0 for all i eS,jeT. 4, if det A = 0, then there exists a solution w 9ε 0 of the homogeneous system Au = 0.

Download PDF sample

Rated 4.51 of 5 – based on 14 votes