Abstract
Matrix Pade-type approximants and Pade approximants has been studied by several authors in the scalar case. Some definitions in multivari- ate case have been introduced. In the current work, we define a multivariate homogeneous matrix-type approximants of which generating polynomials have shift. We consider higher-order approximants and introduce multivariate ho- mogeneous matrix Pade approximants. We derive some recurrence relations for generating polynomials and associated polynomials. Finally, numerical example is given to illustrate our results.
Highlights
The matrix Pade approximants has been studied for a long time by several authors [8],[9],[13],[12],[14],[15] to cite juste a few
In the paper [1] we introduced a new family of multivariate matrix Pade approximants
Based on the analysis above, we consider present the following example for computing the multivariate homogeneous matrix Pade approximants to the matrix function
Summary
The matrix Pade approximants has been studied for a long time by several authors [8],[9],[13],[12],[14],[15] to cite juste a few. Zheng et al [14],[15] have defined the multivariate matrix Pade-type approximants and Pade approximants They have generalized the concept of Brezinski in scalar cases [5]. Their definition is based on the bilinear functional c acting on P ( the vector space of all bivariate polynomials whose coefficients are real or complex) defined from its moments by c(uivj) = Ci,j. It generalizes directly the definition in [7]. We restrict our description to the bivariate case, only for notational convenience, we may use the term multivariate in the text
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