ASA006 is a MATLAB program which computes the Cholesky factor of a positive definite symmetric matrix.
ASA006 is Applied Statistics Algorithm 6. Source code for many Applied Statistics Algorithms is available through STATLIB.
If A is a positive definite symmetric matrix, then there is an upper triangular matrix U with the property that
A = U' * UThe matrix U is known as the Cholesky factor of A, and can be used to easily solve linear systems involving A or compute the inverse of A.
The algorithm implemented here uses a compressed storage for both the matrix A and the factor U. This saves some storage, but can make computations a little awkward.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
ASA006 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
ASA007, a MATLAB library which computes the inverse of a symmetric positive definite matrix, and uses a version of ASA006 for for Cholesky factorization.
ASA047, a MATLAB library which implements the Nelder-Mead minimization algorithm, and uses a version of ASA006 for Cholesky factorization.
LAPACK, a FORTRAN90 library which includes routines for Cholesky factorization.
LINPACK, a MATLAB library which includes routines for Cholesky factorization.
NL2SOL, a FORTRAN77 library which solves nonlinear least squares problems, and includes routines for Cholesky factorization.
PPPACK, a FORTRAN77 library which carries out piecewise polynomial interpolation and includes routines for Cholesky factorization.
TOEPLITZ_CHOLESKY, a MATLAB library which computes the Cholesky factorization of a nonnegative definite symmetric Toeplitz matrix.