Parameter optimization in multiquadric response surface approximations

Multiquadric (MQ) response surface approximation uses the function ∑Ci|X-Xi|2+h1/2 to interpolate a given set of data. The performance of MQ approximation depends on the shift parameter h. Efficient methods of computing the optimal shift parameter based on the leave-one-out cross validation techniqu...

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Bibliographic Details
Published inStructural and multidisciplinary optimization Vol. 26; no. 3-4; pp. 219 - 223
Main Author Wang, B P
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.02.2004
Subjects
Approximation
Optimization
Parameters
Response surface methodology
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Summary:Multiquadric (MQ) response surface approximation uses the function ∑Ci|X-Xi|2+h1/2 to interpolate a given set of data. The performance of MQ approximation depends on the shift parameter h. Efficient methods of computing the optimal shift parameter based on the leave-one-out cross validation technique are presented in this paper. We also proved that the condition number of the MQ coefficient matrix is an increasing function of the shift parameter h. Two numerical examples are included to illustrate the proposed formulation.
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-003-0341-4