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Topic: Q: on matrix inverse by partitioning
Replies: 5   Last Post: Jul 18, 1996 6:19 PM

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calvitti@zmo.ces.cwru.edu

Posts: 6
Registered: 12/11/04
Q: on matrix inverse by partitioning
Posted: Jul 15, 1996 9:56 PM
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'numerical recipes' lists the following partitioning method for
finding matrix inverses. given:

A = [ P | Q ] and Inv(A) = [ P* | Q* ]
[ R | S ] [ R* | S* ]

where P and S are square not necessarily of the same size:

P* = Inv(P - Q.Inv(S).R)
Q* = -Inv(P - Q.Inv(S).R).Q.Inv(S)
R* = -Inv(S).R.Inv(P - Q.Inv(S).R)
S* = Inv(S) + Inv(S).R.(P - Q.Inv(S).R).Q.Inv(S)

but states nothing about the case when A is invertible but S is not
for example. does anyone know the set of conditions that A must
satisfy for this algorithm to be valid?

thanks for the info,

alan







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