[R] quadratic form

[Peter Dalgaard]

Peter Dalgaard <p.dalgaard at biostat.ku.dk> writes:

> Alvarez Pedro <palvarez7777 at yahoo.es> writes:
> 
> > On page 22 of the R-introduction guide it's written:
> > 
> > the quadratic form x^{'} A^{-1} x which is used in
> > multivariate computations, should be computed by
> > something like x%*%solve(A,x), rather than computing
> > the inverse of A.
> > 
> > Why isn't it good to compute t(x) %*% solve(A) %*% x?
> 
> It's just a waste of CPU time. For k x k matrices, solution of Ax=b is
> of computational complexity O(k^2) whereas inversion of A is O(k^3).
> This is obviously more important for k=1000 than for k=5.

Erm, Thomas Lumley points out that solution of Ax=b is also of order
k^3 ingeneral (R uses a QR decomposition). So it's just the multiplier
that differs. The savings should still be on the order of k^3 though.

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