On the performance of the Cholesky factorization in interior point methods on Pentium 4 processors

The paper concerns the Cholesky factorization of symmetric positive semidefinite matrices arising in interior point methods. In our investigation we focus on the efficiency of the factorizations when solving large-scale problems. We show that the capabilities of modern processors can be efficiently utilized by special implementation techniques. Through numerical experiments we demonstrate that 3.30 gigaflops sustained and 4.72 gigaflops peak performance can be achieved on a 2.8 GHz Intel Pentium 4 processor when solving large-scale optimization problems.