- 散乱数据拟合的模型方法和理论(第2版)(英文版)
- - 作者：Zongmin Wu|译者:Shengxin Zhu//Wenhao Li//Wenwu Gao
  - 出版社：科学
  - ISBN：9787030748553
  - 出版日期：2023/01/01
  - 页数：176
- 售价：39.2

内容大纲
本书是应用数学与计算数学中有关曲面及多元函数插值、逼近、拟合的入门书籍，从多种物理背景、原理出发，导出相应的散乱数据拟合的数学模型及计算方法，进而逐个进行深入的理论分析。书中介绍了多元散乱数据拟合的一般方法，包括多元散乱数据多项式插值、基于三角剖分的插值方法、Boole和与Coons曲面、Sibson方法或自然邻近法、Shepard方法、Kriging方法、薄板样条方法、MQ拟插值法、径向基函数方法、运动最小二乘法、隐函数样条方法、R函数法等；同时还特别介绍了近年来国际上越来越热并在无网格微分方程数值解方面有诸多应用的径向基函数方法及其相关理论。
作者介绍
目录
Preface to the Second Edition
Preface to the First Edition
Chapter 1 Scattered Data Approximation and Multivariate Polynomial Interpolation
  1.1  Motivation Problems
    1.1.1  Problems from Applications
    1.1.2  Problems from Mathematics
  1.2  Haar Condition for Interpolation
  1.3  Multivariate Polynomial Interpolation for Scattered Data
    1.3.1  Aitken Formula for Multivariate Interpolation
    1.3.2  Newton Formula for Multivariate Polynomial Interpolation
Chapter 2 Local Methods
  2.1  Triangulation and Function Representation on a Triangle
  2.2  Smooth Connection Methods Based on Triangulation
    2.2.1  Linear Interpolation and Piecewise Linear Interpolation
    2.2.2  Nine-Parameter Cubic Method
    2.2.3  Clough-Tocher Method
    2.2.4  Powell-Sabin Method
  2.3  Boole and Coons Patches
  2.4  Subdivision Methods for Scattered Data Approximation
    2.4.1  Chaikin Method
    2.4.2  Doo-Sabin Method
    2.4.3  Four-Point Method
    2.4.4  Butterfly Algorithm
  2.5  Sibson Interpolation or Natural Proximity
    2.5.1  Scattered Data Interpolation with Lipschitz Constant Diminishing Property
    2.5.2  Convergence Theorem of Sibson Interpolation
    2.5.3  Interpolation Convergence Theorem for Interpolation with Lipschitz Constant Diminishing Property
  2.6  Shepard Method
    2.6.1  Shepard Interpolation with Derivative Information
    2.6.2  Generalization of Shepard Method
Chapter 3 Global Methods
  3.1  Random Function Preliminary
  3.2  Kriging Method
    3.2.1  Inverse of Univariate Markov Type Correlation Matrix
    3.2.2  The Solution to Kriging Problem with Univariate Gaussian Iype
Correlation Matrix
    3.2.3  Monotonicity and Boundedness of Kriging Interpolation Operator
    3.2.4  Condition Number of Correlation Matrix
  3.3  Universal Kriging
  3.4  Co-Kriging
    3.4.1  Nugget Effect of Interpolation Operator
    3.4.2  Application of Co-Kriging on Hermite Interpolation
  3.5  Interpolation for Generalized Linear Functionals
  3.6  Splines
  3.7  Multi-Quadric Methods
  3.8  MQ Quasi-interpolation for Higher Order Derivative Approximation
  3.9  Stability for Derivative Approximation with FD and M
  3.10  Radial Basis Functions
    3.10.1  Radial Basis Function Interpolation
    3.10.2  Existence of Radial Basis Function Interpolation

Chapter 4 Theory on Radial Basis Function Interpolation
  4.1  Convergence and Convergence Rate
    4.1.1  Quasi-Interpolation, Strang-Fix Condition and Shift Invariant Space
  4.2  Convergence Results for Scattered Data Radial Basis Function Interpolation
    4.2.1  Error Estimation
    4.2.2  Construction of Admissible Vectors
  4.3  Positive Definite Radial Basis Functions
  4.4  Bochner Theory for Radial Basis Functions
  4.5  Radial Functions and Strang-Fix Conditions
Chapter 5 Other Scattered Data Interpolation Methods
  5.1  Moving Least Squares
    5.1.1  Least Squares
    5.1.2  Moving Least Squares
    5.1.3  Interpolating Moving Least Squares Methods
    5.1.4  Divide and Conquer on General Domain
  5.2  Convergence Analysis of Shepard Methods
    5.2.1  Convergence Analysis for the Shepard Method
  5.3  Implicit Splines
    5.3.1  Other Scattered Data Interpolation Methods
  5.4  Partition of Unity
Chapter 6 Scatter Data Interpolation for Numerical Solutions of PDEs
  5.5  R-function
  6.1  Generalized Functional Interpolations and Numerical Methods for PDEs
  6.2  Other Multivariate Approximation Methods for PDEs
    6.2.1  Least Squares Methods
    6.2.2  Collocation
    6.2.3  Galerkin Method
    6.2.4  Golberg Method
Bibliography

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