On L₁ Approximation II: Computation for Discrete Functions and Discretization Effects

Previous article Next article On L₁ Approximation II: Computation for Discrete Functions and Discretization EffectsKarl H. UsowKarl H. Usowhttps://doi.org/10.1137/0704022PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] F. Y. Edgeworth, On a new method of reducing observations relating to several quantities, Philos. Mag. (5), 24 (1888), 185–191 Google Scholar[2] T. S. Motzkin and , J. L. Walsh, Least pth power polynomials on a finite point set, Trans. Amer. Math. Soc., 83 (1956), 371–396 MR0081991 0072.25206 Google Scholar[3] John R. Rice, The approximation of functions. Vol. I: Linear theory, Addison-Wesley Publishing Co., Reading, Mass.-London, 1964xi+203 MR0166520 0114.27001 Google Scholar[4] John R. Rice and , John S. White, Norms for smoothing and estimation, SIAM Rev., 6 (1964), 243–256 10.1137/1006061 MR0168069 0121.34102 LinkISIGoogle Scholar[5] Walter D. Fisher, A note on curve fitting with minimum deviations by linear programming, J. Amer. Statist. Assoc., 56 (1961), 359–362 MR0129115 0099.14302 CrossrefISIGoogle Scholar[6] Ian Barrodale and , Andrew Young, Algorithms for best L1 and L∞ linear approximations on a discrete set, Numer. Math., 8 (1966), 295–306 10.1007/BF02162565 MR0196912 0173.18801 CrossrefISIGoogle Scholar[7] Karl H. Usow, On L1 approximation. I. Computation for continuous functions and continuous dependence, SIAM J. Numer. Anal., 4 (1967), 70–88 10.1137/0704007 MR0217498 0153.17701 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Regression Lines: Method of Least Absolute Deviations29 September 2014 Cross Ref Regression Lines: Method of Least p th Powers29 September 2014 Cross Ref An L₁-Method for the Design of Linear-Phase FIR Digital FiltersIEEE Transactions on Signal Processing, Vol. 55, No. 11 Cross Ref Regression Lines: Method of Least Absolute Deviations15 August 2006 Cross Ref Regression Lines: Method of Least p th Powers15 August 2006 Cross Ref Least Absolute Deviation Estimation of Linear Econometric Models: A Literature ReviewSSRN Electronic Journal, Vol. 50 Cross Ref Least Absolute Deviation Estimation of Multi-Equation Linear Econometric Models: A Study Based on Monte Carlo ExperimentsSSRN Electronic Journal, Vol. 11 Cross Ref Approximation in normed linear spaces Cross Ref Approximation in normed linear spacesJournal of Computational and Applied Mathematics, Vol. 121, No. 1-2 Cross Ref Minimization technique for a convex function with application to multiple regression model27 June 2007 | Optimization, Vol. 19, No. 2 Cross Ref A new lad curve-fitting algorithm: Slightly overdetermined equation systems in L1Discrete Applied Mathematics, Vol. 7, No. 1 Cross Ref Computational Algorithms for Calculating Least Absolute Value and Chebyshev Estimates for Multiple RegressionAmerican Journal of Mathematical and Management Sciences, Vol. 4, No. 1-2 Cross Ref An on-line adaptation for discretel₁linear estimationIEEE Transactions on Automatic Control, Vol. 29, No. 1 Cross Ref Simple but powerful goal programming models for discriminant problemsEuropean Journal of Operational Research, Vol. 7, No. 1 Cross Ref A new descent algorithm for the least absolute value regression problem27 June 2007 | Communications in Statistics - Simulation and Computation, Vol. 10, No. 5 Cross Ref On strong unicity of 𝐿₁-approximation1 January 1981 | Proceedings of the American Mathematical Society, Vol. 83, No. 4 Cross Ref Applications and Implementation.Decision Sciences, Vol. 12, No. 1 Cross Ref Least Absolute Deviations Curve-FittingPeter Bloomfield and William Steiger14 July 2006 | SIAM Journal on Scientific and Statistical Computing, Vol. 1, No. 2AbstractPDF (1190 KB)L₁-Approximation of Completely Monotonic Functions by Sums of ExponentialsDavid W. 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