R help - Oct 2011 - How to calculate determinant and inverse matrix of a specific structure

Hi All,

I have a specific structure matrix, which is a AR(1) matrix plus a diagonal
matrix, i.e., 
Mat = sigma^2 * M(rho) + tau^2 * I,
where M(rho)_ij = rho^abs(i-j). 

How can I calculate det(Mat) and solve(Mat) efficiently? I'm using the det()
and solve() functions now, but since I'm calculating in nested loops for
tons of iterations, my Mat matrix is a 24*24 matrix, and later I'll need to
make the size larger, the calculation spends too much time. I tried to
calculate the determinant by hand, but the result is another series, and
it'll be another nested loop in the code. I wonder if there's any way to
improve the efficiency of this calculation of the specific structure matrix.

Thank you very much.

Abby

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