论文信息 - Fast and Stable Reduction of Diagonal Plus Semi-Separable Matrices to Tridiagonal and Bidiagonal Form

Fast and Stable Reduction of Diagonal Plus Semi-Separable Matrices to Tridiagonal and Bidiagonal Form

A two-way chasing algorithm to reduce a diagonal plus a symmetric semi-separable matrix to a symmetric tridiagonal one and an algorithm to reduce a diagonal plus an unsymmetric semi-separable matrix to a bidiagonal one are considered. Both algorithms are fast and stable, requiring a computational cost of N2, where N is the order of the considered matrix.

N. Mastronardi | S. Chandrasekaran | S. van Huffel

[1] Yu Hen Hu,et al. Parallel VLSI computing array implementation for signal subspace updating algorithm , 1989, IEEE Trans. Acoust. Speech Signal Process..

[2] H. Schwarz. Tridiagonalization of a symetric band matrix , 1968 .

[3] J. H. Wilkinson. The algebraic eigenvalue problem , 1966 .

[4] Åke Björck,et al. Numerical methods for least square problems , 1996 .

[5] G. Stewart. Introduction to matrix computations , 1973 .

[6] Gene H. Golub,et al. Matrix computations , 1983 .

[7] D. Fasino,et al. Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form , 2001 .

[8] L. Eldén. Algorithms for the regularization of ill-conditioned least squares problems , 1977 .

[9] Sabine Van Huffel,et al. Efficient reduction algorithms for bordered band matrices , 1995, Numer. Linear Algebra Appl..

[10] S. Chandrasekaran,et al. Fast and stable eigendecomposition of symmetric banded plus semi-separable matrices , 2000 .

[11] B. Parlett. The Symmetric Eigenvalue Problem , 1981 .