Re: Large number of equations with large number of unknowns
- To: mathgroup at smc.vnet.net
- Subject: [mg27563] Re: [mg27498] Large number of equations with large number of unknowns
- From: "Mark Harder" <harderm at ucs.orst.edu>
- Date: Wed, 7 Mar 2001 04:08:02 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Derek,
You say you have linearly independent equations that you are trying to
solve for the "values" of the variables with Solve[]. However, I always
thought Solve was for solving nonlinear equations , Polynomial systems, and
mixtures. A look at the implementation notes in the Book reveals some of
its methods, and they seem to be based on Groebner bases, variable
substitution methods, and construction of Inverse Functions in code that is
500 pages long. None of them are made for solving linear systems. There are
specialized methods for solving Linear Systems of equations in Mathematica
(and elsewhere) and I find it hard to believe they can't handle an 80x80
system with ease.
I recommend you begin with the add-on package
"LinearAlgebra`MatrixManipulation" which contains the function
LinearEquationsToMatrices[eqns,vars]. You give it your equations (with
double equals, ==) and a list of the 80 symbolic variables, and it returns
the matrix of coefficients of the system (which can be either symbolic or
numeric). With that, you can use several methods -- There is a
GaussianElimination package in "LinearAlgebra`, which contains functions for
obtaining the LU decomposition of the coefficient matrix and solving the
system with the decomposition. See the documentation for details.
Good Luck
-mark harder
-----Original Message-----
From: Derek <drek1976 at yahoo.com>
To: mathgroup at smc.vnet.net
Subject: [mg27563] [mg27498] Large number of equations with large number of unknowns
>Hi all
>
>I have 80 equations, containing a total of 80 unknowns (not all equations
>contain exactly 80 unknowns). These linearly independent equations were
>obtained after a long process involving various manipulations like the
>method of moments, in pursuant of forming the mixed potential integral
>equation, used for modelling a microstrip patch antenna. I have tried using
>"Solve" but it is not able to deal with so many unknowns.
>
>I would thus like to know if anyone out there knows of any
>code/method/command to find the values of the unknowns in such a large
>system with so many equations. Would be extremely grateful for any help
>rendered.
>
>Thanks in advance
>
>Derek
>
>