Open AccessON APPROXIMATE METHODS OF TANGENT HYPERBOLAS
Author(s) -
Indrek Kaldo,
O Vaarmann
Publication year - 2002
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2002.9637197
Subject(s) - hyperbola , tangent , mathematics , banach space , computation , convergence (economics) , rate of convergence , mathematical optimization , operator (biology) , nonlinear system , iterative method , newton's method , computer science , algorithm , mathematical analysis , key (lock) , geometry , biochemistry , chemistry , physics , computer security , repressor , quantum mechanics , transcription factor , economics , gene , economic growth
For solving a nonlinear operator equation in Banach space setting approximate variants of the method of tangent hyperbolas are considered. This family of approximate methods includes as special cases methods based on the use of iterative methods to obtain a cheap solution of limited accuracy for associated linear equations at each iteration step as well. A local convergence theorem and rate of convergence for the methods under discussion are given. Computational aspects and possibilities of organizing parallel computation are discussed. Computational experience with various multiprocessors indicates that performance of parallel methods depends critically on efficient load balancing. Problems of allocating subproblems to the processors are also briefly discussed.