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Linear L₁ Approximation for a Discrete Point Set and L₁ Solutions of Overdetermined Linear Equations

Author:

Nabih N. AbdelmalekAuthors Info & Claims

Journal of the ACM (JACM), Volume 18, Issue 1

Pages 41 - 47

https://doi.org/10.1145/321623.321628

Published: 01 January 1971 Publication History

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References

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BARRODALE, I., AND YOUNG, A. Algorithms for best Li and L~ linear approximations on a discrete set. Numer. Math. 8 (1966), 295-306.

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SREEDHARAN, ~V. P. Solutions of overdetermined linear equations with minimized error on abstract norm. Numer. Math. lS (1969), 146-151.

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Cited By

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Kennedy WGentle JKennedy WGentle J(2020)Model Fitting Based on Criteria Other Than Least SquaresStatistical Computing10.1201/9780203738672-11(513-540)Online publication date: 17-Dec-2020
https://doi.org/10.1201/9780203738672-11
Micchelli CZhao T(2013)On discrete l-regularizationAdvances in Computational Mathematics10.1007/s10444-011-9247-738:2(441-454)Online publication date: 1-Feb-2013
https://dl.acm.org/doi/10.1007/s10444-011-9247-7
Abdelmalek NMalek W(2008)PreliminariesNumerical Linear Approximation in C10.1201/9781584889793-10(51-64)Online publication date: 19-May-2008
https://doi.org/10.1201/9781584889793-10
Show More Cited By

Index Terms

Linear L₁ Approximation for a Discrete Point Set and L₁ Solutions of Overdetermined Linear Equations
1. Mathematics of computing
  1. Discrete mathematics
  2. Mathematical analysis
    1. Functional analysis
      1. Approximation
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

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Published In

Journal of the ACM Volume 18, Issue 1

Jan. 1971

136 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321623

Editor:
Gerard Salton

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 01 January 1971

Published in JACM Volume 18, Issue 1

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View all

Kennedy WGentle JKennedy WGentle J(2020)Model Fitting Based on Criteria Other Than Least SquaresStatistical Computing10.1201/9780203738672-11(513-540)Online publication date: 17-Dec-2020
https://doi.org/10.1201/9780203738672-11
Micchelli CZhao T(2013)On discrete l-regularizationAdvances in Computational Mathematics10.1007/s10444-011-9247-738:2(441-454)Online publication date: 1-Feb-2013
https://dl.acm.org/doi/10.1007/s10444-011-9247-7
Abdelmalek NMalek W(2008)PreliminariesNumerical Linear Approximation in C10.1201/9781584889793-10(51-64)Online publication date: 19-May-2008
https://doi.org/10.1201/9781584889793-10
Gentle J(2007)Least absolute values estimation: an introductionCommunications in Statistics - Simulation and Computation10.1080/036109177088120476:4(313-328)Online publication date: 27-Jun-2007
https://doi.org/10.1080/03610917708812047
Watson G(2001)Approximation in normed linear spacesNumerical Analysis: Historical Developments in the 20th Century10.1016/B978-0-444-50617-7.50004-5(41-76)Online publication date: 2001
https://doi.org/10.1016/B978-0-444-50617-7.50004-5
Watson G(2000)Approximation in normal linear spacesJournal of Computational and Applied Mathematics10.1016/S0377-0427(00)00333-2121:1-2(1-36)Online publication date: 1-Sep-2000
https://dl.acm.org/doi/10.1016/S0377-0427%2800%2900333-2
Branham RBranham R(1990)Nonlinear MethodsScientific Data Analysis10.1007/978-1-4612-3362-6_7(168-198)Online publication date: 1990
https://doi.org/10.1007/978-1-4612-3362-6_7
Branham RBranham R(1990)The L1 MethodScientific Data Analysis10.1007/978-1-4612-3362-6_6(133-167)Online publication date: 1990
https://doi.org/10.1007/978-1-4612-3362-6_6
Dunham C(1987)Varying norms and constraintsJournal of Approximation Theory10.1016/0021-9045(87)90091-851:1(19-26)Online publication date: 1-Sep-1987
https://dl.acm.org/doi/10.1016/0021-9045%2887%2990091-8
Ward R(1984)An on-line adaptation for discrete<tex>l_{1}</tex>linear estimationIEEE Transactions on Automatic Control10.1109/TAC.1984.110337529:1(67-71)Online publication date: Jan-1984
https://doi.org/10.1109/TAC.1984.1103375
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New characterizations of l1 solutions to overdetermined systems of linear equations

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New characterizations of l₁ solutions to overdetermined systems of linear equations