Tea Time Numerical Analysis

Dublin Core

Title

Tea Time Numerical Analysis

Subject

Numerical Analysis

Description

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.

Creator

Leon Brin,

Source

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

Publisher

Independent

Date

2016

Contributor

Baihaqi

Rights

Creative Commons

Format

PDF

Language

English

Type

Textbooks

Files

Collection

Citation

Leon Brin,, “Tea Time Numerical Analysis,” Open Educational Resource (OER) - USK Library, accessed July 23, 2024, http://uilis.usk.ac.id/oer/items/show/2853.

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