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Perturbation theory of eigenvalue problems
Franz Rellich,B. J. Berkowitz +1 more
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The article was published on 1969-01-01 and is currently open access. It has received 600 citations till now. The article focuses on the topics: Inverse iteration & Eigenvalue perturbation.read more
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Error analysis and Cramer–Rao bound for convolutional beamspace
Po-Chih Chen,P.P. Vaidyanathan +1 more
TL;DR: In this article , the performance and Cramer-Rao bound for a recently proposed beamspace method, called convolutional beamspace (CBS), are studied. And the variance is derived from the asymptotic probability distribution of the eigenvectors of an average finite-snapshot covariance matrix, while the bias due to the filtered stopband sources is given by first-order perturbation analysis.
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Spectral resolutions for non-self-adjoint block convolution operators
TL;DR: In this article , the spectral theory for a class of non-self-adjoint block convolution operators is discussed. But the main results are applied to periodic Jacobi matrices and not to the general case of operators defined on Banach spaces.
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Local uniform convergence and eventual positivity of solutions to biharmonic heat equations
TL;DR: In this paper , the evolution equation associated with the biharmonic operator on infinite cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions was studied and the authors derived the local eventual positivity of solutions.
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Vector-wise Joint Diagonalization of Almost Commuting Matrices
Bowen Li,Jianfeng Lu,Ziang Yu +2 more
TL;DR: This work aims to numerically construct exactly commuting matrices close to given almost commuting ones, which is equivalent to the joint approximate diagonalization problem, and proposes a fast and robust vector-wise joint diagonalization (VJD) algorithm, which constructs the orthogonal similarity transform by sequentially finding approximate common eigenvectors.
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Shape perturbation of Grushin eigenvalues
TL;DR: In this article, the spectral problem for the Grushin Laplacian subject to homogeneous Dirichlet boundary conditions on a bounded open subset of $\mathbb{R}^N$ was considered.