hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

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We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

A new approach is presented to obtain a convex set of robust D—stabilizing fixed structure controllers, relying on Cauchy's argument principle. A convex set of D—stabilizing controllers around an initial D—stabilizing controller for a multi-model set is re ...

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices. In the first part, we consider algorithms for building ...

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...

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 ...

We give a construction of an efficient one-out-of-many proof system, in which a prover shows that he knows the pre-image for one element in a set, based on the hardness of lattice problems. The construction employs the recent zero-knowledge framework of Ly ...

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smal ...

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

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

A convex set of robust D—stabilizing controllers using Cauchy's argument principle

The double exponential runtime is tight for 2-stage stochastic ILPs

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

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Iterative refinement of Schur decompositions

Optimal denoising of rotationally invariant rectangular matrices

Robust Differentiable SVD

Fast global spectral methods for three-dimensional partial differential equations

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

BLOOM: Bimodal Lattice One-out-of-Many Proofs and Applications

Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems