How bad are symmetric Pick matrices?
نویسندگان
چکیده
Let P be a symmetric positive definite Pick matrix of order n. The following facts will be proven here: (a) P is the Gram matrix of a set of rational functions, with respect to a inner product defined in terms of a “generating function” associated to P ; (b) Its condition number is lower-bounded by a function growing exponentially in n; (c) P can be effectively preconditioned by the Pick matrix generated by the same nodes and a constant function.
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