On the Best Approximation Algorithm by Low-Rank Matrices in Chebyshev's Norm

被引：4

作者：

Zamarashkin, N. L. ^{[1
]}

Morozov, S., V ^{[1
]}

Tyrtyshnikov, E. E. ^{[1
]}

机构：

[1] Russian Acad Sci, Marchuk Inst Numer Math, Moscow 119333, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2022年 / 62卷 / 05期

基金：

俄罗斯科学基金会;

关键词：

approximation by low-rank matrices; Remez algorithm; Chebyshev's approximation;

D O I：

10.1134/S0965542522050141

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem of approximation by low-rank matrices is found everywhere in computational mathematics. Traditionally, this problem is solved in the spectral or Frobenius norm, where the approximation efficiency is associated with the rate of decrease of the matrix singular values. However, recent results show that this requirement is not necessary in other norms. In this paper, a method for solving the problem of approximating by low-rank matrices in Chebyshev's norm is proposed. It makes it possible to construct effective approximations of matrices for which singular values do not decrease in an acceptable amount time.

引用

页码：701 / 718

页数：18

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