作者：（罗）安娜玛利亚·登特
页数：181
出版社：哈尔滨工业大学出版社
出版日期：2021
ISBN：9787560343266
电子书格式：pdf/epub/txt
内容简介
本书是一部英文原版数学专著,着重研究多项式内插法的问题寻找一个经过所有点P1且每点重数为m的多项式P(x).虽然多项式是许多数学方法的构架,例如有限元和样条,以及函数逼近或关于数值格式的定理几乎总是通过多项式化为局部插值,但是这样的理论仍是不够的.计算满足在任意一般点的集合上满足特定重数条件的多项式空间的维数的问题可以再任意维数形式化.这个问题的很一般形式仍没有被解决,唯已知的有关高维的重数为2的情况,是在1988年由J.Alexander和A.Hirschowitz解决的.本书讨论了这个问题,并且给出了作者相信是更容易得到该定理的另一个方法，书中用到了R.A.rentz和G.G.Lorentz基于二维情况发展的方法的一些变化。
目录
0 Introduction
1 Algebraic Geometry Approach
1.1 Lagrange interpolation
1.2 Uniform Bivariate Hermite Interpolation
1.3 Dimension Problem
1.4 What is known
2 Approximation Theory Approach
2.1 Introduction and Basic Notation
2.2 Shifts and Algorithm
2.3 Triangles and Hermite Problems
3 The Alexander-Hirschowitz Theorem
3.1 Basic Definitions and the Theorem
3.2 Coalescence in Dimension 2
3.3 Dimension 2 Pyramids
3.4 Coalescence in Higher Dimension
3.5 Dimension 3 Pyramid
4 Toric Surfaces
4.1 Linear Systems of Curves in P1 X P1
4.2 Linear Systems of Curves in General Toric Surfaces
5 Future Work
5.1 Alexander-Hirschowitz Theorem and Dimension N
5.2 General Toric Surfaces
编辑手记
1 Algebraic Geometry Approach
1.1 Lagrange interpolation
1.2 Uniform Bivariate Hermite Interpolation
1.3 Dimension Problem
1.4 What is known
2 Approximation Theory Approach
2.1 Introduction and Basic Notation
2.2 Shifts and Algorithm
2.3 Triangles and Hermite Problems
3 The Alexander-Hirschowitz Theorem
3.1 Basic Definitions and the Theorem
3.2 Coalescence in Dimension 2
3.3 Dimension 2 Pyramids
3.4 Coalescence in Higher Dimension
3.5 Dimension 3 Pyramid
4 Toric Surfaces
4.1 Linear Systems of Curves in P1 X P1
4.2 Linear Systems of Curves in General Toric Surfaces
5 Future Work
5.1 Alexander-Hirschowitz Theorem and Dimension N
5.2 General Toric Surfaces
编辑手记
