13 November 2000 How bad are symmetric Pick matrices?
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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.
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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


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