Solving linear equations systems with > 9 variables accurately?
06-05-2015, 06:28 PM (This post was last modified: 06-05-2015 06:30 PM by Dieter.)
Post: #1
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
Solving linear equations systems with > 9 variables accurately?
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
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 Messages In This Thread Solving linear equations systems with > 9 variables accurately? - Dieter - 06-05-2015 06:28 PM RE: Solving linear equations systems with > 9 variables accurately? - Werner - 06-05-2015, 08:11 PM RE: Solving linear equations systems with > 9 variables accurately? - Marcio - 06-05-2015, 08:36 PM RE: Solving linear equations systems with > 9 variables accurately? - Dieter - 06-06-2015, 07:19 PM RE: Solving linear equations systems with > 9 variables accurately? - Bernd Grubert - 06-08-2015, 11:51 AM RE: Solving linear equations systems with > 9 variables accurately? - Marcio - 06-08-2015, 12:20 PM RE: Solving linear equations systems with > 9 variables accurately? - DMaier - 06-14-2015, 05:40 AM RE: Solving linear equations systems with > 9 variables accurately? - Paul Dale - 06-08-2015, 09:47 PM RE: Solving linear equations systems with > 9 variables accurately? - Dieter - 06-09-2015, 08:22 PM RE: Solving linear equations systems with > 9 variables accurately? - Paul Dale - 06-09-2015, 10:01 PM RE: Solving linear equations systems with > 9 variables accurately? - Dieter - 06-11-2015, 10:54 AM

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