## 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.

#### Abstract

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.
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