23 Jun
2004
23 Jun
'04
10:42 a.m.
I've had many an argument with my father over
this. He
insists on using
the binomial expansion. I prefer the Newton iteration, which
converges
very quickly
[ To find sqrt(A)
Set X(0) = A/2 (or some other suitable initial guess)
Repeat
X(N+1) = ( (A/X(N)) + X(N) ) / 2
Unti X(N) and X(N+1) are sufficiently close
Return X(N+1)
]
There's also a method I learnt long ago
that is laid out in the same way as
a long division. I've forgotten it
because it seemed moderately pointless!
I've forgotten it so thoroughly thatI've
even forgotten whether it had a name or not.
I expect that there may well be a similar
method for the cube root.
If push came to shove (i.e. no calculator,
no computer, no slide rule, no log tables)
I'd go for Newton Raphson too. I cannot
remember that one either, but I can
remember that on previous occasions when
I've needed it I've been able to regenerate it
from first principles :-)
Antonio
--
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Antonio Carlini arcarlini(a)iee.org