A Smallest Singular Value Method for Solving Inverse Eigenvalue Problems
نویسنده
چکیده
Utilizing the properties of the smallest singular value of a matrix, we propose a new, efficient and reliable algorithm for solving nonsymmetric matrix inverse eigenvalue problems, and compare it with a known method. We also present numerical experiments which illustrate our results.
منابع مشابه
Preconditioned Iterative Methods for Linear Systems, Eigenvalue and Singular Value Problems
In the present dissertation we consider three crucial problems of numerical linear algebra: solution of a linear system, an eigenvalue, and a singular value problem. We focus on the solution methods which are iterative by their nature, matrix-free, preconditioned and require a fixed amount of computational work per iteration. In particular, this manuscript aims to contribute to the areas of res...
متن کاملOn the Convergence of a New Rayleigh Quotient Method with Applications to Large Eigenproblems
In this paper we propose a variant of the Rayleigh quotient method to compute an eigenvalue and corresponding eigenvectors of a matrix. It is based on the observation that eigenvectors of a matrix with eigenvalue zero are also singular vectors corresponding to zero singular values. Instead of computing eigenvector approximations by the inverse power method, we take them to be the singular vecto...
متن کاملSOLVING SINGULAR ODES IN UNBOUNDED DOMAINS WITH SINC-COLLOCATION METHOD
Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...
متن کاملComputation of Pseudospectral Abscissa for Large Scale Nonlinear Eigenvalue Problems
We present an algorithm to compute the pseudospectral abscissa for a nonlinear eigenvalue problem. The algorithm relies on global under-estimator and over-estimator functions for the eigenvalue and singular value functions involved. These global models follow from eigenvalue perturbation theory. The algorithm has three particular features. First, it converges to the globally rightmost point of ...
متن کاملOn the Convergence of the Arnoldi Process for Eigenvalue Problems
This paper takes another look at the convergence of the Arnoldi procedure forsolving nonsymmetric eigenvalue problems. Three different viewpoints are considered. The first usesa bound on the distance from the eigenvector to the Krylov subspace from the smallest singularvalue of matrix consisting of the Krylov basis. A second approach relies on the Schur factorization.Finally, a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006