**S. Bonettini - ****V.
Ruggiero**

The code is a collection of Fortran 90 subroutines for the factorization and
the solution of systems that admit a Cholesky-like factorization (for
example, quasidefinite systems).

It is based on a modification of the
package of Ng and Peyton, that performs the Cholesky factorization of a positive
definite matrix. The package is included in LIPSOL 0.3, downloadable from www.caam.rice.edu/~zhang/lipsol.
The whole process can be subdivided in two phases.The first phase is depending
only on the structure of the matrix and its aims are performing the minimum
degree reordering (ORDMMD), providing the supernodal subdivision (SFINIT) and
computing the symbolic factorization (SYMFCT, BFINIT) of the matrix. These
subroutines belong to the package of Ng and Peyton. In the second phase, the
actual factorization of the matrix is performed by means of the subroutines
INPNV (also from the Ng and Peyton package) and BLKFCT. The last one is derived
from the BLKFCT subroutine of Ng and Peyton, so that it can be used in
combination with the other subroutines of that package, but it produces a
Cholesky-like *LDL ^{T}* factorization (instead of the Cholesky
factorization

The effectiveness of the package of Ng and Peyton, due to a suitable use of the cache memory, is maintained.

**Authors:**

**Silvia Bonettini**

Dept. of Mathematics, University of Modena and Reggio Emilia - ITALY

bonettini.silvia@unimo.it**Valeria Ruggiero**

Dept. of Mathematics, University of Ferrara - ITALY

v.ruggiero@unife.it

This work is supported by the Italian FIRB Project

Parallel Algorithms and Numerical Nonlinear
Optimization (grant RBAU01JYPN), http://dm.unife.it/pn2o

and by the Italian M.I.U.R. Project

Numerical Methods and
Mathematical Software in Applications (grant 2004012559),
http://www.math.unifi.it/~brugnano/Cofin2004.

The file BLKFCLT.F contains all the subroutines needed for the factorization of the matrix and for the solution of the system. All the matrices involved have to be stored in the Compressed Column Storage form. As an example of the subroutines usage, download the file example.f90 .

An extensive numerical experimentation of the package BLKFCLT can be found in the technical report n.64 of the University of Modena and Reggio Emilia. Here, the factorization subroutines are employed in the optimization framework, in the solution of the inner subproblem of an interior-point loop.

- S. Bonettini, V. Ruggiero,
*Some iterative methods for the solution of a reduced symmetric indefinite KKT system*, (2004) - J. W. Liu, E. G. Peyton,
*On finding supernodes for sparse matrix computations*, SIAM J. Matrix Anal. Appl., 14 (1993), 242-252.