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We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…

Numerical Analysis · Mathematics 2021-05-12 Henrik Eisenmann , Yuji Nakatsukasa

A multigrid method is proposed for solving nonlinear eigenvalue problems by the finite element method. With this new scheme, solving nonlinear eigenvalue problem is decomposed to a series of solutions of linear boundary value problems on…

Numerical Analysis · Mathematics 2015-01-09 Hehu Xie

We consider the numerical computation of resonances for metallic grating structures with dispersive media and small slit holes. The underlying eigenvalue problem is nonlinear and the mathematical model is multiscale due to the existence of…

Numerical Analysis · Mathematics 2024-03-08 Yingxia Xi , Junshan Lin , Jiguang Sun

We propose an algorithm for general nonlinear eigenvalue problems to compute physically relevant eigenvalues within a chosen contour. Eigenvalue information is explored by contour integration incorporating different weight functions. The…

Computational Physics · Physics 2020-11-19 Felix Binkowski , Lin Zschiedrich , Sven Burger

The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-12-17 Hesam T. Dashti , Alireza F. Siahpirani , Liya Wang , Mary Kloc , Amir H. Assadi

This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…

Numerical Analysis · Mathematics 2016-11-03 Shanghui Jia , Hehu Xie , Manting Xie , Fei Xu

Recently, a kind of eigensolvers based on contour integral were developed for computing the eigenvalues inside a given region in the complex plane. The CIRR method is a classic example among this kind of methods. In this paper, we propose a…

Numerical Analysis · Mathematics 2015-08-19 Guojian Yin

We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…

Numerical Analysis · Mathematics 2015-11-13 Yunhui He , Yu Li , Hehu Xie

This paper proposes a rational filtering domain decomposition technique for the solution of large and sparse symmetric generalized eigenvalue problems. The proposed technique is purely algebraic and decomposes the eigenvalue problem…

Numerical Analysis · Mathematics 2017-11-28 Vassilis Kalantzis , Yuanzhe Xi , Yousef Saad

This paper proposes a parallel in time (called also time parareal) method to solve Volterra integral equations of the second kind. The parallel in time approach follows the same spirit as the domain decomposition that consists of breaking…

Numerical Analysis · Mathematics 2016-11-26 Xianjuan Li , Tao Tang , Chuanju Xu

We present a method to linearize, without approximation, a specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the nonlinearities are expressed by scalar functions that are defined by a quotient of linear…

Numerical Analysis · Mathematics 2021-05-24 Rob Claes , Elias Jarlebring , Karl Meerbergen , Parikshit Upadhyaya

The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental…

Mathematical Physics · Physics 2020-07-27 Qing-hai Wang

We propose subspace methods for 3-parameter eigenvalue problems. Such problems arise when separation of variables is applied to separable boundary value problems; a particular example is the Helmholtz equation in ellipsoidal and…

Numerical Analysis · Mathematics 2023-09-18 Michiel E. Hochstenbach , Karl Meerbergen , Emre Mengi , Bor Plestenjak

Contour integral algorithms seek to compute a small number of eigenvalues located within a bounded region of the complex plane. These methods can be applied to both linear and nonlinear matrix eigenvalue problems. In the latter case, the…

Numerical Analysis · Mathematics 2026-01-06 Linus Balicki , Mark Embree , Serkan Gugercin

A two-stage batch estimation algorithm for solving a class of nonlinear, static parameter estimation problems that appear in aerospace engineering applications is proposed. It is shown how these problems can be recast into a form suitable…

Signal Processing · Electrical Eng. & Systems 2020-02-18 Kerry Sun , Demoz Gebre-Egziabher

We present two approximation methods for computing eigenfrequencies and eigenmodes of large-scale nonlinear eigenvalue problems resulting from boundary element method (BEM) solutions of some types of acoustic eigenvalue problems in…

Numerical Analysis · Mathematics 2024-09-23 Mohamed El-Guide , Agnieszka Miedlar , Yousef Saad

We propose an efficient numerical method for a non-selfadjoint Steklov eigenvalue problem. The Lagrange finite element is used for discretization. The convergence is proved using the spectral perturbation theory for compact operators. The…

Numerical Analysis · Mathematics 2018-04-10 Juan Liu , Jiguang Sun , Tiara Turner

We propose a multi-threshold change plane regression model which naturally partitions the observed subjects into subgroups with different covariate effects. The underlying grouping variable is a linear function of covariates and thus…

Methodology · Statistics 2018-08-03 Jialiang Li , Yaguang Li , Baisuo Jin

The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…

Numerical Analysis · Mathematics 2020-03-02 Ning Zhang , Xiaole Han , Yunhui He , Hehu Xie , Chun'guang You

Investigating the stability of nonlinear waves often leads to linear or nonlinear eigenvalue problems for differential operators on unbounded domains. In this paper we propose to detect and approximate the point spectra of such operators…

Numerical Analysis · Mathematics 2012-10-16 Wolf-Juergen Beyn , Yuri Latushkin , Jens Rottmann-Matthes