Re: Solving A*x=b when A is full rank but numerically rank deficient

[CdeMills]

Sorry to contradict you. I went one step further:

A=randn(5,5); A=A.'*A; 
AA=A*kron(logspace(34, 4, 5), ones(5,1)); AAmp = AA+mp(0);
X=rand(5,1); B=AA*X;Bmp=AAmp*X; 
AAinv=inv(AAmp.'*AAmp);

double([AA\B AAinv*(AAmp.'*Bmp) X]) 
ans =

   9.4146e-02   9.4146e-02   9.4146e-02
   2.9772e-09   7.1297e-01   7.1297e-01
   9.4146e-17   7.0114e-01   7.0114e-01
   2.9772e-24   1.5793e-01   1.5793e-01
   9.4146e-32   9.4513e-01   9.4513e-01

As you may notice, ALL the solutions are correctly computed in the second
case. 'mp' is a class I'm busy working on, implementing multi-precision
arithmetic. I have to explicitelly invert the design matrix, as the left
division operator still has some issues.

Regards

Pascal



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