SICP Exercises (2.15) A summary of solving problems: an in-depth consideration of interval errors

SICP Exercise 2.15 is the next topic 2.14 , the topic 2.14 mentioned Alyssa The design of the interval calculation module in the parallel resistance calculation will occur problems, this problem is found by Lem. Then, a person called Eva also found this problem, and she also has more in-depth thinking.

Eva feels that if a formula can be written in a form, where non-accurate variables do not recur, then the Alyssa system will produce a tighter bounds.

Therefore, she felt that in calculating the shunt resistor, the formula"1/(1/r1 + 1/r2)" than the formula "(R1*R2)/(R1 + R2)" is better.

The topic asks us to see if Eva says it right.

To understand the meaning of the topic is a bit difficult, mainly do not know the "with non-accurate variables" what meaning.

However, we can make an intuitive inference based on the phenomena we observed in exercise 2.14.

In Exercise 2.14, we found that the interval division of Alyssa is problematic, and that dividing the two intervals will enlarge the error.

However, it is worth noting that the implementation of the formula "1/(1/R1 + 1/r2)" When the Lem defines an interval called one, the value is (1 1), this is a definite interval, there is no error, in the interval division of the use of it will not cause error widening problem.

such as one/(100 200), is

(1 1)/(100 200)

+ (1 1) * (1/100 1/200)

+ (1/100 1/200)

The further calculation of one/(one/(100 200)) is

(1 1)/(1/100 1/200)

(1 1) * (100 200)

(100 200)

That is, if we have defined interval one as (1 1), then one/(one/a) or a, will not cause the problem of the interval error to become larger.

Therefore, as mentioned in topic 2.15, the use of one's program Part2 is a better program.

SICP Exercises (2.15) A summary of solving problems: an in-depth thinking of interval errors