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MATHICSE Technical Report : Fast computation of spectral projectors of banded matrices

Publications associées (44)

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MATHICSE Technical Report : A fast spectral divide-and-conquer method for banded matrices

Daniel Kressner, Ana Susnjara

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. For this purpose, we c ...

MATHICSE2018

Fast Computation Of Spectral Projectors Of Banded Matrices

Daniel Kressner, Ana Susnjara

We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of small relative s ...

Siam Publications2017

MATHICSE Technical Report : Low-rank updates and a divideand- conquer method for linear matrix equations

Daniel Kressner, Stefano Massei

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...

MATHICSE2017

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image, or sketch, of the matrix. These methods can preserve structural properties of the input matrix, such as positive-semidefinite ...

Society for Industrial and Applied Mathematics2017

Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data

Volkan Cevher, Alp Yurtsever

Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retai ...

2017

ALS Scheme using Extent-based Constraints for the Analysis of Chemical Reaction Systems

Dominique Bonvin, Julien Léo Billeter, Michael Amrhein

Multivariate curve resolution via alternating least squares (ALS) is used to resolve the concentration profiles C and the pure component spectra E of S species from the multivariate absorbance data A, assuming the bilinear model ...

2016

Randomized Single-View Algorithms for Low-Rank Matrix Approximation

Volkan Cevher, Alp Yurtsever

This paper develops a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semideni ...

Under review2016

Fast recovery and approximation of hidden Cauchy structure

Robert Gerhard Jérôme Luce

We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a given matrix by ...

Elsevier Science Inc2016

Soft optical composites for tunable transmittance

Pedro Miguel Nunes Pereira de Almeida Reis, Sanjeev Kumar

We introduce a soft composite that is actuated mechanically to achieve switchable and tunable optical transmittance. Our design comprises a series of parallel opaque platelets embedded into an optically clear silicone-based elastomer matrix. Under an appli ...

2016

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We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first

k

eigenvectors of the similarity matrix' Laplacian, whose computati ...

Ieee2016

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We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first

k

eigenvectors of the similarity matrix' Laplacian, whose computati ...

Ieee2016