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Inexact block Newton methods for solving nonlinear equations

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
162
Issue
3
Identifiers
DOI: 10.1016/j.amc.2004.03.002
Keywords
  • Nonlinear Equations
  • Block-Iterative Solutions
  • Parallel Computation
  • Inexact Newton Methods
  • Load Flows
Disciplines
  • Computer Science

Abstract

Abstract In the paper two parallelizable inexact block Newton methods are presented for solving large and sparse nonlinear equations. The basic idea is simple and direct. Combining the simplified Newton method with the component averaging (CAV) method [Parallel Comput. 27 (2001) 777] results in an inexact Newton method, called simplified Newton-CAV method. Parallel tests of the algorithm are implemented on a message-passing distributed-memory multiprocessor architecture such as a cluster of workstations. The results show that the new algorithm can achieve good performance. Moreover as a development of the simplified Newton-CAV method, the overlapped block Newton-CAV method is further proposed and discussed.

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