This is a very general question regarding the maximum size of a set of linear equations to be solved by today's fastest hardware, in the form:
X = AX + B
A: NxN matrix of floats, it is sparse.
B: N-vector of floats.
solve for X.
This becomes X(I-A) = B which is best solved using factorisation (and not matrix inversion) as I read here:
http://www.johndcook.com/blog/2010/01/19/dont-invert-that-matrix/
Do you know yourselfs or have a reference to a benchmark or paper which gives some maximum value for N with today's fastest hardware? Most benchmarks I have seen use N < 10,000. I am thinking about N>10x10^6 or more to be processed within a month.
Please consider not only the computational dimension but also storage for A. It can be a problem: e.g. assuming N = 1 x 10^6, storage would be 1x10^12 x 4 bytes / (1024x1024x1024) = 4 Terrabytes for totally dense matrix, which is about manageable I guess.
Lastly, can the method to solve the system be parallelised so that I can make the assumption that with parallelisation N can be pretty large?
thanks in advance, bliako
