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The proof of the asymptotic quadratic convergence is provided for the parallel two-sided block-Jacobi EVD algorithm with dynamic ordering for Hermitian matrices. The discussion covers the case of well-separated eigenvalues as well as clusters of eigenvalues. Having p processors, each parallel iteration step consists of zeroing 2p off-diagonal blocks chosen by dynamic ordering with the aim to maximize the decrease of the off-diagonal Frobenius norm. Numerical experiments illustrate and confirm the developed theory. [ABSTRACT FROM AUTHOR]

The inverse eigenvalue problem and the associated optimal approximation problem for Hermitian reflexive matrices with respect to a normal { k + 1 } -potent matrix are considered. First, we study the existence of the solutions of the associated inverse eigenvalue problem and present an explicit form for them. Then, when such a solution exists, an expression for the solution to the corresponding optimal approximation problem is obtained. [ABSTRACT FROM AUTHOR]

A method for the computation ofinverses of a given matrixis derived, based on the full-rankdecomposition of an appropriate matrix. As a corollary, a new method considering the advantages of full-rankdecomposition is developed. It is then specialized to the set of polynomial matrices. Therefore, an algorithm for efficient symbolic computation ofinverses of a polynomial matrix is proposed. An additional diagonal matrixyields to avoiding the computation of entries containing square roots of polynomials, therefore increasing the algorithm’s performances. Some implementation details and comparative processing times to other similar methods are provided, illustrating the algorithm’s efficiency. [ABSTRACT FROM AUTHOR]

This paper is concerned with several variants of the Hermitian and skew-Hermitian splitting iteration method to solve a class of complex symmetric linear systems. Theoretical analysis shows that several Hermitian and skew-Hermitian splitting based iteration methods are unconditionally convergent. Numerical experiments from an n-degree-of-freedom linear system are reported to illustrate the efficiency of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We give a simple proof of a determinantal inequality due to Marcus (1976). [ABSTRACT FROM AUTHOR]