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Introduction to Eigenvalue Problems
This chapter provides an overview of the literature concerning explicit eigenvalue bounds achieved through numerical methods. It outlines the rapid...
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Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems
This monograph presents a study of newly developed guaranteed computational methodologies for eigenvalue problems of self-adjoint differential...
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Analysis of eigenvalue condition numbers for a class of randomized numerical methods for singular matrix pencils
The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues....
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Multiscale asymptotic analysis and algorithm for the quadratic eigenvalue problem in composite materials
A novel second-order two-scale(SOTS) asymptotic analysis and computational approach are developed for solving the quadratic eigenvalue problem(QEP)...
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A Novel Domain Decomposition Method for Eigenvalue Problems
A novel domain decomposition method is proposed in this paper to solve eigenvalue problems. Both the simple and multiple eigenvalues are considered...
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A Robust Randomized Indicator Method for Accurate Symmetric Eigenvalue Detection
We propose a robust randomized indicator method for the reliable detection of eigenvalue existence within an interval for symmetric matrices A . An...
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Eigenvalue programming beyond matrices
In this paper we analyze and solve eigenvalue programs, which consist of the task of minimizing a function subject to constraints on the...
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A discontinuous Galerkin method for Maxwell’s transmission eigenvalue problem
We propose an interior penalty discontinuous Galerkin (IPDG) method for the Maxwell’s transmission eigenvalue problem. First we reformulate the...
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Analysis of a Fourier–Galerkin Method for the Transmission Eigenvalue Problem based on a Boundary Integral Formulation
We consider the computation of the transmission eigenvalue problem based on a boundary integral formulation. The problem is formulated as the...
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Explicit Eigenvalue Bounds for Various Differential Operators
This chapter extends the theorem in Chap. 3 and applies it, in conjunction with the conforming and...
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Multilevel local defect-correction method for the non-selfadjoint Steklov eigenvalue problems
In this paper, we design a multilevel local defect-correction method to solve the non-selfadjoint Steklov eigenvalue problems. Since the computation...
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Multilevel Monte Carlo Methods for Stochastic Convection–Diffusion Eigenvalue Problems
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection–diffusion...
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Manifolds with Density and the First Steklov Eigenvalue
There are many interesting eigenvalue problems in a variety of settings; one of them is the well-known Steklov eigenvalue problem. In this work, we...
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Rectangular eigenvalue problems
Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are...
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Jacobi method for dual quaternion Hermitian eigenvalue problems and applications
Eigenvalue decomposition of quaternion Hermitian matrices is a crucial mathematical tool for color image reconstruction and recognition. Quaternion...
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Second-Order Three-Scale Asymptotic Analysis and Algorithms for Steklov Eigenvalue Problems in Composite Domain with Hierarchical Cavities
A top–down strategy based on the second-order asymptotic method is proposed for solving the Steklov eigenvalue problems on composite perforated...
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The Infinity Laplacian Eigenvalue Problem: Reformulation and a Numerical Scheme
In this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for...
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An Augmented Two-Scale Finite Element Method for Eigenvalue Problems
In this paper, an augmented two-scale finite element method is proposed for a class of linear and nonlinear eigenvalue problems on tensor-product...
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Generalized eigenvalue problem for interval matrices
In this paper, the generalized eigenvalue problem for a pair of interval matrices is studied. First, the interval enclosures of every generalized...
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On a Nonlinear Dirichlet Eigenvalue Problem
In this work, considering a mixed operator composed of the p-Laplacian and the Laplacian, we study a generalized spectral problem with Dirichlet...