math function speed
mccaugh at uiucdcsm.UUCP
mccaugh at uiucdcsm.UUCP
Sat Feb 21 15:30:00 AEST 1987
A numerical-analyst named McConnell makes chronic contributions to the APL
Conference Proceedings...in particular, I believe the 1983 edition has an
article by him definiteively addressing the "square-root" problem. It is
really quite informative.
Our own Prof. Gear presents a convincing strategy in his "Computer Organ-
ization and Programming" (2nd edition) for speeding up square-root compu-
tation on the IBM-360/370 (he presents the strategy without proof: I have
a proof in case anyone is interested); not that it is necessarily optimal,
but it is a "speed-up".
No, Newton's (actually, Newton-Raphson's) Method is not "optimal": it only
converges quadratically; for a really nice cubically-converging version,
look at Franz's "Elements of Numerical Analysis". However, fewer itera-
tions are bought at the price of more ocmputations per iteration.....
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