Density-matrix-based algorithm for solving eigenvalue problems

A Density Matrix-based Algorithm for Solving Eigenvalue Problems

A new numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques, and takes its inspiration from the contour integration and density matrix representation in quantum mechanics. It will be shown that this new...

On an enumerative algorithm for solving eigenvalue complementarity problems

In this paper, we discuss the solution of linear and quadratic eigenvalue complementarity problems (EiCPs) using an enumerative algorithm of the type introduced by Júdice et al. [1]. Procedures for computing the interval that contains all the eigenvalues of the linear EiCP are first presented. A nonlinear programming (NLP) model for the quadratic EiCP is formulated next, and a necessary and suf...

Homotopy-determinant Algorithm for Solving Nonsymmetric Eigenvalue Problems

The eigenvalues of a matrix A are the zeros of its characteristic polynomial fiX) = dtt[A XI]. With Hyman's method of determinant evaluation, a new homotopy continuation method, homotopy-determinant method, is developed in this paper for finding all eigenvalues of a real upper Hessenberg matrix. In contrast to other homotopy continuation methods, the homotopy-determinant method calculates eigen...

genetic algorithm based on explicit memory for solving dynamic problems

nowadays, it is common to find optimal point of the dynamic problem; dynamic problems whose optimal point changes over time require algorithms which dynamically adapt the search space instability. in the most of them, the exploitation of some information from the past allows to quickly adapt after an environmental change (some optimal points change). this is the idea underlining the use of memo...

Solving nonlinear eigenvalue problems