کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4632626 | 1340650 | 2010 | 15 صفحه PDF | دانلود رایگان |
Our basic motivation is a direct method for computing the gradient of the pseudo-inverse of well-conditioned system with respect to a scalar, proposed in [13] by Layton. In the present paper we combine the Layton’s method together with the representation of the Moore–Penrose inverse of one-variable polynomial matrix from [24] and developed an algorithm for computing the gradient of the Moore–Penrose inverse for one-variable polynomial matrix. Moreover, using the representation of various types of pseudo-inverses from [26], based on the Grevile’s partitioning method, we derive more general algorithms for computing {1}, {1, 3} and {1, 4} inverses of one-variable rational and polynomial matrices. Introduced algorithms are implemented in the programming language MATHEMATICA. Illustrative examples on analytical matrices are presented.
Journal: Applied Mathematics and Computation - Volume 216, Issue 7, 1 June 2010, Pages 2092–2106