Solutions to a quadratic inverse eigenvalue problem

General Solutions for a Class of Inverse Quadratic Eigenvalue Problems

Based on various matrix decompositions, we compare different techniques for solving the inverse quadratic eigenvalue problem, where n× n real symmetric matrices M , C and K are constructed so that the quadratic pencil Q(λ) = λM + λC + K yields good approximations for the given k eigenpairs. We discuss the case where M is positive definite for 1≤ k ≤ n, and a general solution to this problem for...

An Algebraic Solution to the Spectral Factorization Problem

The problem of giving a spectral factorization of a class of matrices arising in Wiener filtering theory and network synthesis is tackled via an kgebralc procedure. A quadratic matrix quation involving only constant matrices is shown to possess solutions which directly define a solution to the spectral factorization problem. A spectral factor with a stable inverse is defined by that unique solu...

Inverse Laplace transform method for multiple solutions of the fractional Sturm-Liouville problems

In this paper, inverse Laplace transform method is applied to analytical solution of the fractional Sturm-Liouville problems. The method introduces a powerful tool for solving the eigenvalues of the fractional Sturm-Liouville problems. The results  how that the simplicity and efficiency of this method.

Some results on the symmetric doubly stochastic inverse eigenvalue problem

‎The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$‎, ‎to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$‎. ‎If there exists an $ntimes n$ symmetric doubly stochastic ...

Solutions of the Partially Described Inverse Quadratic Eigenvalue Problem