Publication Date

1987

Document Type

Dissertation/Thesis

First Advisor

Datta, Karabi

Degree Name

M.S. (Master of Science)

Department

Department of Mathematical Sciences

LCSH

Factorization (Mathematics)

Abstract

A new factorization, the Quadrant Interlocking Factorization (QIF), is used to solve the linear system Ax = b in O(n²) steps using O(n²) processors. The matrix A is factored into a product of its quadrant interlocking factors W and Z, i.e., A = WZ, instead of the usual LU factorization. Variations of the WZ factorization are derived, namely, WDZ, WDW^(t) and WWt which are analogous to the variations of the LU factorization, namely, LDU, LDL^(t) and LL^(t), respectively. The inertia of a nonsingular symmetric matrix A is found using the WDW^(t) factorization. The QZ factorization of a symmetric positive definite matrix A is presented. This factorization is analogous to the QR factorization of A. The QZ factorization is used implicitly to compute the eigenvalues of a symmetric positive definite matrix in 0(nlog₂n) steps per iteration using 0(n²) processors. A new algorithm is used to solve for the singular values of a square matrix using the WZ and WW^(t) factorizations in 0(nlog₂n) steps per iteration using O(n²) processors. The algorithms discussed in this thesis are well suited for Single Instruction Multiple Data (SIMD) machines.

Comments

Bibliography: pages [65]-69.

Extent

vi, 97 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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