The Shooting Method for Solving 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.

Direct multiple shooting method for solving approximate shortest path problems

An integral method for solving nonlinear eigenvalue problems

We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the resolvent operator, applied to at least k column vectors, where k is the number of eigenvalues inside the contour. The theorem of Keldysh is employed to show t...

A numerical method for solving inverse eigenvalue problems

Based on QR~\ike décomposition with column pivoting, a new and efficient numerical method for solving symmetrie matrix inverse eigenvalue problems is proposed, which is suitable for both the distinct and multiple eigenvalue cases. A locally quadratic convergence analysis is given. Some numerical experiments are presented to illustrate our results. Résumé. Basée sur la décomposition QR-iype avec...

A Jacobi-Davidson Method for Solving Complex Symmetric Eigenvalue Problems

We discuss variants of the Jacobi–Davidson method for solving the generalized complex-symmetric eigenvalue problem. The Jacobi–Davidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean inner product xy in C by the bilinear form x y. The Rayleigh quotient based on this bilinear form leads to an asymptotical...