Mathematica loop

• To: mathgroup at smc.vnet.net
• Subject: [mg125796] Mathematica loop
• From: Amatya <asinha at rhsmith.umd.edu>
• Date: Tue, 3 Apr 2012 04:45:28 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Hi,

I have a vector of n=5 variables x, that are the solution of "n=5" non-linear equations. I have i= 1 to 100 vectors of coefficient data "ci" of the non linear equations, and for each of those vectors "ci", I want to solve the system of non-linear equations and return a solution vector x. So in the end I want 100x5 matrix where each row represents different coefficients and each column represents one of the variables of x.

Also, all of the non-linear equations are very sensitive to starting points in the FindRoot. I need some flexibility so I can specify a different starting point and domain in which FindRoot looks for the solution, for each of the 100 values of the input parameters. Is there a clean way to do this?

My algorithm should basically do this:

Initial search point: a1=something,...,a5=something
For i = 1 to 100
x/.FindRoot[{f1(x;ci)==0,..,f5(x;ci)==0},{{x1,a1}...{x5,a5}}]
Store results in a Matrix
a1=new start value according to formula based on i
.. a5= new value according to formula based on i
i=i+1

Is it possible to do this using Table or something? Solve a 100 FindRoots in one shot giving all the initial search points and coefficient values as vector or matrix input?

Thanks

```

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