Randomized Algorithms for Scientific Computing (RASC)

no code implementations • 19 Apr 2021 • Aydin Buluc, Tamara G. Kolda, Stefan M. Wild, Mihai Anitescu, Anthony DeGennaro, John Jakeman, Chandrika Kamath, Ramakrishnan Kannan, Miles E. Lopes, Per-Gunnar Martinsson, Kary Myers, Jelani Nelson, Juan M. Restrepo, C. Seshadhri, Draguna Vrabie, Brendt Wohlberg, Stephen J. Wright, Chao Yang, Peter Zwart

Randomized algorithms have propelled advances in artificial intelligence and represent a foundational research area in advancing AI for Science.

Corrected Trapezoidal Rules for Boundary Integral Equations in Three Dimensions

1 code implementation • 6 Jul 2020 • BoWei Wu, Per-Gunnar Martinsson

The key finding of the manuscript is that the convergence order can be greatly improved by modifying only a very small number of elements in the coefficient matrix.

Numerical Analysis Numerical Analysis 65R20 (primary) 65D32, 45B05 (secondary)

Computing rank-revealing factorizations of matrices stored out-of-core

no code implementations • 17 Feb 2020 • Nathan Heavner, Per-Gunnar Martinsson, Gregorio Quintana-Ortí

This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in RAM, and must instead be stored on slow external memory devices such as solid-state or spinning disk hard drives (out-of-core or out-of-memory).

Randomized methods for matrix computations

1 code implementation • 6 Jul 2016 • Per-Gunnar Martinsson

The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices.

Numerical Analysis

Householder QR Factorization with Randomization for Column Pivoting (HQRRP). FLAME Working Note #78

2 code implementations • 8 Dec 2015 • Per-Gunnar Martinsson, Gregorio Quintana-Orti, Nathan Heavner, Robert van de Geijn

A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrix-matrix multiplications, which greatly limits the benefits that can be derived from so-called blocking of algorithms.

Numerical Analysis Numerical Analysis

A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices

1 code implementation • 24 Mar 2015 • Per-Gunnar Martinsson, Sergey Voronin

The method takes as input a tolerance $\varepsilon$ and an $m\times n$ matrix $A$, and returns an approximate low rank factorization of $A$ that is accurate to within precision $\varepsilon$ in the Frobenius norm (or some other easily computed norm).

Numerical Analysis

RSVDPACK: An implementation of randomized algorithms for computing the singular value, interpolative, and CUR decompositions of matrices on multi-core and GPU architectures

5 code implementations • 18 Feb 2015 • Sergey Voronin, Per-Gunnar Martinsson

The ID and CUR factorizations pick subsets of the rows/columns of a matrix to use as bases for its row/column space.

Numerical Analysis Mathematical Software

Efficient Algorithms for CUR and Interpolative Matrix Decompositions

1 code implementation • 29 Dec 2014 • Sergey Voronin, Per-Gunnar Martinsson

The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions.

Numerical Analysis Numerical Analysis

Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions

10 code implementations • 22 Sep 2009 • Nathan Halko, Per-Gunnar Martinsson, Joel A. Tropp

These methods use random sampling to identify a subspace that captures most of the action of a matrix.

Numerical Analysis Probability