Print Email Facebook Twitter Globalization technique for projected Newton–Krylov methods Title Globalization technique for projected Newton–Krylov methods Author Chen, Jinhai (Princeton University) Vuik, Cornelis (TU Delft Numerical Analysis) Date 2017-10-11 Abstract Large-scale systems of nonlinear equations appear in many applications. In various applications, the solution of the nonlinear equations should also be in a certain interval. A typical application is a discretized system of reaction diffusion equations. It is well known that chemical species should be positive otherwise the solution is not physical and in general blow up occurs. Recently, a projected Newton method has been developed, which can be used to solve this type of problems. A drawback is that the projected Newton method is not globally convergent. This motivates us to develop a new feasible projected Newton–Krylov algorithm for solving a constrained system of nonlinear equations. Combined with a projected gradient direction, our feasible projected Newton–Krylov algorithm circumvents the non-descent drawback of search directions which appear in the classical projected Newton methods. Global and local superlinear convergence of our approach is established under some standard assumptions. Numerical experiments are used to illustrate that the new projected Newton method is globally convergent and is a significate complementarity for Newton–Krylov algorithms known in the literature. Subject nonlinear equations with constraintsprojected Newton–Krylov methodprojected gradient directionglobal convergence To reference this document use: http://resolver.tudelft.nl/uuid:43c0393c-9601-4247-8f5a-47c0c7c770a1 DOI https://doi.org/10.1002/nme.5426 ISSN 0029-5981 Source International Journal for Numerical Methods in Engineering, 110 (7), 661-674 Part of collection Institutional Repository Document type journal article Rights © 2017 Jinhai Chen, Cornelis Vuik Files PDF Chen_et_al_2017_Internati ... eering.pdf 320.72 KB Close viewer /islandora/object/uuid:43c0393c-9601-4247-8f5a-47c0c7c770a1/datastream/OBJ/view