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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Numerical solution of large sets of algebraic nonlinear equations

Author: Ph. L. Toint
Journal: Math. Comp. 46 (1986), 175-189
MSC: Primary 65H10
MathSciNet review: 815839
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Abstract: This paper describes the application of the partitioned updating quasi-Newton methods for the solution of high-dimensional systems of algebraic nonlinear equations. This concept was introduced and successfully tested in nonlinear optimization of partially separable functions (see [6]). Here its application to the case of nonlinear equations is explored. Nonlinear systems of this nature arise in many large-scale applications, including finite elements and econometry. It is shown that the method presents some advantages in efficiency over competing algorithms, and that use of the partially separable structure of the system can lead to significant improvements also in the more classical discrete Newton method.

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Article copyright: © Copyright 1986 American Mathematical Society