Inverses of Multivariable Polynomial Matrices by Discrete Fourier Transforms

Abstract

Two discrete Fourier transform based algorithms are proposed for the computation of the Moore-Penrose and Drazin inverse of a multivariable polynomial matrix.

On a special case of the two-variable Newton interpolation polynomial

“…Based on the values of p (x, y) at the set of pointsS (k1,k2) ∆ create the zero order table of initial values D 0 which has been defined in (13).…”

“…Polynomial interpolation plays a crucial role in a number of applications such as : the calculation of the determinantal polynomial [8], [9], the computation of the transfer function of generalized n-dimensional systems [10], the solutions of polynomial matrix Diophantine equations [11], and the computation of the inverse or the generalized inverse of multivariable polynomial matrices [12], [13], [9], [14]. The Newton multivariate polynomial interpolation can be applied both to triangular and rectangular bases.…”

The technique "evaluation-interpolation" in parallel processing with matlab

“…calculation of the transfer function matrix of a system [2], solution of Auto-Regressive equations [1], coding and cryptography [5] etc. The inverse of a polynomial matrix can be computed either by using symbolic algorithms, like the Leverrier-Faddev algorithm [4], or numerical algorithms [3,10,6,9]. Among those algorithms it is shown that DFT interpolation techniques are the most promising as concerns the running time, in contrast to the symbolic ones which are accurate but time consuming.…”

A study on new right/left inverses of nonsquare polynomial matrices

“…Whilst the task of the Moore-Penrose inversion of polynomial matrices (or rational matrices) has attracted considerable research interest (Ben-Israel and Greville, 2003;Karampetakis and Tzekis, 2001;Kon'kova and Kublanovskaya, 1996;Stanimirović, 2003;Stanimirović and Petković, 2006;Varga, 2001;Vologiannidis and Karampetakis, 2004;Zhang, 1989), the problem of right/left inverting nonsquare (full normal rank) polynomial matrices has not been given proper attention by the academia. The suggested control applications (Bańka and Dworak, 2006;Chen and Hara, 2001;Ferreira, 1988;Hautus and Heymann, 1983;Quadrat, 2004;Trentelman et al, 2001;Williams and Antsaklis, 1996) have not ended up with algorithms for obtaining right/left polynomial matrix inverses and their quantification.…”