Matrix methods are increasingly popular for polynomial root-finding. The idea is to approximate the roots as the eigenvalues of the companion or generalized companion matrix associated with an input polynomial. The algorithms also solve secular equation. QR algorithm is the most customary method for eigen-solving, but we explore the inverse Rayleigh quotient iteration instead, which turns out t...

in the linear system ax = b the points x are sometimes constrained to lie in a given subspace s of column space of a. drazin inverse for any singular or nonsingular matrix, exist and is unique. in this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of drazin inverse in solving such systems is investigated. constrained linear system arise ...

In this paper, an iterative scheme is proposed to find the roots of a nonlinear equation. It is shown that this iterative method has fourth order convergence in the neighborhood of the root. Based on this iterative scheme, we propose the main contribution of this paper as a new high-order computational algorithm for finding an approximate inverse of a square matrix. The analytical discussions s...

several representations of the generalized drazin inverse of an anti-triangular block matrix in banach algebra are given in terms of the generalized banachiewicz--schur form.

In this paper we study singular values of a matrix whose one entry varies while all other entries are prescribed. In particular, we find the possible pth singular value of such a matrix, and we define explicitly the unknown entry such that the completed matrix has the minimal possible pth singular value. This in turn determines possible pth singular value of a matrix under rank one perturbation...

We estabish an analog of the Poincare-Cauchy separation theorem for normal matrices in terms of majorization. Moreover, we present a solution to the inverse spectral problem (Borgtype result) for a normal matrix. Using this result we essentially generalize and complement the known Gauss–Lucas theorem on the geometry of the roots of a complex polynomial and of its derivative. In turn the last re...

‎This paper presents some results of an annihilated element in Banach algebra‎, ‎and in specific case‎, ‎for any square matrix‎. The developed method significantly improves the computational aspects of transformations calculus and especially for finding powers and roots of any annihilated element‎. ‎An example is given to compare the proposed method with some other methods to show the efficienc...

We present a generic algorithm for computing discrete logarithms in a finite abelian p-group H, improving the Pohlig–Hellman algorithm and its generalization to noncyclic groups by Teske. We then give a direct method to compute a basis for H without using a relation matrix. The problem of computing a basis for some or all of the Sylow p-subgroups of an arbitrary finite abelian group G is addres...

We describe a recurrence method for computing primary pth roots of a matrix A with a cost, in terms of elementary arithmetic operations and memory, which is logarithmic with respect to p. When A is real and the primary root is real as well, the algorithm is based on the real Schur form of A and uses real arithmetic. The numerical experiments confirm the good behavior of the new algorithm in fin...

The computation of the roots of positive definite matrices arises in nuclear magnetic resonance, control theory, lattice quantum chromo-dynamics QCD , and several other areas of applications. The Cauchy integral theorem which arises in complex analysis can be used for computing f(A), in particular the roots of A, where A is a square matrix. The Cauchy integral can be approximated by using the t...