Search Results for author: Per-Gunnar Martinsson

Found 9 papers, 7 papers with code

Corrected Trapezoidal Rules for Boundary Integral Equations in Three Dimensions

1 code implementation6 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 implementations17 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 implementation6 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

1 code implementation8 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 implementation24 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 implementations18 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 implementation29 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

9 code implementations22 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

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