Publications related to Fast hierarchical solvers for symmetric eigenvalue problems

MATHICSE Technical Report : A reduced basis approach to large-scale pseudospectra computation

For studying spectral properties of a non-normal matrix A ∈ Cn×n, information about its spectrum σ(A) alone is usually not enough. Effects of perturbations on σ(A) can be studied by computing ε-pseudospectra, that is the level-sets of the resolvent norm fu ...

MATHICSE2016

Accelerated Spectral Clustering Using Graph Filtering of Random Signals

Pierre Vandergheynst, Rémi Gribonval, Gilles Puy, Nicolas Tremblay

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

Projection Methods For Large-Scale T-Sylvester Equations

Daniel Kressner

The matrix Sylvester equation for congruence, or T-Sylvester equation, has recently attracted considerable attention as a consequence of its close relation to palindromic eigenvalue problems. The theory concerning T-Sylvester equations is rather well under ...

Amer Mathematical Soc2016

Converse Bounds for Noisy Group Testing with Arbitrary Measurement Matrices

Volkan Cevher, Jonathan Mark Scarlett

We consider the group testing problem, in which one seeks to identify a subset of defective items within a larger set of items based on a number of noisy tests. While matching achievability and converse bounds are known in several cases of interest for i.i ...

Ieee2016

Iterative signal separation based multiple phase estimation in digital holographic interferometry

Pramod Rastogi, Rishikesh Dilip Kulkarni

We propose a new method for signal separation from a multicomponent interference field recorded in a digital holographic interferometry setup. The setup consisting of multiple object illuminating beams results in an interference field containing multiple s ...

Optical Society of America2015

A reduced basis localized orthogonal decomposition

Assyr Abdulle, Patrick Henning

In this work we combine the framework of the Reduced Basis method (RB) with the framework of the Localized Orthogonal Decomposition (LOD) in order to solve parametrized elliptic multiscale problems. The idea of the LOD is to split a high dimensional Finite ...

2015

MATHICSE Technical Report: Fast recovery and approximation of hidden Cauchy structure

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 ...

MATHICSE2015

Measurement and Shaping of Biphoton Spectral Wave Functions

In this work we present a simple method to reconstruct the complex spectral wave function of a biphoton, and hence gain complete information about the spectral and temporal properties of a photon pair. The technique, which relies on quantum interference, i ...

Amer Physical Soc2015

Evaluating functions of positive-definite matrices using colored-noise thermostats

Michele Ceriotti, Michele Parrinello

Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scal ...

Amer Physical Soc2014

Structured Sparse Coding for Image Denoising or Pattern Detection

Pascal Frossard, Sofia Karygianni

Sparsity has been one of the major drives in signal processing in the last decade. Structured sparsity has also lately emerged as a way to enrich signal priors towards more meaningful and accurate representations. In this paper we propose a new structured ...

2014

Fast hierarchical solvers for symmetric eigenvalue problems

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MATHICSE Technical Report : A reduced basis approach to large-scale pseudospectra computation

Accelerated Spectral Clustering Using Graph Filtering of Random Signals

Projection Methods For Large-Scale T-Sylvester Equations

Converse Bounds for Noisy Group Testing with Arbitrary Measurement Matrices

Iterative signal separation based multiple phase estimation in digital holographic interferometry

A reduced basis localized orthogonal decomposition

MATHICSE Technical Report: Fast recovery and approximation of hidden Cauchy structure

Measurement and Shaping of Biphoton Spectral Wave Functions

Evaluating functions of positive-definite matrices using colored-noise thermostats

Structured Sparse Coding for Image Denoising or Pattern Detection

Projection Methods For Large-Scale T-Sylvester Equations

Evaluating functions of positive-definite matrices using colored-noise thermostats

Structured Sparse Coding for Image Denoising or Pattern Detection

A reduced basis localized orthogonal decomposition

MATHICSE Technical Report : A reduced basis approach to large-scale pseudospectra computation

MATHICSE Technical Report: Fast recovery and approximation of hidden Cauchy structure

Converse Bounds for Noisy Group Testing with Arbitrary Measurement Matrices

Iterative signal separation based multiple phase estimation in digital holographic interferometry

Accelerated Spectral Clustering Using Graph Filtering of Random Signals

Measurement and Shaping of Biphoton Spectral Wave Functions