toeplitz, a FORTRAN90 code 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 package was written in the early 1980's by a joint working group of American and Soviet mathematicians.

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


The computer code and data files made available on this web page are distributed under the MIT license


toeplitz is available in a FORTRAN90 version.

Related Data and Programs:

BLAS1, a FORTRAN90 code which contains the level 1 Basic Linear Algebra Subprograms.

LINPACK, a FORTRAN90 code which carries out the factorization and solution of linear systems of a variety of types.

test_matrix, a FORTRAN90 code which includes some routines which define sample Toeplitz matrices.


TOEPLITZ_CHOLESKY, a FORTRAN90 code 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:

Last revised on 08 September 2020.