Verified partial eigenvalue computations using contour integrals for Hermitian generalized eigenproblems
TL;DR: A verified computation method for partial eigenvalues of a Hermitian generalized eigenproblem of block Hankel matrices whose entries consist of complex moments is proposed and a truncation error bound of the quadrature is derived.
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About: This article is published in Journal of Computational and Applied Mathematics. The article was published on 01 May 2020. and is currently open access. The article focuses on the topics: Hermitian matrix & Eigenvalues and eigenvectors.
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Citations
Fast verification for the Perron pair of an irreducible nonnegative matrix
TL;DR: Fast algorithms are proposed for calculating error bounds for a numerically computed Perron root and vector of an irreducible nonnegative matrix based on the Collatz--Wielandt theorem and estimating a solution of a linear system whose coefficient matrix is an $M$-matrix.
Complex moment-based methods for differential eigenvalue problems
TL;DR: In this paper , the authors proposed operation analogues of Sakurai-Sugiura-type complex moment-based eigensolvers using higher-order complex moments and analyzed the error bound of the proposed methods.
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Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh-Ritz procedure for generalized Hermitian eigenvalue problems.
TL;DR: In this article, the authors proposed a verified computation method for eigenvalues in a region and the corresponding eigenvectors of generalized Hermitian eigenvalue problems, which uses complex moments to extract the eigencomponents of interest from a random matrix and uses the Rayleigh-Ritz procedure to project a given eigen value problem into a reduced Eigenvalue problem.
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An enhanced argument principle algorithm for exact complex transcendental eigenvalue analysis of damped structures
Xiang Liu,Dalun Tang,Xiao Liu +2 more
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A filter diagonalization for generalized eigenvalue problems based on the Sakurai-Sugiura projection method
TL;DR: The Sakurai-Sugiura projection method, which solves generalized eigenvalue problems to find certain eigenvalues in a given domain, was reformulated by using the resolvent theory.
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Verification of Positive Definiteness
TL;DR: A computational, simple and fast sufficient criterion to verify positive definiteness of a symmetric or Hermitian matrix is presented, based on a floating-point Cholesky decomposition and improves a known result.
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