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CONDITION\ Matrix Condition Number Estimation {#condition-matrix-condition-number-estimation align=”center”} ==================================


CONDITION is a C++ library which implements methods for computing or estimating the condition number of a matrix.

Let ||*|| be a matrix norm, let A be an invertible matrix, and inv(A) the inverse of A. The condition number of A with respect to the norm ||*|| is defined to be

        kappa(A) = ||A|| * ||inv(A)||

If A is not invertible, the condition number is taken to be infinity.

Facts about the condition number include:

The CONDITION library needs access to a copy of the R8LIB library.

Licensing: {#licensing align=”center”}

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

Languages: {#languages align=”center”}

CONDITION 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.

LINPACK_D, a C++ library which solves linear systems using double precision real arithmetic;

NAPACK, a FORTRAN77 library which includes many routines for applied numerical linear algebra tasks, including the matrix condition number, by William Hager.

R8LIB, a C++ library which contains many utility routines using double precision real (R8) arithmetic.

TEST_MAT, a C++ library which defines test matrices for which some of the determinant, eigenvalues, inverse, null vectors, P*L*U factorization or linear system solution are already known.

Reference: {#reference align=”center”}

  1. Alan Cline, Cleve Moler, Pete Stewart, James Wilkinson,\ An estimate for the Condition Number of a Matrix,\ Technical Report TM-310,\ Argonne National Laboratory, 1977.
  2. Alan Cline, Russell Rew,\ A set of counterexamples to three condition number estimators,\ SIAM Journal on Scientific and Statistical Computing,\ Volume 4, Number 4, December 1983, pages 602-611.
  3. William Hager,\ Condition Estimates,\ SIAM Journal on Scientific and Statistical Computing,\ Volume 5, Number 2, June 1984, pages 311-316.
  4. Nicholas Higham,\ A survey of condition number estimation for triangular matrices,\ SIAM Review,\ Volume 9, Number 4, December 1987, pages 575-596.
  5. Diane OLeary,\ Estimating matrix condition numbers,\ SIAM Journal on Scientific and Statistical Computing,\ Volume 1, Number 2, June 1980, pages 205-209.
  6. Pete Stewart,\ Efficient Generation of Random Orthogonal Matrices With an Application to Condition Estimators,\ SIAM Journal on Numerical Analysis,\ Volume 17, Number 3, June 1980, pages 403-409.

Source Code: {#source-code align=”center”}

Examples and Tests: {#examples-and-tests align=”center”}

List of Routines: {#list-of-routines align=”center”}

You can go up one level to the C++ source codes.


Last revised on 04 October 2012.