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Mathematics of Computation

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A hybrid algorithm for solving sparse nonlinear systems of equations

Authors: J. E. Dennis and Guang Ye Li
Journal: Math. Comp. 50 (1988), 155-166
MSC: Primary 65H10
MathSciNet review: 917823
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Abstract: This paper presents a hybrid algorithm for solving sparse nonlinear systems of equations. The algorithm is based on dividing the columns of the Jacobian into two parts and using different algorithms on each part. The hybrid algorithm incorporates advantages of both component algorithms by exploiting the special structure of the Jacobian to obtain a good approximation to the Jacobian, using as little effort as possible. A Kantorovich-type analysis and a locally q-superlinear convergence result for this algorithm are given.

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Keywords: Finite difference, Jacobian, <I>q</I>-superlinear convergence, Kantorovich type analysis, sparsity, nonlinear system of equations
Article copyright: © Copyright 1988 American Mathematical Society