I solve recursively a series of linear systems of ever increasing number of unknowns, proven to have a unique solution, each of which is expressed as a function of all the previous unknowns. So Y[i]=sum(c[i][j]*X[i][j],j=1..nops(X[i])), and most c[i][j]'s are nonzero.
I successfully used solve(Y[i],X[i]) and SolveTools[Linear](Y[i],X[i]) to get each Y[i] solution but, as i increases, the solution time increases exponentially.
For example, in my system (P4 2.66GHz, 2GB RAM) solving a system of 15 variables takes about 6 seconds, while one of 21 variables needs about 250 seconds!
Is this to be expected? I need to solve to about 40 variables this way but it doesn't seem possible with solution time increasing at this rate.
any input would be much appreciated
PS. As the coefficients of X[i]'s in the system include sums and products of X[m]'s, m