Optimal bounds for solving tridiagonal systems with preconditioning
Journal Article
·
· SIAM J. Comput.; (United States)
- Dipartimento di Matematica e Informatica, Univ. di Udine, 6-33100 Udine (IT)
Let (1) Tx=f be a linear tridiagonal system system of n equations in the unknown x/sub 1/, ..., x/sub n/. It is proved that 3n-2 (nonscalar) multiplications/divisions are necessary to solve (1) in a straight-line program excluding divisions by elements of f. This bound is optimal if the cost of preconditioning of T is not counted. Analogous results are obtained in case (i) T is bidiagonal and (ii) T and f are both centrosymmetric. The existence of parallel algorithms to solve (1) with preconditioning and with minimal multiplicative redundancy is also discussed.
- OSTI ID:
- 6525141
- Journal Information:
- SIAM J. Comput.; (United States), Vol. 17:5
- Country of Publication:
- United States
- Language:
- English
Similar Records
Preconditioned polynomial iterative acceleration methods for block tridiagonal systems
Analysis of the recursive doubling algorithm
A remark on band-Toeplitz preconditions for Hermitian Toeplitz systems
Conference
·
Mon Sep 01 00:00:00 EDT 1986
·
OSTI ID:6525141
Analysis of the recursive doubling algorithm
Technical Report
·
Wed Dec 01 00:00:00 EST 1976
·
OSTI ID:6525141
A remark on band-Toeplitz preconditions for Hermitian Toeplitz systems
Conference
·
Sat Dec 31 00:00:00 EST 1994
·
OSTI ID:6525141