Fast textured algorithms and their parallel implementations /
| Main Author: | |
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| Other Authors: | , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
1990.
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| Subjects: | |
| Online Access: | ProQuest, Abstract Link to OAKTrust copy |
| Abstract: | A novel parallel processing approach, textured decomposition (TD) method, is proposed and investigated. The method attempts to utilize the inherent parallelism of the classical iterative approach and cleverly exploits local behavior properties of systems, achieving an impressive convergence speed. In this dissertation, we first introduce the concept of textured decomposition of a linear system and analyze convergence properties of the textured algorithms for a large class of banded linear systems. We have shown that for many banded linear algebraic systems arising from scientific and engineering applications, such as point diagonally dominant systems, block diagonally dominant systems, M -matrices and skew-symmetric tridiagonal systems, the textured algorithms converge and have a better convergence speed than the associated Jacobi algorithms. We have also shown that for any systems which possess certain local behavior properties, the convergence rate of the classical iterative algorithms such as Jacobi type algorithms can be inproved by using the textured decomposition methods. Applications of textured decomposition method to the numerical solution of partial differential equations (PDEs) are then examined. We have applied the textured decomposition methods, together with the recursion, reordering and preconditioning techniques, to the numerical solution of several important classes of PDEs, such as elliptic equations, parabolic equations and first order PDEs... |
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| Item Description: | Typescript (photocopy). Vita. "Major subject: Electrical engineering." |
| Physical Description: | xi, 165 leaves : illustrations ; 29 cm |
| Bibliography: | Includes bibliographical references. |