From: Johannes H Andersen <johs@madasafish.com>
Subject: Re: solving: inv(A+B)
Date: Sat, 18 Mar 2000 10:30:27 +0000
Newsgroups: comp.soft-sys.matlab,comp.dsp,sci.math
Summary: [missing]

Brett George wrote:
> 
> Is there a method (or identity) in which you could solve the matrix problem
> inv(A+B), in terms of A,B,inv(A) and inv(B)?
> 
> I need this because inv(A) and inv(B) are easy to solve, while there sum is
> not.
> 


If B = UV, then there is the Sherman-Morrisson-Woodbury formula:

    (A+B)^-1  =  A^-1 - A^-1U(I + VA^-1U)^-1VA^-1  .

This may be an advantage if U and V' are of size m x n and n << m . It is the
generalisation of the rank-1 update. 

Johannes