Estimating the Condition Number: LAPACK Computational Routines

This section describes the LAPACK routines for estimating the condition number of a matrix. The condition number is used for analyzing the errors in the solution of a system of linear equations (see Error Analysis). Since the condition number may be arbitrarily large when the matrix is nearly singular, the routines actually compute the reciprocal condition number.

?gecon
Estimates the reciprocal of the condition number of a general matrix in the 1-norm or the infinity-norm.
?gbcon
Estimates the reciprocal of the condition number of a band matrix in the 1-norm or the infinity-norm.
?gtcon
Estimates the reciprocal of the condition number of a tridiagonal matrix.
?pocon
Estimates the reciprocal of the condition number of a symmetric (Hermitian) positive-definite matrix.
?ppcon
Estimates the reciprocal of the condition number of a packed symmetric (Hermitian) positive-definite matrix.
?pbcon
Estimates the reciprocal of the condition number of a symmetric (Hermitian) positive-definite band matrix.
?ptcon
Estimates the reciprocal of the condition number of a symmetric (Hermitian) positive-definite tridiagonal matrix.
?sycon
Estimates the reciprocal of the condition number of a symmetric matrix.
?sycon_3
Estimates the reciprocal of the condition number (in the 1-norm) of a real or complex symmetric matrix A using the factorization computed by ?sytrf_rk.
?hecon
Estimates the reciprocal of the condition number of a Hermitian matrix.
?hecon_3
Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian matrix A.
?spcon
Estimates the reciprocal of the condition number of a packed symmetric matrix.
?hpcon
Estimates the reciprocal of the condition number of a packed Hermitian matrix.
?trcon
Estimates the reciprocal of the condition number of a triangular matrix.
?tpcon
Estimates the reciprocal of the condition number of a packed triangular matrix.
?tbcon
Estimates the reciprocal of the condition number of a triangular band matrix.