A modification on strictly positive definite RBF-DQ method based on matrix decomposition. (March 2017)

• Record Type: Journal Article
• Authors: Kazem, Saeed; Hatam, Ali
• Is Part Of: Engineering analysis with boundary elements. Volume 76(2017:Mar.)
• Page Start: 90
• Page End: 98
• Publication Date: 2017-03
• Subjects: 65M20 -- 65M06; Radial basis functions -- Strictly positive definite functions -- Positive definite matrix -- Matrix decomposition; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2017.01.001
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: The infinitely smooth RBF methods are theoretically spectrally accurate for applying on scattered data interpolation, and also partial differential equations, but the interpolation matrices of them are extremely ill-conditioned especially for strictly positive definite ones. Therefore, an efficient technique to recover this problem is too important. In this article, a general matrix decomposition method for strictly positive definite RBFs interpolation matrix has been investigated. In the current decomposition the RBFs interpolation matrix is obtained as multiplication of some well-conditioned matrices. This decomposition has been applied to RBF-DQ method and its results more accurate weight coefficients when we involve solving PDEs.