The Waveguide Eigenvalue Problem and the Tensor Infinite Arnoldi Method
نویسندگان
چکیده
منابع مشابه
The Waveguide Eigenvalue Problem and the Tensor Infinite Arnoldi Method
We present a new computational approach for a class of large-scale nonlinear eigenvalue problems (NEPs) that are nonlinear in the eigenvalue. The contribution of this paper is two-fold. We derive a new iterative algorithm for NEPs, the tensor infinite Arnoldi method (TIAR), which is applicable to a general class of NEPs, and we show how to specialize the algorithm to a specific NEP: the wavegui...
متن کاملAn Arnoldi like method for the delay eigenvalue problem
The method called Arnoldi is currently a very popular method to solve largescale eigenvalue problems. The general purpose of this paper is to generalize Arnoldi to the characteristic equation of a delay-differential equation (DDE), here called a delay eigenvalue problem. The DDE can equivalently be expressed with a linear infinite dimensional operator which eigenvalues are the solutions to the ...
متن کاملComputing a Partial Schur Factorization of Nonlinear Eigenvalue Problems Using the Infinite Arnoldi Method
The partial Schur factorization can be used to represent several eigenpairs of a matrix in a numerically robust way. Different adaptions of the Arnoldi method are often used to compute partial Schur factorizations. We propose here a technique to compute a partial Schur factorization of a nonlinear eigenvalue problem (NEP). The technique is inspired by the algorithm in [8], now called the infini...
متن کاملThe Quadratic Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem
The Quadratic Arnoldi algorithm is an Arnoldi algorithm for the solution of the quadratic eigenvalue problem, that exploits the structure of the Krylov vectors. This allows us to reduce the memory requirements by about a half. The method is an alternative to the Second Order Arnoldi method (SOAR). In the SOAR method it is not clear how to perform an implicit restart. We discuss various choices ...
متن کاملAn Arnoldi Method for Nonlinear Eigenvalue Problems
For the nonlinear eigenvalue problem T (λ)x = 0 we propose an iterative projection method for computing a few eigenvalues close to a given parameter. The current search space is expanded by a generalization of the shift-and-invert Arnoldi method. The resulting projected eigenproblems of small dimension are solved by inverse iteration. The method is applied to a rational eigenvalue problem gover...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2017
ISSN: 1064-8275,1095-7197
DOI: 10.1137/15m1044667