Constrained Overdetermined Linear Systems in L1.

TOMS552 is a FORTRAN90 library which computes a solution of an overdetermined constrained linear system, minimizing the error in the L1 norm.

TOMS552 is an implementation of ACM TOMS algorithm 552.

The overdetermined linear system being solved is

A * X = B.
The equality constraints have the form:
C * X = D
and the inequality constraints have the form:
E * X >= F.
The program is required to seek a solution X which satisfies the constraints, and which minimizes the L1 norm (sum of absolute values of components) of A*X-B.

The original, true, correct version of ACM TOMS 552 is available in the TOMS subdirectory of the NETLIB web site.


TOMS552 is available in a FORTRAN77 version and a FORTRAN90 version.


Ian Barrodale,
Frank Roberts.


  1. Ian Barrodale, Frank Roberts,
    Algorithm 552: Solution of the Constrained L1 Approximation Problem,
    ACM Transactions on Mathematical Software,
    Volume 6, Number 2, March 1980, pages 231-235.
  2. Helmuth Spaeth,
    Mathematical Algorithms for Linear Regression,
    Academic Press, 1991,
    ISBN: 0-12-656460-4,
    LC: QA278.2.S6313.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.

Last revised on 28 December 2007.