Padé Approximants to Matrix Stieltjes Series: Convergence and Related Properties
Sankar Basu · SIAM Journal on Matrix Analysis and Applications · 1989
Following earlier work on Padé approximants to matrix Stieltjes series and their network theoretic relevance, it is shown that certain paradiagonal sequences of matrix Padé approximants to the series under consideration always converge. Interpretations of this result in terms of representation of impedances of RC distributed multiport networks are given. Matricial generalizations of the classical Hamburger and Stieltjes moment problems are discussed in this context. Matrix polynomials of the second kind orthogonal on the real line, which fall out as numerators of the matrix Padé approximants of certain orders, are singled out and their properties are studied.