Solving Overdetermined 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...

Solving nonlinear eigenvalue problems

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.

Solving Eigenvalue Problems on Networks of Processors

In recent times the work on networks of processors has become very important, due to the low cost and the availability of these systems. This is why it is interesting to study algorithms on networks of processors. In this paper we study on networks of processors different Eigenvalue Solvers. In particular, the Power method, deflation, Givens algorithm, Davidson methods and Jacobi methods are an...

Solving inverse cone-constrained eigenvalue problems

We compare various algorithms for constructing a matrix of order n whose Pareto spectrum contains a prescribed set Λ = {λ1, . . . , λp} of reals. In order to avoid overdetermination one assumes that p does not exceed n2. The inverse Pareto eigenvalue problem under consideration is formulated as an underdetermined system of nonlinear equations. We also address the issue of computing Lorentz spec...