We propose a finite algorithm for computing Drazin inverse of two-variable polynomial matrices based on Greville s finite algorithm for computing Drazin inverse of a constant matrix. Also a three-dimensional recursive algorithm to do that is deduced. Examples show that these methods are feasible and the implementation is developed in the symbolic package MATLAB. 2002 Elsevier Inc. All rights re...

Conditions for a quadratic permutation polynomial (QPP) to be self-inverse over the ring Zm of modular integers are given. If m = 2n, necessary and sufficient conditions for a QPP to be self-inverse are determined. Additional properties of QPP over modular integers as well as examples of monomial permutation polynomials are also provided. Mathematics Subject Classification: 12E10, 11B83

Let A be a bounded linear operator on a Banach space such that the resolvent of A is rational. If 0 is in the spectrum of A, then it is well known that A is Drazin invertible. We investigate spectral properties of the Drazin inverse of A. For example we show that the Drazin inverse of A is a polynomial in A.

We investigate the approximation properties of trigonometric polynomials and prove some direct and inverse theorems for polynomial approximation in weighted rearrangement invariant spaces.

For a given pair of s-dimensional real Laurent polynomials (~a(z),~b(z)), which has a certain type of symmetry and satisfies the dual condition~b(z) T ~a(z) = 1, an s× s Laurent polynomial matrix A(z) (together with its inverse A−1(z)) is called a symmetric Laurent polynomial matrix extension of the dual pair (~a(z),~b(z)) if A(z) has similar symmetry, the inverse A−1(Z) also is a Laurent polyn...

The quasi-interpolation operators of Clément and Scott-Zhang type are generalized to the hp-context. New polynomial lifting and inverse estimates are presented as well.

It is well known that the degree-raised Bernstein-B ezier coeecients of degree n of a polynomial g converge to g at the rate 1=n. In this paper we consider the polynomial An(g) of degree n interpolating the coeecients. We show how An can be viewed as an inverse to the Bernstein polynomial operator and that the derivatives An(g) (r) converge uniformly to g (r) at the rate 1=n for all r. We also ...

if the polynomial has no roots in [−1, 1]. If the inverse polynomial is decomposed into partial fractions, the an are linear combinations of simple functions of the polynomial roots. If the first k of the coefficients an are known, the others become linear combinations of these with expansion coefficients derived recursively from the bj ’s. On a closely related theme, finding a polynomial with ...