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Multi-color incomplete cholesky conjugate gradient methods for vector computers. ph.d. thesis
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Poole, E. L. |
| Copyright Year | 1986 |
| Description | In this research, we are concerned with the solution on vector computers of linear systems of equations, Ax = b, where A is a larger, sparse symmetric positive definite matrix. We solve the system using an iterative method, the incomplete Cholesky conjugate gradient method (ICCG). We apply a multi-color strategy to obtain p-color matrices for which a block-oriented ICCG method is implemented on the CYBER 205. (A p-colored matrix is a matrix which can be partitioned into a pXp block matrix where the diagonal blocks are diagonal matrices). This algorithm, which is based on a no-fill strategy, achieves O(N/p) length vector operations in both the decomposition of A and in the forward and back solves necessary at each iteration of the method. We discuss the natural ordering of the unknowns as an ordering that minimizes the number of diagonals in the matrix and define multi-color orderings in terms of disjoint sets of the unknowns. We give necessary and sufficient conditions to determine which multi-color orderings of the unknowns correpond to p-color matrices. A performance model is given which is used both to predict execution time for ICCG methods and also to compare an ICCG method to conjugate gradient without preconditioning or another ICCG method. Results are given from runs on the CYBER 205 at NASA's Langley Research Center for four model problems. |
| File Size | 3865157 |
| Page Count | 126 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19860019188 |
| Archival Resource Key | ark:/13960/t6353j560 |
| Language | English |
| Publisher Date | 1986-05-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Linear Systems Conjugate Gradient Method Finite Element Method Iterative Solution Vector Analysis Cdc Cyber 205 Computer Cholesky Factorization Matrices Mathematics Computer Programs Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Thesis |
