Solution of Toeplitz linear systems

TOEPLITZ is a FORTRAN77 library which solves a variety of Toeplitz and circulant linear systems.

The package can also handle circulant Toeplitz systems, and some other more complicated but related forms.

The TOEPLITZ package was written in the early 1980's by a joint working group of American and Soviet mathematicians.

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


The toeplitz.f file is in the public domain.

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


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

Related Data and Programs:

BLAS1, a FORTRAN77 library which contains the level 1 Basic Linear Algebra Subprograms.

LINPACK, a FORTRAN77 library which carries out the factorization and solution of linear systems of a variety of types.

LINPLUS, a FORTRAN77 library which includes some routines for manipulating Toeplitz matrices.

TEST_MAT, a FORTRAN77 library which includes some routines which define sample Toeplitz matrices.

TOEPLITZ_CHOLESKY, a FORTRAN77 library which computes the Cholesky factorization of a nonnegative definite symmetric Toeplitz matrix.


  1. Oleg Arushanian, MK Samarin, Valentin Voevodin, Evgeny Tyrtyshnikov, Burton Garbow, James Boyle, Wayne Cowell, Kenneth Dritz,
    The TOEPLITZ Package User's Guide,
    Argonne National Laboratory,
    ANL-83-16, 1983.
  2. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
    LINPACK User's Guide,
    SIAM, 1979,
    ISBN13: 978-0-898711-72-1.
  3. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
    Basic Linear Algebra Subprograms for Fortran Usage,
    Algorithm 539,
    ACM Transactions on Mathematical Software,
    Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

Examples and Tests:

List of Routines:

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

Last revised on 27 August 2013.