On orthogonal linear \(\ell_1\) approximation

DOI10.1007/BF01400354zbMath0633.65010OpenAlexW2064346177MaRDI QIDQ1096313

Helmuth Späth, G. Alistair Watson

Publication date: 1987

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133211

zbMATH Keywords

algorithmstabilityconvergenceminimization problemdata fittinglocal solutionsconcave quadratic programming problemorthogonal \(\ell _ 1\)-approximationorthogonal \(\ell _ 1\)-fitting

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Numerical mathematical programming methods (65K05) Quadratic programming (90C20) Best approximation, Chebyshev systems (41A50)

Related Items (10)

A pure \(L_1\)-norm principal component analysis ⋮ \(l_p\)-recovery of the most significant subspace among multiple subspaces with outliers ⋮ An algorithm for fitting circular arcs to data using the \(l_1\) norm ⋮ Minsum hyperspheres in normed spaces ⋮ Unnamed Item ⋮ Three points method for searching the best least absolute deviations plane ⋮ Median hyperplanes in normed spaces -- a survey ⋮ THE BEST LEAST ABSOLUTE DEVIATIONS LINE – PROPERTIES AND TWO EFFICIENT METHODS FOR ITS DERIVATION ⋮ Robust computation of linear models by convex relaxation ⋮ Estimating the matrix \(p\)-norm

Cites Work

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• An Analysis of the Total Least Squares Problem
• An Analysis of the Total Approximation Problem in Separable Norms, and an Algorithm for the Total $l_1 $ Problem
• Numerical Methods for Linear Orthogonal L_p Approximation
• Minimization Techniques for Piecewise Differentiable Functions: The $l_1$ Solution to an Overdetermined Linear System
• An Improved Algorithm for Discrete $l_1 $ Linear Approximation

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