The old round off problem?
Sat Mar 4 22:33:26 CET 2006
"sam" <samschul at pacbell.net> writes:
> Hello all, I am taking a class in scientific programming at the local
> college. My problem is that the following difference produces round off
> errors as the value of x increases. For x >= 19 the diference goes to
> zero.I understand the problem, but am curious as to whether their
> exists a solution. [f(x) = cosh^2(x) - sinh^2(x) = 1]
The usual way is to notice that the difference goes to zero because
the lowest order terms of the Taylor series for cosh^2 and sinh^2 are
equal and cancel each other out. The solution is to write down the
series for (cosh^2(x) - sinh^2(x)) and add up a few non-cancelled terms.
All these series should converge very fast.
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