数值分析是做什么用的.ppt

?提问:数值分析是做什么用的? 数值分析输入复杂问题或运算...... ),(,)( ,, ln,,xf dx d dx xf bxAxax ba x????????计算机近似解第一章误差/* Error */ §1 误差的背景介绍/* Introduction */ 1. 来源与分类/* Source & Classification */ ?从实际问题中抽象出数学模型——模型误差/* Modeling Error */ ?通过测量得到模型中参数的值——观测误差/* Measurement Error */ ?求近似解——方法误差 (截断误差/* Truncation Error * / ) ?机器字长有限——舍入误差/* Roundoff Error */ §1 Introduction: Source & Classification The following problem can be solved either the easy way or the hard way. Two trains 200 miles apart are moving toward each other; each one is going at a speed of 50 miles per hour. A fly starting on the front of one of them flies back and forth between them at a rate of 75 miles per hour. It does this until the trains collide and crush the fly to death. What is the total distance the fly has flown? The fly actually hits each train an infinite number of times before it gets crushed, and one could solve the problem the hard way with pencil and paper by summing an infinite series of distances. The easy way is as follows: Since the trains are 200 miles apart and each train is going 50 miles an hour, it takes 2 hours for the trains to collide. Therefore the fly was flying for two hours. Since the fly was flying at a rate of 75 miles per hour, the fly must have flown 150 miles. That's all there is to it. When this problem was posed to John von Neumann, he immediately replied, "150 miles." "It is very strange," said the poser, "but nearly everyone tries to sum the infinite series." "What do you mean, strange?" asked Von Neumann. "That's how I did it!" §1 Introduction: Source & Classification 大家一起猜? ????dx e 2x 101 1 / e 解法之一: 将作 Taylor 展开后再积分 2xe ?...9 1!4 17 1!3 15 1!2 13 11 ) ...!4!3!2 1( 10 8642 10?????????????????? dx xxxx dx e 2xS 4R 4/* Remainder */ 743 0 024 010 333 01 42 1 10 13 11 4....S????????? 001 02 0005 0..???|舍入误差/* Roundoff Error * / | 006 0 001 0 005 0 10 2... dx e -x????的总体误差计算= ……由截去部分/* excluded terms */引起, 10 4???S dx e 2x取则... 11 1!5 19 1