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Zbl 1204.65055
Shin, Byeong-Chun; Darvishi, M.T.; Kim, Chang-Hyun
A comparison of the Newton-Krylov method with high order Newton-like methods to solve nonlinear systems. (English)
[J] Appl. Math. Comput. 217, No. 7, 3190-3198 (2010). ISSN 0096-3003

Summary: We compare the CPU time and error estimates of some variants of Newton method of the third and fourth-order convergence with those of the Newton-Krylov method used to solve systems of nonlinear equations. By expanding some numerical experiments we show that the use of Newton-Krylov method is better in the cost and accuracy points of view than the use of other high order Newton-like methods when the system is sparse and its size is large.

MSC 2000:: *65H10 Systems of nonlinear equations (numerical methods)

Keywords: Newton-Krylov method; system of nonlinear equations; GMRES; CPU time; iteration number; comparison of methods; Newton method; numerical experiments

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Zentralblatt MATH Berlin [Germany]