ASA007
Inverse of a Symmetric Positive Definite Matrix

ASA007 is a MATLAB program, using double precision arithmetic, which computes the inverse of a symmetric positive definite matrix.

ASA007 is Applied Statistics Algorithm 7. Source code for many Applied Statistics Algorithms is available through STATLIB.

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.

Related Data and Programs:

ASA006 is a MATLAB library which computes the Cholesky factorization of a symmetric positive definite matrix. A version of this routine is used by ASA007.

ASA007 is also available in a C++ version and a FORTRAN77 version and a FORTRAN90 version

ASA047 is a MATLAB library which implements the Nelder-Mead minimization algorithm, and uses a version of ASA007 for the computation.

LAPACK is a FORTRAN90 library which includes routines to compute the inverse of symmetric positive matrix.

LINPACK is a MATLAB library which includes routines to compute the inverse of symmetric positive matrix.

Reference:

1. Michael Healy,
   Algorithm AS 7: Inversion of a Positive Semi-Definite Symmetric Matrix,
   Applied Statistics,
   Volume 17, Number 2, 1968, pages 198-199.

Source Code:

• cholesky.m computes the Cholesky factorization of a PDS matrix.
• syminv.m computes the inverse of a symmetric matrix.
• timestamp.m prints out the current YMDHMS date as a timestamp.

Examples and Tests:

• asa007_test.m, a sample calling program.
• asa007_test01.m, tests SYMINV on a simple matrix.
• asa007_test02.m, tests SYMINV on the Hilbert matrix.
• asa007_test_output.txt, the output file.

You can go up one level to the MATLAB source codes.