The algorithm which estimates the condition number of a symmetric positive definite matrix is similar to the algorithm with estimates condition number of a general matrix, the only difference is that, during the evaluation, Cholesky decomposition is used instead of LU-decomposition. Therefore, we will not examine the principles of the algorithm here, since it can be found by following the link above.

This algorithm speeds up the calculations as it uses Cholesky decomposition which is generated twice as fast as LU-decomposition. A restriction of this algorithm is that it is only applicable for positive definite symmetric matrices. If you need to evaluate the condition number of an arbitrary symmetric matrix, you can use algorithm on the basis of LDLT-decomposition.

This module consists of two subroutines: SPDMatrixCholeskyRCond and SPDMatrixRCond. The first subroutine estimates the condition number of a matrix given by Cholesky decomposition, and the second one estimates the condition number of a matrix whose Cholesky decomposition hasn't been generated yet. Because 1-norm and ∞-norm of symmetric matrices are equal, there is no individual subroutine for each type of norm.

This algorithm is transferred from the LAPACK library.

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C#

C# 1.0 source.
spdrcond.csharp.zip - Condition number estimate of a symmetric positive definite matrix

C++

C++ source.
spdrcond.cpp.zip - Condition number estimate of a symmetric positive definite matrix
ablas.zip - optimized basic linear algebra subroutines with SSE2 support (for C++ sources only)

C++, multiple precision arithmetic

C++ source. MPFR/GMP is used.
GMP source is available from gmplib.org. MPFR source is available from www.mpfr.org.
spdrcond.mpfr.zip - Condition number estimate of a symmetric positive definite matrix
mpfr.zip - precompiled Win32 MPFR/GMP binaries

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
spdrcond.delphi.zip - Condition number estimate of a symmetric positive definite matrix

Visual Basic 6

Visual Basic 6 source.
spdrcond.vb6.zip - Condition number estimate of a symmetric positive definite matrix

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
spdrcond.zonnon.zip - Condition number estimate of a symmetric positive definite matrix