﻿ 二元分次插值适定性问题研究 Research on Posedness of Binary Graded Interpolation

Vol.05 No.04(2016), Article ID:19033,5 pages
10.12677/AAM.2016.54077

Research on Posedness of Binary Graded Interpolation

Xiaoqian Fan, Ying Liu, Lihong Cui

Liaoning Normal University, Dalian Liaoning

Received: Nov. 4th, 2016; accepted: Nov. 19th, 2016; published: Nov. 24th, 2016

ABSTRACT

The paper studies from the posedness of bivariate polynomial interpolation. Based on the methods of “adding a horizontal line” and “adding vertical line” in constructing well-posed node group of binary interpolation, this paper further researches and discusses the posedness of binary graded interpolation, and gives geometrical structure and basic characteristics of well-posed node group of binary graded interpolation, then constructs the method that adds parabola for the well-posed node group of binary graded interpolation and generalizes the existing research results. Finally, the numerical examples are given to verify the research results.

Keywords:Well-Posed Node Group, Binary Graded Interpolation, Algebraic Curve

1. 前言

2. 基本概念和定理

(2.1)

(2.2)

3. 主要定理及证明

4. 具体构造方法及实验示例

a. 若

……

b. 若，则先用(a)方法，再用梁学章老师提到的定理1.1方法构造。

Figure 1. The effect picture of binary graded interpolation

Research on Posedness of Binary Graded Interpolation[J]. 应用数学进展, 2016, 05(04): 657-661. http://dx.doi.org/10.12677/AAM.2016.54077

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