On approximate methods of tangent hyperbolas
Abstract
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.
Apie hiperbolinio tangento aproksimacijos metodus
Santrauka. Netiesinių operatorinų lygčių Banacho erdvėje sprendimui nagrinėjami kraštinių hiperbolių metodo variantai. Šių metodu šeima apima specialiuosius metodus, pagrįstus iteraciniais metodais, kurie įgalina gauti blogą sprendinį su tam tikru tikslumu, sprendžiant susijusias tiesines lygtis kiekvienoje iteracijoje. Pateikta lokalaus konvergavimo teorema bei konvergavimo greitis. Svarstoma skaičiavimų išlygiagretinimo galimybės. Skaičiavimo eksperimentas su įvairiais multi‐procesoriais rodo, kad lygiagrečiųjų metodu vykdymas priklauso iš esmės nuo atliekamo darbo išbalansavimo.
First Published Online: 14 Oct 2010
Keywords:
nonlinear equations, Banach spaces, methods with the high order of convergence, approximate variants of methods, parallel computationHow to Cite
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Copyright (c) 2002 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2002 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.