Re: Programming question : Newton's method

On Fri, 29 Oct 1999, James Nelson wrote:

> I noticed the conversation. Since nobody mentioned it. I will.
>
> I good method for solving many equations is "Newton's method". I can get a
> math book out on this, but it more or less involves this:
>
> Make a guess of the square root based on whatever simple criteria.
> square it
> what is the difference between that and the expected answer?
> adjust the number according to how far off you are
> square it
> what is the difference between that and the expected answer?
> adjust the number according to how far off you are
> square it
> what is the difference between that and the expected answer?
> adjust the number according to how far off you are
> square it
>
> Generally, if correctly implemented, it is accurate to several decimal
> places after 3 iterations.
> This is probably more code than a look up table, but you should be familiar
> with this technique for solving complex equations.

        Yeah, computing the first derivative of the function is generally
more complicated than a lookup table ;)

        Actually, for this example, Newton-Raphson approximation wouldn't
work. Newton-Raphson is generally used to find the roots of a function:

        i.e. For which values of x are <insert your nasty, but not too bad
to differentiate function here> = 0

Joe

>
>
> ----- Original Message -----
> From: jeff hendrix <jhendrix@Quark.Com>
> To: <vectorlist@lists.cc.utexas.edu>
> Sent: Thursday, October 28, 1999 5:14 PM
> Subject: RE: Programming question
>
>
> > Thanks for all the replies.
> > These posts have got some of the wheels turning in my brain.
> > Just a few comments.
> >
> > Previously I was think of using a "reverse" lookup table like Zonn
> > suggested, and I might go that route now after he suggested doing a binary
> > search on it. (binary search had slipped my mind and I was planning on
> > starting at one end and just moving through the table, which would have
> > averaged 128 loops) I'm actually currently doing lots of calculations with
> > data from lookup tables. I.E.- collision detection.
> >
> > I had considered using gravity in something like 16 steps, but I still
> need
> > the straight line distance to determine which ring I'm in. (as well as to
> > normalize the vectors)
> >
> > The problem with doing equations like this
> > if (distanceX < 10)
> > scaleX = 1;
> > if (distanceX < 20)
> > scaleX = 2;
> > if (distanceX < 30)
> > scaleX = 4;
> > ...etc...
> > speed.x += gravity_constant/scaleX;
> > is that it doesn't take into consideration the actual distance from the
> sun.
> > You could be 500 y units away and 10 x units and it will end up pulling
> > harder in the x direction. Both vectors must first be normalized to
> properly
> > divide the gravitational pull between them.
> >
> > Rodger, I also couldn't get this to properly work, but if you do find the
> > proper equation, it might be worth a try.
> > Take the smaller of xlength or ylength, multiply it time 3, divide
> > by 2, and add the result to the larger of xlength or ylength. The
> > result is a close approximation of the square root of the sum of
> > the squares.
> >
> > I have also toyed with the idea of doing linear gravity, I'm just afraid
> > that you won't be able to orbit properly. (I get upset in gravitar because
> > you can't quite orbit the planet that you can fly in circles around)
> >
> > Clay, I threw a few numbers into these equations
> > "real dist" = sqrt(x^2+y^2), "fake dist" = ((X*2)+(Y*2))/4
> > and in a circular obit, the gravity gets stronger when you have only an x
> or
> > y offset and weaker when your at one of the 45 degree angles from the sun.
> > (making the gravity rings a square turned 45 degrees). But this might be
> ok
> > consider how little time it takes to calculate.
> >
> >
> > thanks
> > -jeff
> >
> >
>

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Joseph J. Welser jwelser@ccwf.cc.utexas.edu
Design Engineer -- Crystal Semiconductor Corporation
Ph.D. Student in E.E. -- University of Texas at Austin
Work: jwelser_at_crystal.cirrus.com http://www.crystal.com
P.O. Box 17847; Austin, TX 78760
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Received on Fri Oct 29 09:12:23 1999