Anderson accelerated preconditioning iterative method for RBF interpolation

被引：1

作者：

Liu, Chengzhi ^{[1
]}

Li, Juncheng ^{[1
]}

Hu, Lijuan ^{[1
]}

机构：

[1] Hunan Univ Humanities Sci & Technol, Sch Math & Finance, Loud 417000, Peoples R China

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2024年 / 169卷

基金：

中国国家自然科学基金;

关键词：

DCPI; Preconditioning technique; Anderson acceleration; Radial basis function; Quasi-interpolation; QUASI-INTERPOLATION; SCATTERED DATA; SURFACE RECONSTRUCTION; KRYLOV METHODS; APPROXIMATION;

D O I：

10.1016/j.enganabound.2024.105970

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Traditional RBF interpolation involves solving a linear system, making it computationally expensive for large datasets. Iterative-based quasi-interpolation combines RBF interpolation with iterative methods to enhance accuracy and convergence. To enhance efficiency and accuracy, we in this paper propose a novel method for RBF quasi-interpolation that combines Anderson acceleration with the asynchronous DCPI, termed Anderson-DCPI. The method alternates between the preconditioning iterative method and Anderson extrapolation, aiming to improve convergence rates. We demonstrate the convergence of Anderson-DCPI for positive definite RBF kernel functions and validate its effectiveness through a series of numerical examples.

引用

页数：10

共 39 条

[1] ITERATIVE PROCEDURES FOR NONLINEAR INTEGRAL EQUATIONS [J].

ANDERSON, DG .

JOURNAL OF THE ACM, 1965, 12 (04) :547-&

[2] Numerical experiments on the condition number of the interpolation matrices for radial basis functions [J].

Boyd, John P. ;

Gildersleeve, Kenneth W. .

APPLIED NUMERICAL MATHEMATICS, 2011, 61 (04) :443-459

[3] ON QUASI-INTERPOLATION BY RADIAL BASIS FUNCTIONS WITH SCATTERED CENTERS [J].

BUHMANN, MD ;

DYN, N ;

LEVIN, D .

CONSTRUCTIVE APPROXIMATION, 1995, 11 (02) :239-254

[4] Shape preserving surface reconstruction using locally anisotropic radial basis function interpolants [J].

Casciola, G. ;

Lazzaro, D. ;

Montefusco, L. B. ;

Morigi, S. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 51 (08) :1185-1198

[5] Fast Surface Reconstruction Technique Based on Anderson Accelerated I-PIA Method [J].

Dai, Jingguo ;

Yi, Yeqing ;

Liu, Chengzhi .

IEEE ACCESS, 2023, 11 :141500-141511

[6] On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation [J].

Davydov, Oleg ;

Dang Thi Oanh .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (05) :2143-2161

[7] A Rescaled Method for RBF Approximation [J].

De Marchi, Stefano ;

Idda, Andrea ;

Santin, Gabriele .

APPROXIMATION THEORY XV, 2017, 201 :39-59

[8] A new stable basis for radial basis function interpolation [J].

De Marchi, Stefano ;

Santin, Gabriele .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 253 :1-13

[9] A rational RBF interpolation with conditionally positive definite kernels [J].

Farazandeh, Elham ;

Mirzaei, Davoud .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2021, 47 (05)

[10]

Fasshauer GE, P CURVES SURFACES AV

← 1 2 3 4 →