Extended abstract: Partial row projection methods
- Indiana Univ., Bloomington, IN (United States)
Accelerated row projection (RP) algorithms for solving linear systems Ax = b are a class of iterative methods which in theory converge for any nonsingular matrix. RP methods are by definition ones that require finding the orthogonal projection of vectors onto the null space of block rows of the matrix. The Kaczmarz form, considered here because it has a better spectrum for iterative methods, has an iteration matrix that is the product of such projectors. Because straightforward Kaczmarz method converges slowly for practical problems, typically an outer CG acceleration is applied. Definiteness, symmetry, or localization of the eigenvalues, of the coefficient matrix is not required. In spite of this robustness, work has generally been limited to structured systems such as block tridiagonal matrices because unlike many iterative solvers, RP methods cannot be implemented by simply supplying a matrix-vector multiplication routine. Finding the orthogonal projection of vectors onto the null space of block rows of the matrix in practice requires accessing the actual entries in the matrix. This report introduces a new partial RP algorithm which retains advantages of the RP methods.
- Research Organization:
- Front Range Scientific Computations, Inc., Lakewood, CO (United States)
- OSTI ID:
- 440727
- Report Number(s):
- CONF-9604167-Vol.2; ON: DE96015307; CNN: Grant CDA-9309746; Grant CDA-9303189; Grant ASC-9502292; TRN: 97:000721-0049
- Resource Relation:
- Conference: Copper Mountain conference on iterative methods, Copper Mountain, CO (United States), 9-13 Apr 1996; Other Information: PBD: [1996]; Related Information: Is Part Of Copper Mountain conference on iterative methods: Proceedings: Volume 2; PB: 242 p.
- Country of Publication:
- United States
- Language:
- English
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