| 摘要:（摘要内容经过系统自动伪原创处理以避免复制，下载原文正常，内容请直接查看目录。） Bernstein多项式是由俄国数学家Bernstein在证实Weierstrass定理时提出的。Bernstein多项式因为其优越的性质，在盘算机帮助几何设计，切近亲近论，金融数学中有异常普遍的应用。但是，Bernstein算子的收敛速度较慢，因此许多学者对其停止了改良，如Sablonniere结构了左Bernstein算子，俄语论文题目，Phillips提出了q一Bernstein算子等。本文重要运用Bernstein算子及其二次迭代的线性组合，俄语论文网站，来结构高精度拟插值算子。与二次Bernstein算子的Boolean和迭代比拟较，本文结构的高精度拟插值算子在某些场所收敛速度更快。 Abstract: Bernstein polynomials are proposed by the Russian mathematician Bernstein in the verification of the Weierstrass theorem. Bernstein polynomials because of its superior properties, computers help geometric design and close to the closest theory, financial mathematics have abnormal generally use. However, the convergence speed of Bernstein operator is slow, so many scholars have stopped the improvement, such as the Sablonniere structure of the left Bernstein operator, Phillips proposed q a Bernstein operator, etc.. In this paper, we use the linear combination of Bernstein operator and its two iteration to construct high precision quasi interpolation operators. Compared with the Boolean and iteration of the two Bernstein operators, the high accuracy quasi interpolation operator in this paper converges faster in some places. 目录: 摘要 4-5 Abstract 5 前言 6-8 第一章 基础知识 8-11 §1.1 Bernstein多项式,Bernstein算子的定义及性质 8-9 §1.2 Bernstein算子的收敛性质 9-11 第二章 高精度拟插值算子的构造措施及主要结果 11-20 §2.1 Bernstein算子的迭代 11-12 §2.2 Bernstein算子的Boolean和迭代 12-14 §2.3 Bernstein算子迭代的线性组合 14-19 §2.4 小结 19-20 第三章 数值试验 20-25 §3.1 数值例子 20-24 §3.2 小结 24-25 参考文献 25-27 致谢 27-28 |
