Generalized inverse matrix Padé approximation on the basis of scalar products (Q1595122)
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scientific article; zbMATH DE number 1559346
| Language | Label | Description | Also known as |
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| English | Generalized inverse matrix Padé approximation on the basis of scalar products |
scientific article; zbMATH DE number 1559346 |
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Generalized inverse matrix Padé approximation on the basis of scalar products (English)
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3 September 2001
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An axiomatic definition to matrix Padé approximants is presented as an extension of that by \textit{P. R. Graves-Morris} and \textit{C. D. Jenkins} [Constructive Approximation 2, 263-289 (1986; Zbl 0614.41010)]. The expression for this approximant has a matrix numerator and a scalar denominator. It does not need any multiplication of matrices. The representations of this approximant type are provided with three forms: (i) by explicit determinantal formulas for the denominator scalar polynomials and the numerator matrix polynomials, (ii) by an \(\varepsilon\)-algorithm, and (iii) by Thiele-type continued fraction. Equivalence relations for the three representations are proposed.
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generalized inverse
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matrix Padé approximation
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epsilon algorithm
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Thiele-type continued fraction
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