Generalized inverse matrix Padé approximation on the basis of scalar products
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.
scientific article; zbMATH DE number 1559346
scientific article