Tea Time Numerical Analysis

Tea Time Numerical Analysis

Numerical Analysis

Numerical methods are designed to approximate one thing or another. Sometimes roots, sometimes derivatives or definite integrals, or curves, or solutions of differential equations. As numerical methods produce only approximations to these things, it is important to have some idea how accurate they are. Sometimes accuracy comes down to careful algebraic analysis—sometimes careful analysis of the calculus, and often careful analysis of Taylor polynomials. But before we can tackle those details, we should discuss just how error and, therefore, accuracy are measured. There are two basic measurements of accuracy: absolute error and relative error. Suppose that p is the value we are approximating, and p˜ is an approximation of p. Then p˜ misses the mark by exactly the quantity p˜− p, the so-called error. Of course, p˜ − p will be negative when p˜ misses low. That is, when the approximation p˜ is less than the exact value p. On the other hand, p˜ − p will be positive when p˜ misses high. But generally, we are not concerned with whether our approximation is too high or too low. We just want to know how far off it is. Thus, we most often talk about the absolute error, |p˜ − p|. You might recognize the expression |p˜ − p| as the distance between p˜ and p, and that’s not a bad way to think about absolute error.

Leon Brin,

https://lqbrin.github.io/tea-time-numerical/index.html

Independent

2016

Baihaqi

Creative Commons

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English

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