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Brent's Method for Multiple Nonlinear Equations Without Derivatives
Syntax [x, nfun] = brent(function f, fval, xini, step, mfun)
See Also snewton , dnlsq

Description
Solves multiple nonlinear scalar valued equations of a scalar argument using a combination of bisection, linear interpolation and Brent's method. The return value x is matrix with the same type and dimension as xini, such that

     f  (x  ) = fval 
      ij  ij        ij
The real, double-precision or complex matrix xini specifies the starting point when Brent's method is applied to solve the corresponding equation above. The matrix fval has the same type and dimension as xini and specifies the right hand side of the equation. The scalar step has the same type as x and specifies the initial step size with respect to x for bracketing the minimum.

The integer scalar mfun specifies the maximum number of evaluations of f to attempt. If the method cannot not converge in mfun calls to f, brent returns the current estimate of x and with
     nfun = mfun + 1
Otherwise, the return value of nfun is the number of evaluations of f that was used by brent

f(x)
The returns the element-by-element a matrix valued function f(x) where x is a matrix with the same type and dimension as xini.

Example
The following example uses brent to compute the square roots of 1, 2, 3 and 4 (though we would normally use the sqrt function for this task).
     clear
     function f(x) begin
          return x^2.
     end
     fval  = double(seq(4))
     xini  = 1d0 + rand(4, 1)
     step  = .1d0
     mfun  = 100
     [x, nfun] = brent(function f, fval, xini, step, mfun) 
     print x
 returns
     {
     1
     1.41421
     1.73205
     2
     }
 which are the square roots of 1, 2, 3, and 4 respectively.