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B. Scheichl:
"SPARSOL";
Publication type: numerical software, project: SPARSOL provides the novel components C05QSF (nagf_roots_sparsys_func_expert) / c05qsc (nag_zero_sparse_nonlin_eqns_easy) for the NAG Fortran / C Libraries (Mark 23, released 2011 / 2012); 2009.

SPARSOL is designed to find a root of a large sparse system of nonlinear algebraic equations, i.e. one having Jacobians where the ratio between the numbers of nominal non-zero entries and the overall entries is small. In each Newton step the resulting linear system is solved in a memory-saving manner according to the sparsity pattern of the Jacobian. As a global strategy ensuring robustness in the sense of convergence from arbitrary starting points, a modification of Powell's hybrid method is adopted. Amongst other things, the algorithm features automated detection and economical internal usage of the sparsity pattern of the equations and computation of the Jacobians, supplemented with the possibility of a secant update in each Newton step, as long as the such approximated and the actual Jacobians are sufficiently close.

automated Jacobian calculation, double dogleg step, model-trust region method, Powell's hybrid method, sparse nonlinear equations, sparse secant update, sparsity pattern detection