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A multigrid method is proposed in this paper to solve eigenvalue problems by the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to a series of…
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…
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…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
We propose a multigrid correction scheme to solve a new Steklov eigenvalue problem in inverse scattering. With this scheme, solving an eigenvalue problem in a fine finite element space is reduced to solve a series of boundary value problems…
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…
In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential…
In this paper, a full (nested) multigrid scheme is proposed to solve eigenvalue problems. The idea here is to use the multilevel correction method to transform the solution of eigenvalue problem to a series of solutions of the corresponding…
Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding critical points of a quadratic function…
We present a new power method to obtain solutions of eigenvalue problems. The method can determine not only the dominant or lowest eigenvalues but also all eigenvalues without the need for a deflation procedure. The method uses a functional…
A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in multigrid method, solving the eigenvalue problem in the finest space is…
A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by smoothing steps on a series of multilevel finite…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
This paper proposes and analyzes a new weak Galerkin method for the eigenvalue problem by using the shifted-inverse power technique. A high order lower bound can be obtained at a relatively low cost via the proposed method. The error…
In this paper, some enhanced error estimates are derived for the augmented subspace methods which are designed for solving eigenvalue problems. We will show that the augmented subspace methods have the second order convergence rate which is…
Low-rank tensor methods for the approximate solution of second-order elliptic partial differential equations in high dimensions have recently attracted significant attention. A critical issue is to rigorously bound the error of such…
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…
In this article, we study eigenvalue problems associated to self-adjoint operators and their approximation obtained by subspace projection, as used in the reduced basis method for instance. We provide error bounds between the exact…
In this paper, we first establish the convergence criteria of the residual iteration method for solving quadratic eigenvalue problem- s. We analyze the impact of shift point and the subspace expansion on the convergence of this method. In…