Matrix-valued continued fractions

• Published in: Journal of approximation theory Vol. 120; no. 1; pp. 136 - 152
• Main Authors: Zhao, Huan-xi, Zhu, Gongqin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 2003
• Subjects: Approximants formula; Convergence criteria; Matrix-valued continued fractions; Recurrence relation; Samelson matrix inverse; Convergence criteria; Approximants formula; Recurrence relation; 41A20; 65F30; 65D05; Matrix-valued continued fractions; Samelson matrix inverse
• ISSN: 0021-9045; 1096-0430
• DOI: 10.1016/S0021-9045(02)00016-3

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.