Solving multiple independent non linear equations

Hi,

I have a large number (order of 1 Milion) of non linear equations that I want to solve simultaneously.

The equations are of the form

func(x)-(a_i*x+b_i)==0

Where func is some non linear function like sin(x) (for example) and a_i, b_i are given - these equations just calculate the intersection point of some non linear function of x with many linear functions. Note that the variable x is not the same in all equations - the equations are independent. I can provide a good approximation to the solution which can be used for initializing some algorithm.

I took a look on the documentation of fzero or fsolve but I am not sure I can use them.

My current approach is to calculate second order Taylor approximations of func and intersect the linear functions with them, but I think that this is not fast, not accurate and not elegant.

Does anybody know how to do this?

Thanks

H.

Answer 1

[Alan Weiss]

I can think of two ways:

1. Use fzero in a loop, solving one component at a time.
2. Use fsolve with the following options:

 'Algorithm' = 'trust-region-reflective'
 'JacobPattern' = speye(n) % , where n is the number of equations you have
 'PrecondBandWidth' = 0

Alan Weiss

MATLAB mathematical toolbox documentation