LAWSON is a FORTRAN90 library which solves least squares problems.
The most common least squares problems considers an overdetermined M by N linear system A*X=B. A least squares solution X is sought which has the property that, although it generally is not a solution of the system, it is the best approximation to a solution, in the sense that it minimizes the L2 norm of the residual R=A*X-B.
In some cases, a unique solution to the system A*X=B will exist, and in that case the least squares solution will coincide with what is ordinarily meant by a solution.
In underdetermined cases, where multiple solutions exist, the least squares solution is usually taken to be that solution X which has minimum L2 norm, that is, which minimizes ||X||.
LAWSON is available in a FORTRAN77 version and a FORTRAN90 version.
BRENT, a FORTRAN90 library which contains Richard Brent's routines for finding the zero, local minimizer, or global minimizer of a scalar function of a scalar argument, without the use of derivative information.
BVLS, a FORTRAN90 library which applies least squares methods to solve a linear system for which lower and upper constraints may have been placed on every variable.
DQED, a FORTRAN90 library which solves constrained least squares problems.
ENTRUST, a MATLAB program which solves problems in scalar optimization or nonlinear least squares.
MINPACK, a FORTRAN90 library which solves systems of nonlinear equations, or the least squares minimization of the residual of a set of linear or nonlinear equations.
NL2SOL, a FORTRAN90 library which implements an adaptive nonlinear least-squares algorithm.
QR_SOLVE, a FORTRAN90 library which computes the least squares solution of a linear system A*x=b.
PRAXIS, a FORTRAN90 library which minimizes a scalar function of several variables.
TEST_LS, a FORTRAN90 library which implements linear least squares test problems of the form A*x=b.
TEST_OPT, a FORTRAN90 library which defines test problems requiring the minimization of a scalar function of several variables.
TOMS611, a FORTRAN90 library which seeks the minimizer of a scalar functional of multiple variables.
You can go up one level to the FORTRAN90 source codes.