13 November 2000 How bad are symmetric Pick matrices?
Author Affiliations +
Abstract
Let P be a symmetric positive definite Pick matrix of order n. The following facts will be proven here: (1) P is the Gram matrix of a set of rational functions, with respect to an inner product defined in terms of a 'generating function' associated to P; (2) Its condition number is lower-bounded by a function growing exponentially in n. (3) P can be effectively preconditioned by the Pick matrix generated by the same nodes and a constant function.
© (2000) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Dario Fasino, Vadim Olshevsky, "How bad are symmetric Pick matrices?", Proc. SPIE 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X, (13 November 2000); doi: 10.1117/12.406491; https://doi.org/10.1117/12.406491
PROCEEDINGS
10 PAGES


SHARE
RELATED CONTENT

Numerical properties of the LLL method
Proceedings of SPIE (September 18 2007)
Alternative To The SVD: Rank Revealing QR-Factorizations
Proceedings of SPIE (April 04 1986)
Solution of the Yule-Walker equations
Proceedings of SPIE (December 01 1991)
Architecture Of An Advanced Signal Processor
Proceedings of SPIE (July 30 1982)

Back to Top