A finite algorithm for generalized inverses of polynomial and rational matrices

There are proposed two types of finite algorithms for symbolic computation of outer inverses of a given polynomial or rational matrix, based on the extension of the Leverrier-Faddeev algorithm. The implementation of the algorithm corresponding to rational matrices is developed in the symbolic package MATHEMATICA.

[1]  Nicholas P. Karampetakis,et al.  Generalized inverses of two-variable polynomial matrices and applications , 1997 .

[2]  Jun Ji.  A finite algorithm for the Drazin inverse of a polynomial matrix , 2002, Appl. Math. Comput..

[3]  Guorong Wang,et al.  A new extension of Leverrier's algorithm , 1993 .

[4]  Milan B. Tasic,et al.  Drazin inverse of one-variable polynomial matrices , 2001 .

[5]  A. Doma.  Generalized Inverses of Matrices and Its Applications. , 1983 .

[6]  Jun Ji.  An alternative limit expression of Drazin inverse and its application , 1994 .

[7]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[8]  Stephen Wolfram,et al.  Mathematica: a system for doing mathematics by computer (2nd ed.) , 1991 .

[9]  Henry P. Decell.  An application of the Cayley-Hamilton theorem to generalized matrix inversion. , 1965 .

[10]  P. Tzekis,et al.  ON THE COMPUTATION OF THE GENERALIZED INVERSE OF A POLYNOMIAL MATRIX , 1999 .

[11]  Lawrence S. Kroll.  Mathematica--A System for Doing Mathematics by Computer. , 1989 .

[12]  R. E. Hartwig.  More on the Souriau–Frame Algorithm and the Drazin Inverse , 1976 .

[13]  Nicholas P. Karampetakis,et al.  The Computation and Application of the Generalized Inverse via Maple , 1998, J. Symb. Comput..

[14]  Predrag S. Stanimirovic,et al.  SYMBOLIC IMPLEMENTATION OF LEVERRIER-FADDEEV ALGORITHM AND APPLICATIONS , .

[15]  Predrag S. Stanimirovic,et al.  Limit representations of generalized inverses and related methods , 1999, Appl. Math. Comput..

[16]  T. Greville,et al.  The Souriau-Frame algorithm and the Drazin pseudoinverse , 1973 .

[17]  Nicholas P. Karampetakis,et al.  Computation of the Generalized Inverse of a Polynomial Matrix and Applications , 1997 .

[18]  Gerhard Zielke,et al.  Report on test matrices for generalized inverses , 1986, Computing.