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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. 相似文献
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Pseudo-Schur complements and their properties 总被引:1,自引:0,他引:1
M. Redivo-Zaglia 《Applied Numerical Mathematics》2004,50(3-4):511-519
The notion of Schur complement of a partitioned matrix with a square nonsingular block is well known and it has many applications in various branches of mathematics. When the block is rectangular or singular, pseudo-Schur complements can be defined and studied. In particular, they satisfy an extension of the quotient property for Schur complements. A new proof of this property is given in this paper and various related topics are discussed. 相似文献
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