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Custom tolerance tests


From: Joza
Subject: Custom tolerance tests
Date: Tue, 23 Oct 2012 06:06:33 -0700 (PDT)

Normally, when I write a zero finding algorithm, at stage k, my convergence
test tests whether or not the obtained value is less than machine epsilon
times the the previous value. 

IF   x_k < mach_eps x_(k-1)   then STOP

But if you use say fzero or fsolve, the built-in functions, oen can only set
an absolute tolerance. That is, one can only set a value such that the
algorithm will stop when it obtains a value less than the specified
tolerance. You cannot use the kind of test above, where you test consecutive
values.

Is there a way around this that I am not aware of? What would be the best
way to specify the tolerance for say, fzero, in line with the tolerance test
above?



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