A two-dimensional matrix Pade-type approximation in the inner product space

作者：Tao Youtian; Gu Chuanqing

来源：Journal of Computational and Applied Mathematics, 2009, 231(2): 680-695.

DOI：10.1016/j.cam.2009.04.013

• Multivariate matrix-valued Pade-type approximants
• Linear functional
• Recursive algorithm
• Determinantal expression
• Realization problem
• 2-D linear systems

By introducing a bivariate matrix-valued linear functional on the scalar polynomial space. a general two-dimensional (2-D) matrix Pade-type approximant (BMPTA) in the inner product space is defined in this paper. The coefficients of its denominator polynomials are determined by taking the direct inner product of matrices. The remainder formula is developed and an algorithm for the numerator polynomials is presented when the generating polynomials are given in advance. By means of the Hankel-like coefficient matrix, a determinantal expression of BMPTA is presented. Moreover, to avoid the computation of the determinants, two efficient recursive algorithms are proposed. At the end the method of BMPTA is applied to partial realization problems of 2-D linear systems.

• 出版日期2009-9-15
• 单位巢湖学院; 上海大学