Open AccessA Geometric Study of Convergence: The Nonlinear Conjugate Gradient Method
Author(s) -
ANA CLARA DE SOUZA OLIVEIRA,
Sandra A. Santos
Publication year - 2016
Publication title -
anais do congresso de iniciação científica da unicamp
Language(s) - English
Resource type - Conference proceedings
ISSN - 2447-5114
DOI - 10.19146/pibic-2016-51818
Subject(s) - conjugate gradient method , convergence (economics) , nonlinear conjugate gradient method , nonlinear system , computer science , mathematics , conjugate , derivation of the conjugate gradient method , mathematical analysis , algorithm , gradient descent , artificial intelligence , physics , artificial neural network , quantum mechanics , economics , economic growth
The Conjugate Gradient Method (CG) is a numerical method for solving quadratic problems, which can be used to minimize any differentiable function. In this study, we have analyzed the efficiency of CG for quadratic problems and implemented a version of this method for nonlinear systems in the least-squares formulation. We have also prepared a geometric analysis of the convergence of its nonlinear version, in order to evaluate the dependence of its efficiency with the starting point.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom