BibTeX
@INCOLLECTION{
         Walther2012OtE,
       title = "On the Efficient Computation of Sparsity Patterns for {H}essians",
       doi = "10.1007/978-3-642-30023-3_13",
       author = "Andrea Walther",
       abstract = "The exploitation of sparsity forms an important ingredient for the efficient
         solution of large-scale problems. For this purpose, this paper discusses two algorithms to detect
         the sparsity pattern of Hessians: An approach for the computation of exact sparsity patterns and a
         second one for the overestimation of sparsity patterns. For both algorithms, corresponding
         complexity results are stated. Subsequently, new data structures and set operations are presented
         yielding a new complexity result together with an alternative implementation of the exact approach.
         For several test problems, the obtained runtimes confirm the new theoretical result, i.e., a
         significant reduction in the runtime needed by the exact approach. A comparison with the runtime
         required for the overestimation of the sparsity pattern is included together with a corresponding
         discussion. Finally, possible directions for future research are stated.",
       pages = "139--149",
       crossref = "Forth2012RAi",
       booktitle = "Recent Advances in Algorithmic Differentiation",
       series = "Lecture Notes in Computational Science and Engineering",
       publisher = "Springer",
       address = "Berlin",
       volume = "87",
       editor = "Shaun Forth and Paul Hovland and Eric Phipps and Jean Utke and Andrea Walther",
       isbn = "978-3-540-68935-5",
       issn = "1439-7358",
       year = "2012",
       ad_theotech = "Hessian, Sparsity"
}