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The second smallest normalized Laplacian eigenvalue of unicyclic graphs
In this paper, the unique graph with the minimal second smallest normalized Laplacian eigenvalue of unicyclic graphs with fixed girth is determined.
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Upper Bounds on the Smallest Positive Eigenvalue of Trees
In this article, we undertake the problem of finding the first four trees on a fixed number of vertices with the maximum smallest positive...
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Shifted Inverse Power Method for Computing the Smallest M-Eigenvalue of a Fourth-Order Partially Symmetric Tensor
The strong ellipticity condition (abbr. SE-condition) of the displacement equations of equilibrium for general nonlinearly elastic materials plays an...
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Recent Progress on Graphs with Fixed Smallest Adjacency Eigenvalue: A Survey
We give a survey on graphs with fixed smallest adjacency eigenvalue, especially on graphs with large minimal valency and also on graphs with good...
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Eigenvalue Problems of Second Order Linear Elliptic Operators
Eigenvalue problems have a wide range of applications. In particular, the existence of positive solutions to second order semi-linear and...
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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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Eigenvalue Problems
One of the central problems considered in this chapter is: given an \(n \times n\)...
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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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Extremal inverse eigenvalue problem for matrices described by a connected unicyclic graph
In this paper, we deal with the construction of symmetric matrix whose corresponding graph is connected and unicyclic using some pre-assigned...
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An Efficient GIPM Algorithm for Computing the Smallest V-Singular Value of the Partially Symmetric Tensor
Real partially symmetric tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum...
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Eigenvalue Problems
In this section we investigate the eigenvalue problem for the Laplace–Beltrami operator Δω on the unit sphere...
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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 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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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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On flexible block Chebyshev-Davidson method for solving symmetric generalized eigenvalue problems
In a recent work (J. Sci. Comput. 85 (2020), no. 3), the author generalized the Chebyshev-Davidson method appeared in standard eigenvalue problems to...
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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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Fast SVD-Based Linear Elastic Eigenvalue Problem Solver for Band Structures of 3D Phononic Crystals
In this article, a Fast Linear Elastic Eigenvalue Problem Solver (FLEEPS) is developed to calculate the band structures of three-dimensional (3D)...
