large linear systems

*To*: mathgroup at smc.vnet.net*Subject*: [mg2564] large linear systems*From*: FERRUCCIO Renzoni <renzoni at fexphds04.tu-graz.ac.at>*Date*: Tue, 21 Nov 1995 09:24:06 -0500

Dear wizs, I have some doubts about solving large linear systems. Suppose that I have to solve: m.x = v with m being a symbolic and complicated matrix and v a vector. The critical point is to find a way to get an answer short enough to be processed by some combination of Simplify, Together, Expand ... I tried: 1) LinearSolve[m,v] 2) ics = {x1,x2,x3,x4,x5,x6,x7,x8,x9}; com[i_] := Apply[ PolynomialGCD, m[[i]] ] Do[ eqn[i] = {Factor @ Numerator @ Together @ ((m[[i]].ics-v[[i]])/com[i]) == 0},{i,1,9}] eq = Join[ Flatten[ Table[eqn[i],{i,1,9}]]]; sol = ics /. Solve[eq,ics][[1]]; The strange thing is that the (2) produce an answer shorter than (1). That's strange because I supposed that a routine (LinearSolve) produced especially for a linear system worked more efficiently that a generic routine for any kind of equations (or systems of equations). My question is: does anyone knows some better way to solve a symbolic linear system without producng enourmous expressions which cannot be processed by Mathematica? Thanks a lot F. Renzoni