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Strict spectral approximation of a matrix and some related problems

Krystyna Ziętak — 1997

Applicationes Mathematicae

We show how the strict spectral approximation can be used to obtain characterizations and properties of solutions of some problems in the linear space of matrices. Namely, we deal with (i) approximation problems with singular values preserving functions, (ii) the Moore-Penrose generalized inverse. Some properties of approximation by positive semi-definite matrices are commented.

Double Chebyshev series for hypergeometric functions of two variables

Krystyna Ziętak — 1983

Mathematica Applicanda

We give formulas for the coefficients of a double Chebyshev series for a hypergeometric function of two variables x and y. We express these coefficients in terms of other hypergeometric functions of two variables. In particular, for hypergeometric functions expressed in terms of corresponding hypergeometric functions of one variable with an argument of the form x+y, the Chebyshev coefficients are values of another hypergeometric function of one variable. In Section 1 we give basic information on...

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