modified-cholesky - Modified Cholesky factorization

About

modified-cholesky contains MATLAB functions that compute a modified Cholesky factorization of a symmetric and possibly indefinite matrix. The algorithm is from

S. H. Cheng and N.J. Higham. "A modified Cholesky algorithm based on a symmetric indefinite factorization". SIAM J. Matrix Anal. Appl., 19(4):1097-1110, 1998.

and uses LDL^T factorization with a symmetric form of rook pivoting proposed by Ashcraft, Grimes, and Lewis. The functions here are based on code originally written by Bobby Cheng and Nick Higham in 1996.

The MATLAB functions are:

• modchol_ldlt: the modified Cholesky function. It calls the built-in MATLAB function ldl to compute the LDL^T factorization.

• modchol_ldlt_m: this is the original version of modchol_ldlt from 1996, where the _m in the name denotes that the LDL^T factorization is computed using pure M-code. The output of this version should be the same as that from modchol_ldlt to within rounding error. The reasons for including this version are as follows.

  • Since the code for the factorization is explicitly included as M-code the _m version is of pedagogical interest. It will also be useful for anyone who wants to modify the factorization to use a different pivoting strategy.
  • The _m version computes the growth factor for the factorization, which this is not available from modchol_ldlt itself.

  Note that the _m version does not exploit symmetry and is not designed to be efficient.

• test_modchol_ldlt: a simple test code.

Requirements

The codes have been developed under MATLAB 2015b.

License

See license.txt for licensing information.