s 2 Error and Significant Digits >相对误差/ relative error*/ e,=2 x的相对误差上限/ relative accuracy*定义为6 A mathematician, a physicist, and an engineer were traveling through Scotland when they saw a black sheep through the window of the train. But what kind ofinformation Aha," says the engineefoes shai》是 Repare black. Hmm, "says the physicist, You mean that some Scottish sheep are black." No, "says the mathematician, "All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black! 注:从6的定义可见,C实际上被偷换成了2,而后才考 察其上限。那么这样的偷换是否合法? 严格的说法是,与是否反映了同一数量级的误差? 关于此问题的详细讨论可见教材第3页。§2 Error and Significant Digits ➢ 相对误差 /* relative error */ x e er * * = Now I wouldn’t call it simple. Say … what is the relative error of 20cm±1cm? Don’t tell me it’s 5% because… But what kind of information does that 5% give us anyway? | | * * * x ε ε x 的相对误差上限 /* relative accuracy */ 定义为 r = A mathematician, a physicist, and an engineer were traveling through Scotland when they saw a black sheep through the window of the train. "Aha," says the engineer, "I see that Scottish sheep are black." "Hmm," says the physicist, "You mean that some Scottish sheep are black." "No," says the mathematician, "All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black!" 注：从 的定义可见， 实际上被偷换成了 ，而后才考 察其上限。那么这样的偷换是否合法？ 严格的说法是， 与 是否反映了同一数量级的误差？ 关于此问题的详细讨论可见教材第3页。 * r e * er * * x e x e * * * x e