Coleman, Thomas F.Verma, Arun2007-04-042007-04-041995-12http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.tc/95-225https://hdl.handle.net/1813/5560This paper is concerned with the efficient computation of sparse Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of a graph coloring technique, bi-coloring, to exploit the sparsity of the Jacobian matrix J and thereby allow for the efficient determination of J using AD software. We analyze both a direct scheme and a substitution process. We discuss the results of numerical experiments indicating significant practical potential of this approach.376377 bytes441930 bytesapplication/pdfapplication/postscripten-UStheory centersparse Jacobian matricesnonlinear systems of equationsnonlinear least squaresgraph coloringbi-coloringautomatic differentiationcomputational differentiationsparse finite differencingpartition problemNP-complete problemsADOL-Ctechnical report