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Proceedings Paper

Minimum-phase LU factorization preconditioner for Toeplitz matrices
Author(s): Robert Ku; C.-C. Jay Kuo
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Paper Abstract

A new preconditioner is proposed for the solution of an N X N Toeplitz system TNx equals b, where TN can be symmetric indefinite or nonsymmetric, by preconditioned iterative methods. The preconditioner FN is obtained based on factorizing the generating function T(z) into the product of two terms corresponding, respectively, to minimum-phase causal and anticausal systems and therefore called the minimum-phase LU (MPLU) factorization preconditioner. Due to the minimum-phase property, (parallel)FN-1(parallel) is bounded. For rational Toeplitz TN with generating function T(z) equals A(z-1)/B(z-1) + C(z)/D(z), where A(z), B(z), C(z), and D(z) are polynomials of orders p1, q1, p2, and q2, we show that the eigenvalues of FN-1TN are repeated exactly at 1 except at most (alpha) F outliers, where (alpha) F depends on p1, q1, p2, q2, and the number (omega) of the roots of T(z) equals A(z-1)D(z) + B(z-1)C(z) outside the unit circle. A preconditioner KN in circulant form generalized from the symmetric case is also presented for comparison.

Paper Details

Date Published: 1 December 1991
PDF: 15 pages
Proc. SPIE 1566, Advanced Signal Processing Algorithms, Architectures, and Implementations II, (1 December 1991); doi: 10.1117/12.49812
Show Author Affiliations
Robert Ku, Univ. of Southern California (United States)
C.-C. Jay Kuo, Univ. of Southern California (United States)

Published in SPIE Proceedings Vol. 1566:
Advanced Signal Processing Algorithms, Architectures, and Implementations II
Franklin T. Luk, Editor(s)

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