On A Perturbation Bound For Invariant Subspaces Of Matrices

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The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...

2021

Graph-Homomorphic Perturbations For Private Decentralized Learning

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Decentralized algorithms for stochastic optimization and learning rely on the diffusion of information through repeated local exchanges of intermediate estimates. Such structures are particularly appealing in situations where agents may be hesitant to shar ...

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A fast spectral divide-and-conquer method for banded matrices

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Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...

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hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

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Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, t ...

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Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

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Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...

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Kinetic Euclidean Distance Matrices

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Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static objects which serve to localize point ...

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It has been well established that Functional Connectomes (FCs), as estimated from functional MRI (fMRI) data, have an individual fingerprint that can be used to identify an individual from a population (subject-identification). Although identification rate ...

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hm-toolbox: Matlab software for HODLR and HSS matrices

Daniel Kressner, Stefano Massei

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The index of singular zeros of harmonic mappings of anti-analytic degree one

Robert Gerhard Jérôme Luce

We study harmonic mappings of the form , where h is an analytic function. In particular, we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the critical set of f, where the Jacobian of f is non-vanishing, it ...

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On The Behavior Of Clamped Plates Under Large Compression

We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical ...

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The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

2021