A geometric property of the least squares solution of linear equations

Aharon Ben-Tal, Marc Teboulle

Research output: Contribution to journalArticlepeer-review

Abstract

We derive an explicit determinantal formula for the least squares solution of an overdetermined system of linear equations. From this formula it follows that the least squares solution lies in the convex hull of the solutions to the square subsystems of the original system. We extend this result and prove that this geometric property holds for a more general class of problems which includes the weighted least squares and lp-norm minimization problems.

Original languageEnglish
Pages (from-to)165-170
Number of pages6
JournalLinear Algebra and Its Applications
Volume139
Issue numberC
DOIs
StatePublished - Oct 1990
Externally publishedYes

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