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From: bas@calmasd.UUCP (Bharath 'Al' Sethuraman)
Newsgroups: net.math
Subject: Accelerating fixed point solutions
Message-ID: <408@calmasd.UUCP>
Date: Fri, 24-May-85 18:53:15 EDT
Article-I.D.: calmasd.408
Posted: Fri May 24 18:53:15 1985
Date-Received: Sun, 26-May-85 22:02:56 EDT
Reply-To: bas@ra.UUCP (Bharath 'Al' Sethuraman)
Distribution: na
Organization: Calma Company, San Diego, CA
Lines: 14

One way of solving the fixed point equation z = f(z), where z is an 
n-dim vector, and f is a (vector) function from Rn to Rn, is by iteration.
That is, one starts with a guess z0, and recursively calculates
                  z1 = f(z0)
                  z2 = f(z1)
                  .........
                  zn = f(zn-1),
hoping that the sequence z0,z1,z2,... converges.  I need some suggestions
on how to accelerate this procedure. (Techniques that might, for example,
compute an improved zn based on a certain number of previous z-sub-i(s).)
I primarily need acceleration techniques for 3 or less dimensions.  Any 
comments on speed,complexity, etc. would also be appreciated.

Thanks!