How bad are symmetric Pick matrices?

Dario Fasino; Vadim Olshevsky

doi:10.1117/12.406491

13 November 2000 How bad are symmetric Pick matrices?

Dario Fasino, Vadim Olshevsky

Proceedings Volume 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X; (2000) https://doi.org/10.1117/12.406491
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

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.

Citation Download Citation

Dario Fasino and Vadim Olshevsky "How bad are symmetric Pick matrices?", Proc. SPIE 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X, (13 November 2000); https://doi.org/10.1117/12.406491

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