On the linear convergence of Newton-Krylov methods

Authors:
Georgi V. Smirnov;Vera Sa
Affiliations:
Faculdade de Ciencias, Departamento de Matematica Aplicada, Centro de Matematica da Universidade do Porto, Universidade do Porto, Porto, Portugal;Faculdade de Ciencias, Departamento de Matematica Aplicada, Centro de Matematica da Universidade do Porto, Universidade do Porto, Porto, Portugal
Venue:
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART II
Year:
2009

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Abstract

Solution of large-scale nonlinear optimization problems and systems of nonlinear equations continues to be a difficult problem. One of the main classes of algorithms for solving these problems is the class of Newton-Krylov methods. In this article the number of iterations of a Krylov subspace method needed to guarantee at least a linear convergence of the respective Newton-Krylov method is studied. The problem is especially complicated if the matrix of the linear system to be solved is nonsymmetric. In the article, explicit estimates for the number of iterations for the Krylov subspace methods are obtained.