#### Publication Date

1987

#### Document Type

Dissertation/Thesis

#### First Advisor

Datta, Karabi

#### Degree Name

M.S. (Master of Science)

#### Legacy 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.

#### Recommended Citation

Briones, Dante Medrano, "The QIF parallel method for linear systems, eigenvalue and singular value computations" (1987). *Graduate Research Theses & Dissertations*. 6124.

https://huskiecommons.lib.niu.edu/allgraduate-thesesdissertations/6124

#### 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

## Comments

Bibliography: pages [65]-69.