《数值计算方法》实验报告 1 什么是数值计算方法及应用与误差计算 1．什么是数值计算方法及应用 计算数学也叫做数值计算方法或数值分析。主要内容包括代数方程、线性代数方程组、微分方程的数值解法，函数的数值逼近问题，矩阵特征值的求法，最优化计算问题，概率统计计算问题等等，还包括解的存在性、唯一性、收敛性和误差分析等理论问题。数值计算方法,是一种研究并解决数学问题的数值近似解方法,是在计算机上使用的解数学问题的方法，简称计算方法。在科学研究和工程技术中都要用到各种计算方法。 例如，在航天航空、地质勘探、汽车制造、桥梁设计、 天气预报和汉字字样设计中都有计算方法的踪影 .Numerical analysis involves the study of methods of computing numerical data. In many problems this implies producing a sequence of approximations by repeating the procedure again and again. People who employ numerical methods for solving problems have to worry about the following issues: the rate of convergence (how long does it take for the method to find the answer), the accuracy (or even validity) of the answer, and the completeness of the response (do other solutions, in addition to the one found, exist).Numerical methods provide approximations to the problems in question. No matter how accurate they are，they do not, in most cases, provide the exact answer. In some instances working out the exact answer by a different approach may not be possible or may be too time consuming and it is in these cases where numerical methods are most often used. The ever-increasing advances in computer technology has enabled many in science and engineering to apply numerical methods to simulate physical phenomena. Numerical methods are often divided into elementary ones such as finding the root of an equation, integrating a function or solving a linear system of equations to intensive ones like the finite element method. Intensiv...
