Abstract:Rutishauser, Gragg and Harrod and finally H.Y. Zha used the same class of chasing algorithms for transforming arrowhead matrices to tridiagonal form. Using a graphical theoretical approach, we propose a new chasing algorithm. Although this algorithm has the same sequential computational complexity and backward error properties as the old algorithms, it is better suited for a pipelined approach. The parallel algorithm for this new chasing method is described, with performance results on the Paragon and nCUBE. Comparison results between the old and the new algorithms are also presented.
- Z. Chen, A parallel implementation of a chasing algorithm, tech. rep., Texas A&M University, 1996. project report.
- Z. Chen, Y. Deng, and S. Oliveira, A parallel implementation of a new chasing algorithm, tech. rep., Texas A&M University, 1996. manuscript.
- Y. Deng, Some applications of pipelining techniques in parallel scientific computing, Master’s thesis, Texas A&M University, 1996.
- Gene H. Golub and Charles F. Van Loan, Matrix computations, 2nd ed., Johns Hopkins Series in the Mathematical Sciences, vol. 3, Johns Hopkins University Press, Baltimore, MD, 1989. MR 1002570
- William B. Gragg and William J. Harrod, The numerically stable reconstruction of Jacobi matrices from spectral data, Numer. Math. 44 (1984), no. 3, 317–335. MR 757489, DOI 10.1007/BF01405565
- H. Rutishauser, On Jacobi rotation patterns, Proc. Sympos. Appl. Math., Vol. XV, Amer. Math. Soc., Providence, R.I., 1963, pp. 219–239. MR 0160321
- D. Stewart, A graph theoretical model of Givens rotations and its implications. Accepted by Linear Alg. Appl., 1996.
- Sabine Van Huffel and Haesun Park, Parallel tri- and bi-diagonalization of bordered bidiagonal matrices, Parallel Comput. 20 (1994), no. 8, 1107–1128. MR 1290523, DOI 10.1016/0167-8191(94)90071-X
- Sabine Van Huffel and Haesun Park, Efficient reduction algorithms for bordered band matrices, Numer. Linear Algebra Appl. 2 (1995), no. 2, 95–113. MR 1323815, DOI 10.1002/nla.1680020204
- Hong Yuan Zha, A two-way chasing scheme for reducing a symmetric arrowhead matrix to tridiagonal form, J. Numer. Linear Algebra Appl. 1 (1992), no. 1, 49–57. MR 1169869
- Suely Oliveira
- Affiliation: Department of Computer Science, Texas A&M University, College Station, Texas 77843
- Email: firstname.lastname@example.org
- Received by editor(s): September 19, 1996
- Additional Notes: This research is supported by NSF grant ASC 9528912 and a Texas A&M University Interdisciplinary Research Initiative Award.
- © Copyright 1998 American Mathematical Society
- Journal: Math. Comp. 67 (1998), 221-235
- MSC (1991): Primary 65F15; Secondary 68R10, 65F50
- DOI: https://doi.org/10.1090/S0025-5718-98-00895-3
- MathSciNet review: 1433266