minpack, a C code which solves systems of nonlinear equations, by Jorge More, Danny Sorenson, Burton Garbow, Kenneth Hillstrom.
MINPACK includes software for solving nonlinear equations and nonlinear least squares problems. Five algorithmic paths each include a core subroutine and an easy-to-use driver. The algorithms proceed either from an analytic specification of the Jacobian matrix or directly from the problem functions. The paths include facilities for systems of equations with a banded Jacobian matrix, for least squares problems with a large amount of data, and for checking the consistency of the Jacobian matrix with the functions.
Given a set of N nonlinear equations in N unknowns, F(X) = 0, Powell's method is used to seek a solution X.
Given a set of M nonlinear functions in N unknowns, F(X), the Levenberg-Marquardt method is used to seek an X which minimizes the L2 norm of the residual ||F(X)||.
The user supplies a subroutine to evaluate the nonlinear function; the jacobian matrix dFi(X)/dXj may also be supplied by the user in a subroutine, or approximated by finite differences.
The original FORTRAN77 version of MINPACK is available through the NETLIB web site.
Minpack Copyright Notice (1999) University of Chicago. All rights reserved
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minpack is available in a C version and a C++ version and a FORTRAN90 version.
fsolve, a C code which solves systems of nonlinear equations, inspired by the fsolve() function in MATLAB, and based on the minpack() minimization package.
llsq, a C code which solves the simple linear least squares problem of finding the formula of a straight line y=a*x+b which minimizes the root-mean-square error to a set of N data points.
qr_solve, a C code which computes the least squares solution of a linear system A*x=b.
test_lls, a C code which implements linear least squares test problems of the form A*x=b.
Original FORTRAN77 version by Jorge More, Danny Sorenson, Burton Garbow, Kenneth Hillstrom. C version by John Burkardt.