An Application of Computer Algebra and Dynamical Systems

An algorithm for the symbolic computation of outer inverses of matrices is presented. The algorithm is based on the exact solution of the first order system of differential equations which appears in corresponding dynamical system. The domain of the algorithm are matrices whose elements are integers, rational numbers as well as one-variable or multiple-variable rational or polynomial expressions.

[1]  Nicholas P. Karampetakis,et al.  DFT calculation of the generalized and Drazin inverse of a polynomial matrix , 2003, Appl. Math. Comput..

[2]  T. Greville,et al.  Some Applications of the Pseudoinverse of a Matrix , 1960 .

[3]  Predrag S. Stanimirovic,et al.  Gradient neural dynamics for solving matrix equations and their applications , 2018, Neurocomputing.

[4]  Basil G. Mertzios,et al.  Computation of the inverse of a polynomial matrix and evaluation of its Laurent expansion , 1991 .

[5]  Jun Wang,et al.  A recurrent neural network for real-time matrix inversion , 1993 .

[6]  Yimin Wei,et al.  Neural network approach to computing outer inverses based on the full rank representation , 2016 .

[7]  J. Rafael Sendra,et al.  Computation of Moore-Penrose generalized inverses of matrices with meromorphic function entries , 2017, Appl. Math. Comput..

[8]  V. Katsikis,et al.  Symbolic computation of AT,S(2)-inverses using QDR factorization , 2012 .

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

[10]  Guorong Wang,et al.  DFT calculation for the {2}-inverse of a polynomial matrix with prescribed image and kernel , 2009, Appl. Math. Comput..

[11]  Predrag S. Stanimirovic,et al.  Recurrent Neural Network for Computing Outer Inverse , 2016, Neural Computation.

[12]  E. V. Krishnamurthy,et al.  Residue Arithmetic Algorithms for Exact Computation of g-Inverses of Matrices , 1976 .

[13]  Luo Fa-long,et al.  Neural network approach to computing matrix inversion , 1992 .

[14]  Milan B. Tasic,et al.  Computation of generalized inverses by using the LDL* decomposition , 2012, Appl. Math. Lett..

[15]  Jun Wang,et al.  Recurrent Neural Networks for Computing Pseudoinverses of Rank-Deficient Matrices , 1997, SIAM J. Sci. Comput..

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

[17]  Marcelo A. Ceballos Numerical evaluation of integrals involving the product of two Bessel functions and a rational fraction arising in some elastodynamic problems , 2017, J. Comput. Appl. Math..

[18]  W. J. Kennedy,et al.  Error-free computation of a reflesive generalized inverse , 1985 .

[19]  Predrag S. Stanimirovic,et al.  Symbolic computation of the Moore–Penrose inverse using a partitioning method , 2005, Int. J. Comput. Math..

[20]  Jun Wang Recurrent neural networks for solving linear matrix equations , 1993 .

[21]  Milan B. Tasic,et al.  Symbolic computation of weighted Moore-Penrose inverse using partitioning method , 2007, Appl. Math. Comput..

[22]  J. Rafael Sendra,et al.  Symbolic computation of Drazin inverses by specializations , 2016, J. Comput. Appl. Math..

[23]  Milan B. Tasic,et al.  Effective partitioning method for computing weighted Moore-Penrose inverse , 2008, Comput. Math. Appl..

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

[25]  Predrag S. Stanimirovic,et al.  Partitioning method for rational and polynomial matrices , 2004, Appl. Math. Comput..

[26]  Yimin Wei Recurrent neural networks for computing weighted Moore-Penrose inverse , 2000, Appl. Math. Comput..

[27]  Yimin Wei,et al.  Numerical and Symbolic Computations of Generalized Inverses , 2018 .