SEMI-INFINITE LINEAR REGRESSION AND ITS APPLICATIONS

Paz Fink Shustin, Haim Avron

Research output: Contribution to journalArticlepeer-review

Abstract

Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least squares problems. In this paper, we explore a variant in which the system's matrix has one infinite dimension (i.e., it is a quasimatrix). We call such problems semi-infinite linear regression problems. As we show, the semi-infinite case arises in several applications, such as supervised learning and function approximation, and allows for novel interpretations of existing algorithms. We explore semi-infinite linear regression rigorously and algorithmically. To that end, we give a formal framework for working with quasimatrices, and generalize several algorithms designed for the finite problem to the infinite case. Finally, we suggest the use of various sampling methods for obtaining an approximate solution.

Original languageEnglish
Pages (from-to)479-511
Number of pages33
JournalSIAM Journal on Matrix Analysis and Applications
Volume43
Issue number1
DOIs
StatePublished - 2022

Keywords

  • chebfun
  • least squares
  • quasimatrix
  • sampling
  • semi-infnite linear regression

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