The Iterative Algorithms Of Bivariate Matrix Valued Stieltjes-Type Rational Interpolants

The summaries of this thesis are the researches on bivariate matrix-valued rationalinterpolants including the iterative algorithms of the bivariate matrix-valued Stieltjestype rational interpolants(BMSRI) and the bivariate matrix-valued Newton-Thiele typerational interpolants.This thesis consists of four chapters.In Chapter1, we review the background of the research on the matrix-valuedrational interpolants and its research status.In chapter2, we introduce some definitions, properties and results of uni-andbivariate scalar continued fraction.In Chapter3, based on the existing definition of BMSRI, we give two efcientiterative algorithms and the corresponding examples. We demonstrate the uniquenessof BMSRI if it exists.In Chapter4, by means of Newton’s diference quotient and Thiele type continuedfraction combined with the generalized inverse matrix, we present a kind of bivariatematrix-valued blending diference quotient. Based on which we construct the bivariateNewton-Thiele type rational interpolants and give its iterative algorithm.