# Randomized Algorithms for Scientific Computing (RASC)

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 implementation6 Jul 2020,

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)

2

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

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

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

Numerical Analysis

7

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

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

6

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

1 code implementation24 Mar 2015,

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

66

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

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

99

# Efficient Algorithms for CUR and Interpolative Matrix Decompositions

1 code implementation29 Dec 2014,

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

Numerical Analysis Numerical Analysis

66

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

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

Numerical Analysis Probability

99
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