论文信息 - DFT calculation of the generalized and Drazin inverse of a polynomial matrix

DFT calculation of the generalized and Drazin inverse of a polynomial matrix

A new algorithm is presented for the determination of the (a) generalized inverse and (b) Drazin inverse, of a polynomial matrix. The proposed algorithms are based on the discrete Fourier transform and thus are computationally fast in contrast to other known algorithms. The above algorithms are implemented in the Mathematica programming language and illustrated via examples.

Nicholas P. Karampetakis | Stavros Vologiannidis

[1] Dan E. Dudgeon,et al. Multidimensional Digital Signal Processing , 1983 .

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

[3] Tolga Güyer,et al. A new method for computing the solutions of differential equation systems using generalized inverse via Maple , 2001, Appl. Math. Comput..

[4] Michael Sebek,et al. Fast Fourier Transform and Linear Polynomial Matrix Equations , 2001 .

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

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

[7] Nicholas P. Karampetakis,et al. On the Computation of the Drazin Inverse of a Polynomial Matrix , 2001 .

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

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

[10] George E. Antoniou. Transfer function computation for generalized n-dimensional systems , 2001, J. Frankl. Inst..

[11] G. Pierobon,et al. FFT calculation of a determinantal polynomial , 1976 .