Large-order shifted 1/Nexpansions through the asymptotic iteration method

Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y = λ0(x)y ′ + s0(x)y is introduced, where λ0(x) 6= 0 and s0(x) are C∞ functions. Applications to Schrödinger type problems, including some with highly singular potentials, are presented. PACS 03.65.Ge Asymptotic iteration method for eigenvalue problems page 2

Inverse, Shifted Inverse, and Rayleigh Quotient Iteration as Newton's Method

Two-norm normalized inverse, shifted inverse, and Rayleigh quotient iteration are well-known algorithms for approximating an eigenvector of a symmetric matrix. In this work we establish rigorously that each one of these three algorithms can be viewed as a standard form of Newton’s method from the nonlinear programming literature, followed by the normalization. This equivalence adds considerable...

The variational iteration method for a class of tenth-order boundary value differential equations

Dynamic Iteration Using Reduced Order Models: A Method for Simulation of Large Scale Modular Systems

We describe a new iterative method, dynamic iteration using reduced order models (DIRM), for simulation of large scale modular systems using reduced order models that preserve the interconnection structure. This method may be compared to the waveform relaxation technique; however, unlike DIRM, waveform relaxation does not take advantage of model reduction techniques. The DIRM method involves si...

On controllability of the real shifted inverse power iteration