Exercise 2.15 · 习题

Exercise 2.15: Eva Lu Ator, another user, has

also noticed the different intervals computed by different but algebraically

equivalent expressions. She says that a formula to compute with intervals using

Alyssa’s system will produce tighter error bounds if it can be written in such

a form that no variable that represents an uncertain number is repeated. Thus,

she says, par2 is a “better” program for parallel resistances than

par1. Is she right? Why?

练习 2.15：另一位用户 Eva Lu Ator 也注意到，不同但代数等价的表达式会产生不同的区间计算结果。她说，若用 Alyssa 的系统进行区间运算的公式能写成使得代表不确定数的变量不重复出现的形式，则会产生更紧的误差界。因此，她说，par2 是比 par1 更好的并联电阻程序。她对吗？为什么？