article · 1996
Parallel Stable Solution Methods for Tridiagonal Linear Systems of Equations
C.R. Dun, M. Hegland, M. R. Osborne
Cited by 0Abstract and details only
Abstract
this paper, the wrap-around partitioning methodology, originally proposed by Hegland [1], is considered for the solution of a tridiagonal matrix. This approach can also be formulated as a generalisation of the cyclic reduction algorithm. However, the wrap-around partitioning algorithm described here can be used in conjunction with partial pivoting or QR factorisation. The algorithm presented here is a recursive implementation of the wrap-around partitioning scheme. This has the added advantage of removing the restriction, common to many cyclic reduction algorithms, that the order of the matrix must be a power of 2. In section 2, the wrap around partitioning scheme is presented in terms of simple bidiagonal matrices. It is shown in Section 5 that tridiagonal matrices can be transformed into block-bidiagonal matrices. Thus, the algorithm for the simple bidiagonal matrix forms a prototype for the tridiagonal algorithm. 2 C.R. Dun, M. Hegland & M.R. Osborne The recursive implementation of the wrap-around partitioning scheme is detailed in Section 3. Numerical results of the simple bidiagonal algorithm are presented in Section 4. In Section 5, issues associated with extending the bidiagonal algorithm to the tridiagonal algorithm are discussed.
Cite this paper
Dun, C., Hegland, M., & Osborne, M. R. (1996). Parallel Stable Solution Methods for Tridiagonal Linear Systems of Equations.
Dun, C.R., et al. “Parallel Stable Solution Methods for Tridiagonal Linear Systems of Equations.” 1996.
Dun, C.R., M. Hegland, and M. R. Osborne. 1996. “Parallel Stable Solution Methods for Tridiagonal Linear Systems of Equations.”
Dun, C., Hegland, M. and Osborne, M.R. (1996) ‘Parallel Stable Solution Methods for Tridiagonal Linear Systems of Equations’.
@article{dun1996parallel,
title = {{Parallel Stable Solution Methods for Tridiagonal Linear Systems of Equations}},
author = {Dun, C.R. and Hegland, M. and Osborne, M. R.},
year = {1996}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.