Algorithm 554: BRENTM, A Fortran Subroutine for the Numerical Solution of Nonlinear Equations [C5]
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BRENTM is a subroutine designed to solve a system of n nonlinear equations in n variables by using a modification of Brent's method (SIAM J. Numer. Anal., 10, 327-344 (1973)). The subroutine does not use any techniques that attempt to obtain global convergence; therefore, convergence is guaranteed only if the initial estimate for the solution is close enough. On the other hand, the code does seem to have a large region of convergence; convergence occurs only at a zero of the function, and if the iteration is not making satisfactory progress, then BRENTM will attempt to diagnose this situation and stop the iteration with an appropriate message. The use is only required to provide a subroutine that calculates components of the function. (RWR)
[1] R. Brent. Some Efficient Algorithms for Solving Systems of Nonlinear Equations , 1973 .
[2] Michel Cosnard,et al. Numerical Solution of Nonlinear Equations , 1979, TOMS.