Graph coloring and the estimation of sparse Jacobian matrices with segmented columns

Trond Steihaug and A.K.M. Shahadat Hossain

Reports in Informatics No. 72, November 1992, Department of Informatics, University of Bergen, Norway.


It is well known that a sparse Jacobian matrix can be estimated by fewer function evaluations than the number of columns by using the CPR technique. An example shows that if the rows of the matrix are partitioned into two blocks then fewer function evaluations are needed. In this paper we show the relationship between estimating the Jacobian matrix by grouping together both rows and columns and the graph coloring problem. We give an easy implementation of the element isolation principle.


(This is a revised version!)