An Application of Computer Algebra and Dynamical Systems

1. Ben-Israel, A., Greville, T.N.E.: Generalized inverses: Theory and Applications, vol. 2. Springer, New York (2003). https://doi.org/10.1007/b97366

   Book  MATH  Google Scholar 

2. Fragulis, G., Mertzios, B.G., Vardulakis, A.I.G.: Computation of the inverse of a polynomial matrix and evaluation of its Laurent expansion. Int. J. Control 53, 431–443 (1991)

   Article  MathSciNet  Google Scholar 

3. Greville, T.N.E.: Some applications of the pseudo-inverse of matrix. SIAM Rev. 3, 15–22 (1960)

   Article  Google Scholar 

4. Jones, J., Karampetakis, N.P., Pugh, A.C.: The computation and application of the generalized inverse vai Maple. J. Symbolic Comput. 25, 99–124 (1998)

   Article  MathSciNet  Google Scholar 

5. Karampetakis, N.P.: Computation of the generalized inverse of a polynomial matrix and applications. Linear Algebra Appl. 252, 35–60 (1997)

   Article  MathSciNet  Google Scholar 

6. Karampetakis, N.P.: Generalized inverses of two-variable polynomial matrices and applications. Circ. Syst. Sign. Process. 16, 439–453 (1997)

   Article  MathSciNet  Google Scholar 

7. Karampetakis, N.P., Vologiannidis, S.: DFT calculation of the generalized and Drazin inverse of a polynomial matrix. Appl. Math. Comput. 143, 501–521 (2003)

   MathSciNet  MATH  Google Scholar 

8. McNulty, S.K., Kennedy, W.J.: Error-free computation of a reflexive generalized inverse. Linear Algebra Appl. 67, 157–167 (1985)

   Article  MathSciNet  Google Scholar 

9. Luo, F.L., Bao, Z.: Neural network approach to computing matrix inversion. Appl. Math. Comput. 47, 109–120 (1992)

   MathSciNet  MATH  Google Scholar 

10. Petković, M.D., Stanimirović, P.S., Tasić, M.B.: Effective partitioning method for computing weighted Moore-Penrose inverse. Comput. Math. Appl. 55, 1720–1734 (2008)

    Article  MathSciNet  Google Scholar 

11. Petković, M.D., Stanimirović, P.S.: Symbolic computation of the Moore-Penrose inverse using partitioning method. Int. J. Comput. Math. 82, 355–367 (2005)

    Article  MathSciNet  Google Scholar 

12. Rao, T.M., Subramanian, K., Krishnamurthy, E.V.: Residue arithmetic algorithms for exact computation of g-Inverses of matrices. SIAM J. Numer. Anal. 13, 155–171 (1976)

    Article  MathSciNet  Google Scholar 

13. Sendra, J.R., Sendra, J.: Symbolic computation of Drazin inverses by specializations. J. Comput. Appl. Math. 301, 201–212 (2016)

    Article  MathSciNet  Google Scholar 

14. Sendra, J.R., Sendra, J.: Computation of moore-penrose generalized inverses of matrices with meromorphic function entries. Appl. Math. Comput. 313, 355–366 (2017)

    Article  MathSciNet  Google Scholar 

15. Stanimirović, I.P., Tasić, M.B.: Computation of generalized inverses by using the \(LDL^*\) decomposition. Appl. Math. Lett. 25, 526–531 (2012)

    Article  MathSciNet  Google Scholar 

16. Stanimirović, P.S., Petković, M.: Gradient neural dynamics for solving matrix equations and their applications. Neurocomputing 306, 200–212 (2018)

    Article  Google Scholar 

17. Stanimirović, P.S., Tasić, M.B.: Partitioning method for rational and polynomial matrices. Appl. Math. Comput. 155, 137–163 (2004)

    MathSciNet  MATH  Google Scholar 

18. Stanimirović, P.S., Pappas, D., Katsikis, V.N., Stanimirović, I.P.: Symbolic computation of \(A^{(2)}_{T, S}\)-inverses using QDR factorization. Linear Algebra Appl. 437, 1317–1331 (2012)

    Article  MathSciNet  Google Scholar 

19. Tasić, M.B., Stanimirović, P.S., Petković, M.D.: Symbolic computation of weighted Moore-Penrose inverse using partitioning method. Appl. Math. Comput. 189, 615–640 (2007)

    MathSciNet  MATH  Google Scholar 

20. Wang, G.R., Wei, Y.M., Qiao, S.Z.: Generalized Inverses: Theory and Computations. Second edition. Developments in Mathematics, vol. 53. Springer, Singapore; Science Press Beijing, Beijing (2018)

    Chapter  Google Scholar 

21. Wang, J.: Recurrent neural networks for solving linear matrix equations. Comput. Math. Appl. 26, 23–34 (1993)

    Article  MathSciNet  Google Scholar 

22. Wang, J.: A recurrent neural network for real-time matrix inversion. Appl. Math. Comput. 55, 89–100 (1993)

    MathSciNet  MATH  Google Scholar 

23. Wang, J.: Recurrent neural networks for computing pseudoinverses of rank-deficient matrices. SIAM J. Sci. Comput. 18, 1479–1493 (1997)

    Article  MathSciNet  Google Scholar 

24. Wei, Y.: Recurrent neural networks for computing weighted Moore-Penrose inverse. Appl. Math. Comput. 116, 279–287 (2000)

    Article  MathSciNet  Google Scholar 

25. Wei, Y.: Integral representation of the generalized inverse \(A^{(2)}_{T, S}\) and its applications. In: Recent Research on Pure and Applied Algebra, pp. 59–65. Nova Science Publisher, New York (2003)

    Google Scholar 

26. Wei, Y., Stanimirović, P.S., Petković, M.D.: Numerical and Symbolic Computations of Generalized Inverses. World Scientific Publishing Co., Pte. Ltd., Hackensack (2018)

    Book  Google Scholar 

27. Wolfram Research Inc., Mathematica, Version 10.0, Champaign, IL (2015)

    Google Scholar 

28. Yu, Y., Wang, G.: DFT calculation for the 2-inverse of a polynomial matrix with prescribed image and kernel. Appl. Math. Comput. 215, 2741–2749 (2009)

    MathSciNet  MATH  Google Scholar 

29. Živković, I., Stanimirović, P.S., Wei, Y.: Recurrent neural network for computing outer inverses. Neural Comput. 28(5), 970–998 (2016)

    Article  MathSciNet  Google Scholar 

Download references