Continuous Decompositions and Coalescing Eigenvalues for Matrices Depending on Parameters

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The Transfer Matrix formalism is ubiquitous when it comes to study wave propagation in various stratified media, applications ranging from Seismology to Quantum Mechanics. A relation between variables at two points in two different layers can be establishe ...

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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 ...

This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified conve ...

Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of x(T) Bx for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number ...

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 ...

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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This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm for constructing ...

The present invention concerns a method of displaying an image on a see-through display. The method comprises: obtaining (101) a first electromagnetic radiation matrix of an object, the first matrix comprising first matrix elements representing radiation i ...

Continuous Decompositions and Coalescing Eigenvalues for Matrices Depending on Parameters

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Spectral Estimators for High-Dimensional Matrix Inference

Randomized low-rank approximation and its applications

Duality and bicrystals on infinite binary matrices

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Preconditioning techniques for generalized Sylvester matrix equations

Optimal denoising of rotationally invariant rectangular matrices

Iterative refinement of Schur decompositions

Harmonic decomposition of the trace of 1D transfer matrices in layered media

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation

Robust Differentiable SVD

Efficient Learning of a Linear Dynamical System with Stability Guarantees

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

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Kinetic Euclidean Distance Matrices

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

Evaporation of Metals during the Thermal Treatment of Oxide Nanomaterials in Cellulose-Based Matrices

Streaming Low-Rank Matrix Approximation With An Application To Scientific Simulation

Method of displaying an image on a see-through display