Hymnia — Band matrix package 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...

Solving nonlinear eigenvalue problems

Solving Overdetermined Eigenvalue Problems

We propose a new interpretation of the generalized overdetermined eigenvalue problem (A− λB)v ≈ 0 for two m × n (m > n) matrices A and B, its stability analysis, and an efficient algorithm for solving it. Usually, the matrix pencil {A− λB} does not have any rank deficient member. Therefore we aim to compute λ for which A − λB is as close as possible to rank deficient; i.e., we search for λ that...

The Shooting Method for Solving Eigenvalue Problems

The shooting method is a numerically effective approach to solving certain eigenvalue problems, such as that arising from the Schrödinger equation for the two-dimensional hydrogen atom with logarithmic potential function. However, no complete proof of its rationale and correctness has been given until now. This paper gives the proof, in a generalized form.

MATLAB tools for solving periodic eigenvalue problems

Software for computing eigenvalues and invariant subspaces of general matrix products is proposed. The implemented algorithms are based on orthogonal transformations of the original data and thus attain numerical backward stability, which enables good accuracy even for small eigenvalues. The prospective toolbox combines the efficiency and robustness of library-style Fortran subroutines based on...