A comparative study of algorithms for reducing the fill-in during Cholesky factorization

Abstract

In this paper several ordering algorithms for the unknowns in geodetic least squares systems are compared. The comparison is restricted to the case of the well known Cholesky factorization of the normal matrixA into a lower triangular factorL. p ]The algorithms which were investigated are: minimum degree, minimum deficiency, nested dissection, reverse Cuthill-McKee, King's-, Snay's-, and Levy's-banker's and Gibbs-King. p ]Also some strategies are presented to reduce the time needed to compute the ordering using a priori information about the way the unknowns are connected to each other. p ]The algorithms are applied to normal matrices of the least squares adjustment of 2D geodetic terrestrial networks, photogrammetric bundle-block adjustments, and a photogrammetric adjustment using independent models. p ]The results show that ordering the unknowns yields a considerable decrease of the cpu time for computing the Cholesky factor, and that in general the minimum degree and Snay's banker's ordering perform best. Furtheron they show that a priori information about the connection structure of the unknowns speeds up the computation of the ordering substantially.