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Re: Convergence Tests - Numerical Algorithms
From: |
Francesco Potortì |
Subject: |
Re: Convergence Tests - Numerical Algorithms |
Date: |
Mon, 01 Oct 2012 11:03:32 +0200 |
>I have been looking at convergence tests, for example, in computing the root
>or the fixed point of a function.
You have already been correctly answered. This is to try a more verbose
answer.
>BETTER:
>IF absolute_value( x_k - x_k-1 ) <=
>4.0*machine_epsilon*absolute_value(x_k)
This works if we have an efficient iterative procedure, which manages to
converge to a value that is very near the smallest representable
difference. In this case "very near" is assumed to be four times.
>BEST:
>IF absolute_value( x_k - x_k-1 ) <= E_tol
>4.0*machine_epsilon*absolute_value(x_k)
Here we do not make such an assumption and rely to a further multiplier,
which we will set, depending on the iterative algortihm, to a value that
may be 1 (as in the above case) to values much bigger than 1. For
example, if we have an algorithm which converges badly we may want
E_tol=1e4, or if we have an algorithm that converges slowly and we don't
want to wait and we don't need so much precision, we may want
E_tol=sqrt(eps).
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- Re: Convergence Tests - Numerical Algorithms,
Francesco Potortì <=