Matrix Padé-type approximant and directional matrix Padé approximant in the inner product space

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Abstract

A new matrix Padé-type approximant (MPTA) is defined in the paper by introducing a generalized linear functional in the inner product space. The expressions of MPTA are provided with the generating function form and the determinant form. Moreover, a directional matrix Padé approximant is also established by giving a set of linearly independent matrices. In the end, it is shown that the method of MPTA can be applied to the reduction problems of the high degree multivariable linear system. © 2003 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Algebraic properties
  • Determinant
  • Directional matrix Padé approximant
  • MPTA
  • Multivariable Fsystem reduction
  • Orthogonal polynomial
  • Scalar product of matrices

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