ICFS: An Incomplete Cholesky Factorization with Limited Memory

Chih-Jen Lin and Jorge Moré

ICFS is an incomplete Cholesky factorization for the solution of large-scale trust region subproblems and positive definite systems of linear equations. This factorization depends on a parameter p that specifies the amount of additional memory that is available; there is no need to specify a drop tolerance.

The current release (Version 1.4) of ICFS , including the MATLAB interface, can be obtained by entering your email address below (so that you can be informed of future ICFS software updates) and downloading the compressed tar file that contains the software.

Email: .

The README file contains instructions on how to install the software.

Our numerical results show that the number of conjugate gradient iterations and the computing time are reduced dramatically for small values of p. Our results also show that in contrast with drop tolerance strategies, the new approach is more stable in terms of number of iterations and memory requirements.

The graph below shows the ratio of the number of conjugate gradient iterations for p > 0 to p = 0 on a set of 10 test problems. In this graph the dash-dotted line is p = 2, the solid line is p = 5, and the dashed line is p = 10.

For additional information on this approach, see Incomplete Cholesky factorizations with limited memory, SIAM Journal on Scientific Computing, 21, pages 24-45, 1999, .

Comments and suggestions should be sent to Chih-Jen Lin or Jorge Moré