[R] invert 160000x160000 matrix

[Patnaik, Tirthankar]

A variety of tricks would need to be used to invert a matrix of this size. If there are any other properties of the matrix that you know (symmetric, positive definite, etc, sparse) then they could be useful too. You could partition the matrix first, then use an in-place inverse technique for each block to individually calculate the blocks-inverses, then combine to get the inverse of the initial matrix. Again, if the implementation is actually solving an Ax-B = 0 system of equations, then there are specific methods for these too, like an LU decomp, for instance. You might also want to check out some texts for this, like the Numerical Recipes. 
How's the matrix stored right now?

Best,
-Tir



Tirthankar Patnaik
India Strategy
Citigroup Investment Research
+91-22-6631 9887

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> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Moshe Olshansky
> Sent: Tuesday, August 14, 2007 6:40 AM
> To: Paul Gilbert; Jiao Yang
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] invert 160000x160000 matrix
> 
> While inverting the matrix may be a problem, if you need to 
> solve an equation A*x = b you do not need to invert A, there 
> exist iterative methods which do need A or inv(A) - all you 
> need to provide is a function that computes A*x for an 
> arbitrary vector x.
> For such a large matrix this may be slow but possible.
> 
> --- Paul Gilbert <pgilbert at bank-banque-canada.ca>
> wrote:
> 
> > I don't think you can define a matrix this large in R, even if you 
> > have the memory. Then, of course, inverting it there may be other 
> > programs that have limitations.
> > 
> > Paul
> > 
> > Jiao Yang wrote:
> > > Can R invert a 160000x160000 matrix with all
> > positive numbers?  Thanks a lot!
> > > 
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