Matrix Padé Fractions and Their Computation
نویسندگان
چکیده
For matrix power series with coefficients over a field, the notion of a matrix power series remainder sequence and its corresponding cofactor sequence are introduced and developed. An algorithm for constructing these sequences is presented. It is shown that the cofactor sequence yields directly a sequence of Pad6 fractions for a matrix power series represented as a quotient B(z)-lA(z). When B(z)-A(z) is normal, the complexity of the algorithm for computing a Pad6 fraction of type (m, n) is O(p3(rn+ n)2), where p is the order of the matrices A(z) and B(z). For a power series that are abnormal for a given (m, n), Pad6 fractions may not exist. However, it is shown that a generalized notion of Pad fraction, the Pad6 form, which is introduced in this paper, does always exist and can be computed by the algorithm. In the abnormal case, the algorithm can reach a complexity of O(p3(m + n)3), depending on the nature of the abnormalities. In the special case of a scalar power series, however, the algorithm complexity is O((rn + n)2), even in the abnormal case. Key words, matrix Pad6 fraction, matrix power series, matrix Pad6 form AMS(MOS) subject classifications. 41A21, 41A63, 68Q40
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عنوان ژورنال:
- SIAM J. Comput.
دوره 18 شماره
صفحات -
تاریخ انتشار 1989