数值分析若干数值问题的数学实验  

Mathematical Experiment of Several Numerical Problems in Numerical Analysis

作　　者：张光辉[1] ZHANG Guang-hui(College of Mathematics and Statistics,Suzhou University,Suzhou,Anhui 234000,China)

机构地区：[1]宿州学院数学与统计学院

出　　处：《河北北方学院学报（自然科学版）》2019年第9期1-5,共5页Journal of Hebei North University:Natural Science Edition

基　　金：宿州学院重点建设课程项目:“数值分析与实验”(szxy2018zdkc01)、“概率论”(szxy2018zdkc44)

摘　　要：目的数值分析课程中存在若干理论结果非常明确,但是用解析方法验证起来比较困难的问题需要验证此类问题的结论。方法结合MATLAB,展开数学实验,进行数值模拟。结果针对牛顿迭代法求非线性方程重根的收敛阶、函数的伯恩斯坦多项式逼近、切比雪夫多项式降阶、豪斯霍尔德变换、蒙特卡洛方法计算积分等问题,用MATLAB编程进行数学实验,给出了数值模拟结果。结论验证了相关问题的预设结论。Objective There are several problems which have clear conclusions but are not easy to verify by numerical analysis.Methods Combining with MATLAB,mathematical experiments and numerical simulation were carried out.Results Aiming at the convergence order of Newton iteration method for finding multiple roots of nonlinear equation,approximation of Bernstein polynomial of function,order reduction of Chebyshev polynomial,House Holder transform and calculation of integral by Monte Carlo method,mathematical experiments were carried out with MATLAB programming,and numerical simulation results were given.Conclusion The preset conclusions are verified.

关 键 词：牛顿迭代法 伯恩斯坦多项式 切比雪夫多项式 蒙特卡洛方法 

分 类 号：O242.2[理学—计算数学]