M.S. (Master of Science)
Department of Mathematical Sciences
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.
Briones, Dante Medrano, "The QIF parallel method for linear systems, eigenvalue and singular value computations" (1987). Graduate Research Theses & Dissertations. 6124.
vi, 97 pages
Northern Illinois University
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