From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik)
Newsgroups: sci.math
Subject: Re: matrix inversion with random numbers
Date: 7 Jan 1997 15:43:36 -0500

In article <21nAjDAQ7T0yEwE4@gocomp.demon.co.uk>,
Richard H Gould  <rhgould@gocomp.demon.co.uk> wrote:
>In article <32D002F9.1BE9@math.okstate.edu>, David Ullrich
><ullrich@math.okstate.edu> writes
>> What makes you think there
>>exist matrix-inversion algorithms that use random numbers?
>>
>I assumed he meant that the matrix elements had no pattern - not
>integers, matrix not sparse, etc.
>
>Again, since no-one has answered, if my interpretation of the question
>is correct, look up the L-U decomposition method.  It's quite elegant
>and easy to code if you want to write a program for matrix inversion.
>-- 
>Richard H Gould 
>rhgould@gocomp.demon.co.uk

Reference for Monte Carlo inversion (basically for matrices A close to 
identity in the sense that  spectral radius(abs(I-A)) < 1 ):

"Matrix Inversion by Monte Carlo Methods" , by Florence Jeanne Oswald; 
article included as Ch. 6 in
 "Mathematical Methods for Digital Computers", edited by A. Ralston and 
  H. Wilf,, John Wiley & Sons, Inc., New York 1960

It seems that the first study in this direction is (as quoted by Oswald): 

G.E. Forsythe and R.A. Leibler: Matrix Inversion by a Monte Carlo Method, 
MTAC, vol. 4, 1950, pp. 127-129.

(I don't know what MTAC stands for.)

Cheers, ZVK (Slavek).

==============================================================================
[MTAC=Math.Tables and other Aids to Computation, later rechristened Mathematics
of Computation -- djr]