Maxvol.jl

Maximum-volume submatrices for Julia
Author Muxas
Popularity
1 Star
Updated Last
2 Years Ago
Started In
December 2019

What is this repo?

This is a repo for Julia implementation of Maxvol-related algorithms.

What is Maxvol?

Maxvol is an algorithm which finds a submatrix of quasi-maximum volume in a given matrix. Submatrices of maximum volume play crucial role in low-rank cross (interpolative) approximations as well as in different optimization problems. More on this can be found in the following literature:

  • S.A. Goreinov, N.L. Zamarashkin and E.E. Tyrtyshnikov, 1997. Pseudo-skeleton approximations by matrices of maximal volume. In Mathematical Notes, 62(4), (pp. 515-519).

  • S.A. Goreinov, E.E. Tyrtyshnikov and N.L. Zamarashkin, 1997. A theory of pseudoskeleton approximations. In Linear algebra and its applications, 261(1-3), (pp. 1-21).

  • S.A. Goreinov, I.V. Oseledets, D.V. Savostyanov, E.E. Tyrtyshnikov and N.L. Zamarashkin, 2010. How to find a good submatrix. In Matrix Methods: Theory, Algorithms And Applications: Dedicated to the Memory of Gene Golub (pp. 247-256).

  • I. Oseledets and E. Tyrtyshnikov, 2010. TT-cross approximation for multidimensional arrays. In Linear Algebra and its Applications, 432(1), (pp. 70-88).

  • D.V. Savostyanov, 2014. Quasioptimality of maximum-volume cross interpolation of tensors. In Linear Algebra and its Applications, 458, (pp. 217-244).

  • N.L. Zamarashkin and A.I. Osinsky, 2016. New accuracy estimates for pseudoskeleton approximations of matrices. In Doklady Mathematics (Vol. 94, No. 3, pp. 643-645).

  • A.I. Osinsky and N.L. Zamarashkin, 2018. Pseudo-skeleton approximations with better accuracy estimates. In Linear Algebra and its Applications, 537, (pp. 221-249).

  • A. Mikhalev and I.V. Oseledets, 2018. Rectangular maximum-volume submatrices and their applications. In Linear Algebra and its Applications, 538, (pp. 187-211).

Installation

As it is a Julia package, it can be installed with a simple

julia> using Pkg
julia> Pkg.add("https://github.com/muxas/maxvol.jl")

Documentation

Is available online here.