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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) |

Jordi GutiĆ©rrez Hermoso-2 wrote:
>* *
>* *
>* 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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