The algorithm for computing the Drazin inverses of two-variable polynomial matrices

Bu, Fanbin; Wei, Yimin

doi:10.1016/s0096-3003(02)00814-7

Cited by 12 publications

(14 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Polynomials in MATHEMATICA are represented in the internal form using the little modified Ef sparse structure. For example, two-variable polynomial p(s 1 , s 2 ) = 4s 9 [4,Power[s1,9], Power[s2, 10]] ].…”

Section: Obviously We Havementioning

confidence: 99%

Effective partitioning method for computing weighted Moore–Penrose inverse

Petković

Stanimirović

Tasić

2008

Computers & Mathematics with Applications

View full text Add to dashboard Cite

We introduce a method and an algorithm for computing the weighted Moore-Penrose inverse of multiple-variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices. These methods and algorithms are generalizations of algorithms developed in [M.B. Tasić, P.S. Stanimirović, M.D. Petković, Symbolic computation of weighted Moore-Penrose inverse using partitioning method, Appl. Math. Comput. 189 (2007) 615-640] to multiple-variable rational and polynomial matrices and improvements of these algorithms on sparse matrices. Also, these methods are generalizations of the partitioning method for computing the Moore-Penrose inverse of rational and polynomial matrices introduced in [P.S. Stanimirović, M.B. Tasić, Partitioning method for rational and polynomial matrices, Appl. Math. Comput. 155 (2004) 137-163; M.D. Petković, P.S. Stanimirović, Symbolic computation of the Moore-Penrose inverse using partitioning method, Internat. J. Comput. Math. 82 (2005) 355-367] to the case of weighted Moore-Penrose inverse. Algorithms are implemented in the symbolic computational package MATHEMATICA.

show abstract

Section: Obviously We Havementioning

confidence: 99%

Effective partitioning method for computing weighted Moore–Penrose inverse

Petković

Stanimirović

Tasić

2008

Computers & Mathematics with Applications

View full text Add to dashboard Cite

show abstract

“…Many authors have addressed the problem of computing Drazin inverses where the matrix entries are indeed polynomials (see e.g. [2], [7], [10], [11]), for special type of matrices (see e.g. [15], [13]), and for weighted Drazin inverses (see [9], [12]).…”

Section: Introductionmentioning

confidence: 99%

Gröbner basis computation of Drazin inverses with multivariate rational function entries

Sendra

2015

Applied Mathematics and Computation

View full text Add to dashboard Cite

In this paper we show how to apply Gröbner bases to compute the Drazin inverse of a matrix with multivariate rational functions as entries. When the coefficients of the rational functions depend on parameters, we give sufficient conditions for the Drazin inverse to specialize properly. In addition, we extend the method to weighted Drazin inverses. We present an empirical analysis that shows a good timing performance of the method.

show abstract

“…The group inverse A # is the unique {1, 2, 5} inverse of A, and exists if and only if ind(A) = min k {k : rank(A k+1 ) = rank(A k )} = 1. A matrix X = A D is said to be the Drazin inverse of A if (1 k ) (for some positive integer k), (2) and (5) are satisfied. In the case ind(A) = 1, the Drazin inverse of A is equal to the group inverse of A.…”

Section: Introductionmentioning

confidence: 99%

Computing generalized inverses using LU factorization of matrix product

Stanimirović

Tasić

2008

International Journal of Computer Mathematics

View full text Add to dashboard Cite

An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and T*(AT*)+, where R and T are rational matrices with appropriate dimensions and corresponding rank. The proposed algorithm is based on these general representations and the Cholesky factorization of symmetric positive matrices. The algorithm is implemented in programming languages MATHEMATICA and DELPHI, and illustrated via examples. Numerical results of the algorithm, corresponding to the Moore-Penrose inverse, are compared with corresponding results obtained by several known methods for computing the Moore-Penrose inverse

show abstract

The algorithm for computing the Drazin inverses of two-variable polynomial matrices

Cited by 12 publications

References 12 publications

Effective partitioning method for computing weighted Moore–Penrose inverse

Effective partitioning method for computing weighted Moore–Penrose inverse

Gröbner basis computation of Drazin inverses with multivariate rational function entries

Computing generalized inverses using LU factorization of matrix product

Contact Info

Product

Resources

About