A Jacobi-Davidson-type projection method for nonlinear eigenvalue problems
نویسندگان
چکیده
This article discusses a projection method for nonlinear eigenvalue problems. The subspace of approximants is constructed by a Jacobi–Davidson type approach, and the arising eigenproblems of small dimension are solved by safeguarded iteration. The method is applied to a rational eigenvalue problem governing the vibrations of tube bundle immersed in an inviscid compressible fluid.
منابع مشابه
A Jacobi-Davidson Method for Nonlinear Eigenproblems
For the nonlinear eigenvalue problem T (λ)x = 0 we consider a Jacobi–Davidson type iterative projection method. The resulting projected nonlinear eigenvalue problems are solved by inverse iteration. The method is applied to a rational eigenvalue problem governing damped vibrations of a structure.
متن کاملProjection Methods for Nonlinear Sparse Eigenvalue Problems
This paper surveys numerical methods for general sparse nonlinear eigenvalue problems with special emphasis on iterative projection methods like Jacobi–Davidson, Arnoldi or rational Krylov methods and the automated multi–level substructuring. We do not review the rich literature on polynomial eigenproblems which take advantage of a linearization of the problem.
متن کاملIterative Projection Methods for Large–scale Nonlinear Eigenvalue Problems
In this presentation we review iterative projection methods for sparse nonlinear eigenvalue problems which have proven to be very efficient. Here the eigenvalue problem is projected to a subspace V of small dimension which yields approximate eigenpairs. If an error tolerance is not met then the search space V is expanded in an iterative way with the aim that some of the eigenvalues of the reduc...
متن کاملElectron energy level calculation for a three dimensional quantum dot
Abstract: In this paper we consider the rational eigenvalue problem governing the relevant energy levels and wave functions of a three dimensional quantum dot. We present iterative projection methods of Arnoldi and of Jacobi–Davidson type for computing a few eigenpairs of this system. Solving the projected nonlinear eigenvalue problems we take advantage of a minmax characterization of the eigen...
متن کاملA Jacobi-Davidson method for two-real-parameter nonlinear eigenvalue problems arising from delay-differential equations
The critical delays of a delay-differential equation can be computed by solving a nonlinear two-parameter eigenvalue problem. The solution of this two-parameter problem can be translated to solving a quadratic eigenvalue problem of squared dimension. We present a structure preserving QR-type method for solving such quadratic eigenvalue problem that only computes real valued critical delays, i.e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Future Generation Comp. Syst.
دوره 20 شماره
صفحات -
تاریخ انتشار 2004