Essentially optimal computation of the inverse of generic polynomial matrices

Essentially optimal computation of the inverse of generic polynomial matrices

We present an inversion algorithm for nonsingular n × n matrices whose entries are degree d polynomials over a field. The algorithm is deterministic and, when n is a power of two, requires O (̃n3d) field operations for a generic input; the soft-O notation O ̃indicates some missing log(nd) factors. Up to such logarithmic factors, this asymptotic complexity is of the same order as the number of dis...

extensions of some polynomial inequalities to the polar derivative

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Computation of the q-th roots of circulant matrices

In this paper, we investigate the reduced form of circulant matrices and we show that the problem of computing the q-th roots of a nonsingular circulant matrix A can be reduced to that of computing the q-th roots of two half size matrices B - C and B + C.

Drazin inverse of one-variable polynomial matrices

There is proposed a representation of the Drazin inverse of a given polynomial square matrix, based on the extension of the Leverrier-Faddeev algorithm. Also, an algorithm for symbolic computation of the Drazin inverse of polynomial matrix is established. This algorithm represents an extension of the papers [5], [7] and a continuation of the papers [8], [9], [10]. The implementation is develope...

Recursive computation of pseudo-inverse of matrices