Linear Least Squares Problem for Y = A*X+B

LLSQ is a FORTRAN77 library which solves the simple linear least squares (LLS) 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.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


LLSQ is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

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, by Charles Lawson and Richard Hanson.

DQED, a FORTRAN77 library which solves constrained least squares problems, by Richard Hanson and Fred Krogh.

LAWSON, a FORTRAN77 library which contains routines for solving least squares problems and singular value decompositions (SVD), by Charles Lawson, Richard Hanson.

MINPACK, a FORTRAN77 library which solves systems of nonlinear equations, or the least squares minimization of the residual of a set of linear or nonlinear equations.

NMS, a FORTRAN77 library which includes a wide variety of numerical software, including solvers for linear systems of equations, interpolation of data, numerical quadrature, linear least squares data fitting, the solution of nonlinear equations, ordinary differential equations, optimization and nonlinear least squares, simulation and random numbers, trigonometric approximation and Fast Fourier Transforms.

QR_SOLVE, a FORTRAN77 library which computes the least squares solution of a linear system A*x=b.

TEST_APPROX, a FORTRAN77 library which defines test problems for approximation, provided as a set of (x,y) data.

TEST_LLS, a FORTRAN77 library which implements linear least squares test problems of the form A*x=b.


  1. David Kahaner, Cleve Moler, Steven Nash,
    Numerical Methods and Software,
    Prentice Hall, 1989,
    ISBN: 0-13-627258-4,
    LC: TA345.K34.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN77 source codes.

Last revised on 08 March 2012.