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## Re: Implementation of mldivide?

 From: CdeMills Subject: Re: Implementation of mldivide? Date: Tue, 26 Jul 2011 12:10:21 -0700 (PDT)

>
>
> I'm not sure what you mean by "analytically". The formula you wrote
> down for the inverse of L is certainly not used by the backslash
> operator. Ignoring that word, the answer is a little complicated,
> because the implementation of the backslash operator is spread out
> over several source files depending on the inputs. You may find these
> answers from the manual more illuminating:
>
>
> http://www.gnu.org/software/octave/doc/interpreter/Techniques-Used-for-Linear-Algebra.html#Techniques-Used-for-Linear-Algebra
>
> http://www.gnu.org/software/octave/doc/interpreter/Sparse-Linear-Algebra.html#Sparse-Linear-Algebra
>
>
With B = inv(L.'*L)*L.'*y,
I can write
dBdZ =
-(inv(L.'*L)*(dLdZ.'*L+L.'*dLdZ)*inv(L.'*L)*L.'*y)+inv(L.'*L)*dLdZ.'*y
i.e. an explicit formula where the derivates dLdZ are apparent.

I should have made clear that the number of lines of L is >> number of
columns, and that the columns are linearly independent. The purpose is to
use noise propagation technique to infer the noise on B caused by the noise
on Z. This way, I need to be able to express the solution in terms of
operations whose derivatives can be computed.

Regards

Pascal

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