2017년 2월 21일 화요일

Method of repetition (numerical computation)

Method of repetition (numerical computation)

With the method of repetition (はんぷくほう British: iterative method) in the field of numerical computation, I use the repetition calculation in technique of the 求根 algorithm. Because algorithm is simple, I am used for a long time.

Table of contents

Algorithmic

It is intended to get value x meeting f (x) = 0 about given function f. The general algorithm of the method of repetition is as follows:

  1. I establish initial value x0Rn. The i = 0 distance.
  2. 漸化式
     
    I demand により xi +1. g is a function to be fixed from f here.
  3. Suitable criterion
     
    But, I stop if managed (I express this with convergence) and assume xi a solution. Otherwise I assume it ii +1 and return to step 2. Usually in a criterion
     
    It is adopted などが.

Example

There are various kinds of methods by how to get of several g of Seki.

Newton method

Several g of Seki to find a point zero of f if function f is a function fluent properly

 

ととれば, this become the Newton method. When I converge, this becomes the second convergence. In other words, a root , とし,

 

Fine weather method

The fine weather methodEnglish versionIn)

 

ととる. When I converge, this becomes the third convergence. In other words,

 

Other

This article is taken from the Japanese Wikipedia Method of repetition (numerical computation)

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