I am dealing with a computations wiith a large weight matrix (5000 by 5000). I am writing to seek your help in estimating an expression as given below:

Trace (W*inverse(I-lambda*W))

W is the large 5000by5000 matrix. Clearly, computing inverse and obtaining
trace is very expensive, probably not possible. I am looking at ways to
compute trace without calculating the inverse. I did find a resource by
Bai,Fahey and Golub (Some large scale matrix computation problems - CiteSeerX) to compute the bounds for trace of a inverse. But i do
not know how i can extend that concept to my expression.

Thanks for helping.