Solving linear equations systems with > 9 variables accurately?

[Dieter]

I am currently designing two rational approximations for the Normal distribution's quantile function, with a working range from 0,5 to 1 E–99. The desired 10-digit accuracy (with a 13-digit implementation in HP41 MCODE) requires solving linear equation systems with 9...11 variables. I usually do this with Excel, but with 10-12 digit target accuracy of the solution this is simply not possible with Excel's 15 digit working precision.

So I did the 9-variable-case on a 34s. and the results came out accurately. Great, so this problem was solved. But 9 unknowns are the maximum the 34s can handle: it requires 81 registers for the matrix, 9 for the right hand side vector and another 9 for the solution, so 99 out of 100 registers are used.

But what can I do for the 10- or 11-variable case? I do not have access to Mathematica, Maple or other commercial math software, and I do not know a way to trick the 34s into handling larger matrices. Does anyone know of a (free) solution that runs on Windows XP/7? Or maybe there is a way using the 34s emulator...?-)

Dieter