Implicit local radial basis function interpolations based on function values

Autor(es)

Yao, Guangming ^[1] ; Duo, Jia ^[2] ; Chen, C. S. ^{[3, 4]} ; Shen, L. H. ^[5]

Afiliação do(s) autor(es)

^[1] Clarkson Univ, Dept Math, Potsdam, NY 13699 - USA

^[2] Heilorigjiang Inst Sci & Technol, Dept Math, Heilongjiang - Peoples R China

^[3] Univ So Mississippi, Dept Math, Hattiesburg, MS 39406 - USA

^[4] Taiyuan Univ Technol, Coll Math, Taiyuan - Peoples R China

^[5] Natl Taiwan Univ, Dept Civil Engn, Taipei - Taiwan

• Tipo de documento: Artigo Científico
• Fonte: Applied Mathematics and Computation; v. 265, p. 91-107, AUG 15 2015.
• Citações Web of Science: 8

Resumo

In this paper we propose two fast localized radial basis function fitting algorithms for solving large-scale scattered data interpolation problems. For each given point in the given data set, a local influence domain containing a small number of nearest neighboring points is established and a global interpolation is performed within this restricted domain. A sparse matrix is formulated based on the global interpolation in these local influence domains. The proposed methods have achieved both low computational cost and minimal memory storage. In comparison with the compactly supported radial basis functions, the proposed fitting algorithms are highly accurate. The numerical examples have provided strong evidence that the two proposed algorithms are indeed highly efficient and accurate. In the two proposed algorithms, we have successfully solved a large-scale interpolation problem with 225,000 interpolation points in two dimensional space. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 09/15098-0 - Avaliando controle de epidemias utilizando modelos matemáticos e computacionais
• Beneficiário: Hyun Mo Yang
• Modalidade de apoio: Auxílio à Pesquisa - Temático