论文信息 - Numerical Stability and Instability in Matrix Sign Function Based Algorithms

Numerical Stability and Instability in Matrix Sign Function Based Algorithms

r s The matrix sign function is the basis of a family of algorithms fo olving a variety of invariant subspace related problems. Rounding t s errors corrupting the computation corrupt the calculated invarian ubspaces. We present a forward and a backward error analysis for. P the invariant subspaces calculated through the matrix sign function roper scaling is essential for numerical stability as well as for rapid x s convergence. We identify some problems upon which the matri ign function algorithms may be expected to perform well and others

R. Byers

[1] William Kahan,et al. A Survey of Error Analysis , 1971, IFIP Congress.

[2] G. Stewart. Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems , 1973 .

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

[4] E. Denman,et al. The matrix sign function and computations in systems , 1976 .

[5] Stability analysis via the extended matrix sign function , 1978 .

[6] J. Varah. On the Separation of Two Matrices , 1979 .

[7] Webb Miller,et al. Software for Roundoff Analysis of Matrix Algorithms , 1980 .

[8] J. D. Roberts,et al. Linear model reduction and solution of the algebraic Riccati equation by use of the sign function , 1980 .

[9] J. Leyva-Ramos,et al. Spectral decomposition of a matrix using the generalized sign matrix , 1981 .

[10] Eugene D. Denman,et al. Roots of real matrices , 1981 .

[11] J. Demmel. A Numerical Analyst's Jordan Canonical Form. , 1983 .

[12] J. L. Howland. The sign matrix and the separation of matrix eigenvalues , 1983 .

[13] C. Loan. How Near is a Stable Matrix to an Unstable Matrix , 1984 .

[14] Judith Gardiner,et al. A generalization of the matrix sign function solution for algebraic Riccati equations , 1985, 1985 24th IEEE Conference on Decision and Control.