Method of repetition (numerical computation)
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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:
- I establish initial value x0 ∈ Rn. The i = 0 distance.
- 漸化式
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- I demand により xi +1. g is a function to be fixed from f here.
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- Suitable criterion
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- But, I stop if managed (I express this with convergence) and assume xi a solution. Otherwise I assume it i → i +1 and return to step 2. Usually in a criterion
- It is adopted などが.
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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
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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