sci.math.num-analysis #38846 (19 + 288 more)                     [1]--[1]--[1]
From: Jay Southard <jsouthard@viewlogic.COM>
[1] Approximation Algorithms
Date: Thu Dec 11 17:30:01 EST 1997

Hi,

Does anyone have a source for numerical approximations?

For example, I recall seeing an approximation for 2-D distance, eg:
        SQRT(A^2 + B^2)

I've come up with:
        assume A >= B >= 0
then
        Approx = A + (1/4)*B
which is about 6% off worst case.  I don't think this was actually the
approximation that I vaugely recall, but you get the idea.

Thanks,

-- jay
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sci.math.num-analysis #38863 (18 + 288 more)                     (1)--[1]--[1]
From: spellucci@mathematik.th-darmstadt.de (Peter Spellucci)
[1] Re: Approximation Algorithms
Date: Fri Dec 12 09:44:32 EST 1997
|>
|>      Approx = A + (1/4)*B
I don't believe in this one. i would guess
A*(1+(B/A)**2/2-(B/A)**4/8+... )
taking the series of sqrt(1+x), after extracting A.
a very good source of approximations for various functions is
Abramowitz&Stegun: Handbook of mathematical functions.
hope this helps
peter
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sci.math.num-analysis #38876 (17 + 288 more)                     (1)--(1)--[1]
From: "James Van Buskirk" <torsop@ix.netcom.com>
[1] Re: Approximation Algorithms
Date: Fri Dec 12 19:58:43 EST 1997

Your mistrust is not misplaced.  The best coefficient for
B above is sqrt(16-sqrt(128))-sqrt(8)+1 for a max relative
error of 5.5%.  This is a lot closer to 1/3 (max error = 5.7%)
than 1/4 (max error = 11.6%).  The series you quote above is
not currently useful as far as I can tell because the time
to execute a division is comparable to the time for a square
root (about 16 clocks throughput) to double precision on
today's processors (at least on alphas).

End of article 38876 (of 38876) -- what next? [npq]