Making conditionally negative definite radial basis function interpolation well-conditioned by adding cardinal basis functions
作者： Saeed Kazem , Edmund A. Chadwick , Ali Hatam
DOI: 10.1016/J.ASEJ.2017.03.013
关键词: Shape parameter 、 Basis function 、 Order (group theory) 、 Condition number 、 Mathematics 、 Positive-definite matrix 、 Discrete mathematics 、 Applied mathematics 、 Basis (linear algebra) 、 Interpolation 、 Linear system
摘要: Abstract A class of basis functions so called well-conditioned RBF (WRBFs) has been introduced. This manipulated by adding cardinal to the conditionally negative definite RBFs order 1, such as Multiquadric 1 + ( ∊ r ) 2 (MQ) and log (LOG). The condition number interpolation matrix arising from this is O N , where center nodes. independent shape parameter therefore applying would recover ill–posed linear system associated with interpolation.
doaj.org参考文章(36)
Gregory F. Fasshauer, Meshfree Approximation Methods with MATLAB ,(2007)
D. Stevens, H. Power, The radial basis function finite collocation approach for capturing sharp fronts in time dependent advection problems Journal of Computational Physics. ,vol. 298, pp. 423- 445 ,(2015) , 10.1016/J.JCP.2015.05.032
Holger Wendland, Scattered Data Approximation ,(2004)
Martin D. Buhmann, Radial Basis Functions: Theory and Implementations ,(2003)
Alfa Heryudono, Elisabeth Larsson, Alison Ramage, Lina von Sydow, Preconditioning for Radial Basis Function Partition of Unity Methods Journal of Scientific Computing. ,vol. 67, pp. 1089- 1109 ,(2016) , 10.1007/S10915-015-0120-6
B. Fornberg, G. Wright, Stable computation of multiquadric interpolants for all values of the shape parameter Computers & Mathematics With Applications. ,vol. 48, pp. 853- 867 ,(2004) , 10.1016/J.CAMWA.2003.08.010
Robert Schaback, Multivariate Interpolation by Polynomials and Radial Basis Functions Constructive Approximation. ,vol. 21, pp. 293- 317 ,(2005) , 10.1007/S00365-004-0585-2
Bengt Fornberg, Elisabeth Larsson, Natasha Flyer, Stable Computations with Gaussian Radial Basis Functions SIAM Journal on Scientific Computing. ,vol. 33, pp. 869- 892 ,(2011) , 10.1137/09076756X
James D. Riley, Solving systems of linear equations with a positive definite, symmetric, but possibly ill-conditioned matrix Mathematics of Computation. ,vol. 9, pp. 96- 101 ,(1955) , 10.1090/S0025-5718-1955-0074915-1
Robin Sibson, G. Stone, Computation of thin-plate splines Siam Journal on Scientific and Statistical Computing. ,vol. 12, pp. 1304- 1313 ,(1991) , 10.1137/0912070