Matrix-valued continued fractions

Authors:
Huan-xi Zhao;Gongqin Zhu
Affiliations:
Department of Mathematics, University of Science & Technology of China, Anhui Hefei, People's Republic of China;Department of Applied Mathematics, Central-South University, Changsha, People's Republic of China
Venue:
Journal of Approximation Theory
Year:
2003

Citing 11
Cited 1

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Abstract

We discuss the properties of matrix-valued continued fractions based on Samelson inverse. We begin to establish a recurrence relation for the approximants of matrix-valued continued fractions. Using this recurrence relation, we obtain a formula for the difference between mth and nth approximants of matrix-valued continued fractions. Based on this formula, we give some necessary and sufficient conditions for the convergence of matrix-valued continued fractions, and at the same time, we give the estimate of the rate of convergence. This paper shows that some famous results in the scalar case can be generalized to the matrix case, even some of them are exact generalizations of the scalar results.