A two-dimensional matrix Padé-type approximation in the inner product space |
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Authors: | Youtian Tao Chuanqing Gu |
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Institution: | a Department of Mathematics, Shanghai University, Shanghai 200444, China b Department of Mathematics, Chaohu College, Chaohu 238000, China |
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Abstract: | By introducing a bivariate matrix-valued linear functional on the scalar polynomial space, a general two-dimensional (2-D) matrix Padé-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. |
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Keywords: | Multivariate matrix-valued Padé -type approximants Linear functional Recursive algorithm Determinantal expression Realization problem 2-D linear systems |
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