Algorithm for the Best Uniform Spline Approximation with Free Knots

An algorithm for the best uniform approximation by a spline with optimal knots is presented in the paper. Differential evolution is used to find optimal knots. It is one of the best evolutionary algorithms, which sustainably finds function’s global optimum in minimum time. Spline coefficients are co...

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Veröffentlicht in:Cybernetics and systems analysis Jg. 55; H. 3; S. 449 - 455
Hauptverfasser: Vakal, L. P., Vakal, E. S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.05.2019
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Approximation
Artificial Intelligence
Control
Evolutionary algorithms
Evolutionary computation
Knots
Mathematics
Mathematics and Statistics
Optimization
Processor Architectures
Software Engineering/Programming and Operating Systems
Software–Hardware Systems
Systems Theory
best uniform approximation
differential evolution
spline
optimal knots
ISSN:1060-0396, 1573-8337
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Abstract An algorithm for the best uniform approximation by a spline with optimal knots is presented in the paper. Differential evolution is used to find optimal knots. It is one of the best evolutionary algorithms, which sustainably finds function’s global optimum in minimum time. Spline coefficients are computed as a solution of a spline-approximation problem with fixed knots. Results of the numerical experiment are given.
AbstractList An algorithm for the best uniform approximation by a spline with optimal knots is presented in the paper. Differential evolution is used to find optimal knots. It is one of the best evolutionary algorithms, which sustainably finds function’s global optimum in minimum time. Spline coefficients are computed as a solution of a spline-approximation problem with fixed knots. Results of the numerical experiment are given.
An algorithm for the best uniform approximation by a spline with optimal knots is presented in the paper. Differential evolution is used to find optimal knots. It is one of the best evolutionary algorithms, which sustainably finds function's global optimum in minimum time. Spline coefficients are computed as a solution of a spline-approximation problem with fixed knots. Results of the numerical experiment are given. Keywords: best uniform approximation, spline, optimal knots, differential evolution.
Audience Academic
Author Vakal, E. S.
Vakal, L. P.
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  surname: Vakal
  fullname: Vakal, E. S.
  organization: Taras Shevchenko National University of Kyiv
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Cites_doi 10.1007/BF01396309
10.1016/0021-9045(69)90033-1
10.1007/s10957-016-1048-1
10.1615/JAutomatInfScien.v48.i11.60
10.1090/S0025-5718-1989-0969492-7
10.1007/BF02437508
10.1137/0705051
10.1007/s10559-017-9978-7
10.1615/JAutomatInfScien.v48.i6.50
10.1093/comjnl/9.3.318
10.1023/A:1008202821328
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Keywords best uniform approximation
differential evolution
spline
optimal knots
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R Storn (152_CR19) 1997; 11
G Nurnberger (152_CR14) 1996; 12
J Barrodale (152_CR7) 1966; 9
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LL Schumaker (152_CR13) 1968; 5
VI Berdyshev (152_CR2) 1999
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NP Korneichuk (152_CR6) 1987
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PS Malachivskii (152_CR5) 2013
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– reference: MalachivskiiPSSkopetskyVVContinuous and Smooth Minimax Spline Approximation [in Ukrainian]2013KyivNaukova Dumka
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– reference: BerdyshevVIPetrakLVApproximation of Functions, Compression of Numerical Information, Applications [in Russian]1999EkaterinburgUrO RAN1206.41002
– reference: PopovBAUniform Spline Approximation [in Russian]1989KyivNaukova Dumka
– reference: VakalLPKalenchuk-PorkhanovaAAVakalESIncreasing the efficiency of Chebyshev segment fractional rational approximationCybern. Syst. Analysis2017535759765368469710.1007/s10559-017-9978-71381.41028
– reference: VakalLPSolving uniform nonlinear approximation problem using continuous genetic algorithmJ. Autom. and Inform. Sci.2016486495910.1615/JAutomatInfScien.v48.i6.50
– reference: L. P. Vakal, “Constructing best Chebyshev spline approximations,” Shtuchnyi Intelekt, No. 2, 94–100 (2017).
– reference: VakalLPSeeking optimal knots for segment approximationJ. Autom. and Inform. Sci.20164811687510.1615/JAutomatInfScien.v48.i11.60
– reference: StechkinSBSubbotinYNSplines in Computing Mathematics [in Russian]1976MoscowNauka0462.65007
– reference: KorneichukNPExact Constants in Approximation Theory [in Russian]1987MoscowNauka
– reference: VakalESKivvaSLMistetskiiGEStelyaOBSolution method for nonlinear parabolic equationsJ. of Math. Sciences19915427817860723.65086
– reference: BarrodaleJYoungAA note on numerical procedures for approximation by spline functionsComput. J.1966931832020227810.1093/comjnl/9.3.3180168.14905
– reference: EschREEastmanWLComputational methods for best spline function approximationJ. of Approximation Theory196921859624052010.1016/0021-9045(69)90033-10181.17604
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– reference: StornRPriceKDifferential evolution — a simple and efficient heuristic for global optimization over continuous spacesJ. of Global Optimization199711341359147955310.1023/A:10082028213280888.90135
– reference: RemezEYFundamentals of Numerical Methods of Chebyshev Approximation [in Russian]1969KyivNaukova Dumka
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Snippet An algorithm for the best uniform approximation by a spline with optimal knots is presented in the paper. Differential evolution is used to find optimal knots....
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SubjectTerms Algorithms
Analysis
Approximation
Artificial Intelligence
Control
Evolutionary algorithms
Evolutionary computation
Knots
Mathematics
Mathematics and Statistics
Optimization
Processor Architectures
Software Engineering/Programming and Operating Systems
Software–Hardware Systems
Systems Theory
Title Algorithm for the Best Uniform Spline Approximation with Free Knots
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