Randomized algorithms in numerical linear algebra

IF 16.3 1区数学 Q1 MATHEMATICS Acta Numerica Pub Date : 2017-05-01 DOI:10.1017/S0962492917000058

R. Kannan, S. Vempala

引用次数: 52

Abstract

This survey provides an introduction to the use of randomization in the design of fast algorithms for numerical linear algebra. These algorithms typically examine only a subset of the input to solve basic problems approximately, including matrix multiplication, regression and low-rank approximation. The survey describes the key ideas and gives complete proofs of the main results in the field. A central unifying idea is sampling the columns (or rows) of a matrix according to their squared lengths.

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数值线性代数中的随机化算法

这项调查介绍了在设计数值线性代数的快速算法时使用随机化。这些算法通常只检查输入的子集，以近似地解决基本问题，包括矩阵乘法、回归和低阶近似。调查描述了关键思想，并对该领域的主要结果提供了完整的证明。统一的核心思想是根据矩阵的列（或行）的平方长度对其进行采样。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Numerica MATHEMATICS-

CiteScore

26.00

自引率

0.70%

发文量

期刊介绍： Acta Numerica stands as the preeminent mathematics journal, ranking highest in both Impact Factor and MCQ metrics. This annual journal features a collection of review articles that showcase survey papers authored by prominent researchers in numerical analysis, scientific computing, and computational mathematics. These papers deliver comprehensive overviews of recent advances, offering state-of-the-art techniques and analyses. Encompassing the entirety of numerical analysis, the articles are crafted in an accessible style, catering to researchers at all levels and serving as valuable teaching aids for advanced instruction. The broad subject areas covered include computational methods in linear algebra, optimization, ordinary and partial differential equations, approximation theory, stochastic analysis, nonlinear dynamical systems, as well as the application of computational techniques in science and engineering. Acta Numerica also delves into the mathematical theory underpinning numerical methods, making it a versatile and authoritative resource in the field of mathematics.

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