Re: Numerical solution of quadratic equations set.

*To*: mathgroup at smc.vnet.net*Subject*: [mg58249] Re: Numerical solution of quadratic equations set.*From*: Peter Pein <petsie at dordos.net>*Date*: Fri, 24 Jun 2005 02:50:17 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Stepan Yakovenko schrieb: > Dear MathGroup experts! > > I've got a system of quadratic equations with many (57) > variables. Number of equations is less (38), so there may > be an infinite set of solutions. Also I've got an > aproximate solution that gives a good discrepancy. I want > Mathematica to find some solution or/and improve the > existing one. I'm interested in real (not complex) > solutions. > > Here's what I've tried with no result: > > NSolve[eq ==== 0, var] - gives no solutions. > FindInstance[eq====0,var,Reals] - gives no solutions. > FindRoot[] says that there's not enough equations (yes, > there isn't, but I'm interested only in one solution). > > I guess there are some options, I've no idea of, that make > these functions work fine. Or may be I'm doing something > wrong? > > I'd be very thankful if you spend some minutes on my > problem if you've got experience in using Mathematica > built-in solvers. > > And, of course the equations and the approximate solution > (just CopyPaste them). > > eq/.sol says that the solution is good. > ... > > ----------------------------------------------------------- Dear Stepan, I've been quite successful by minimizing the sum of squares of the elements of eq: {tomin, start} == {eq . eq, Transpose[{var, var /. sol}]} /. x_?NumericQ :> SetPrecision[x, Max[Precision[x], 100]]; sol2 == FindMinimum[tomin, start, PrecisionGoal -> 32, AccuracyGoal -> 32, WorkingPrecision -> 100, MaxIterations -> 1234][[2]]; N[(tomin /. #1 & ) /@ {sol1, sol2}] yields {1.8553410543246144*^-17, 3.1572401292448315*^-32} If you've got a lot of time and memory, you could try Minimize[{Rationalize[tomin], var \[Element] Reals}, var] but I really don't know how long or how much memory this will need. Peter Pein