Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3
Search results for: conjugacy
3 Study on a Family of Optimal Fourth-Order Multiple-Root Solver
Authors: Young Hee Geum
Abstract:
In this paper,we develop the complex dynamics of a family of optimal fourth-order multiple-root solvers and plot their basins of attraction. Mobius conjugacy maps and extraneous fixed points applied to a prototype quadratic polynomial raised to the power of the known integer multiplicity m are investigated. A 300 x 300 uniform grid centered at the origin covering 3 x 3 square region is chosen to visualize the initial values on each basin of attraction in accordance with a coloring scheme based on their dynamical behavior. The illustrative basins of attractions applied to various test polynomials and the corresponding statistical data for convergence are shown to confirm the theoretical convergence.Keywords: basin of attraction, conjugacy, fourth-order, multiple-root finder
Procedia PDF Downloads 2852 An Elbow Biomechanical Model and Its Coefficients Adjustment
Authors: Jie Bai, Yongsheng Gao, Shengxin Wang, Jie Zhao
Abstract:
Through the establishment of the elbow biomechanical model, it can provide theoretical guide for rehabilitation therapy on the upper limb of the human body. A biomechanical model of the elbow joint can be built by the connection of muscle force model and elbow dynamics. But there are many undetermined coefficients in the model like the optimal joint angle and optimal muscle force which are usually specified as the experimental parameters of other workers. Because of the individual differences, there is a certain deviation of the final result. To this end, the RMS value of the deviation between the actual angle and calculated angle is considered. A set of coefficients which lead to the minimum RMS value will be chosen to be the optimal parameters. The direct search method and the conjugacy search method are used to get the optimal parameters, thus the model can be more accurate and mode adaptability.Keywords: elbow biomechanical model, RMS, direct search, conjugacy search
Procedia PDF Downloads 5411 Global Convergence of a Modified Three-Term Conjugate Gradient Algorithms
Authors: Belloufi Mohammed, Sellami Badreddine
Abstract:
This paper deals with a new nonlinear modified three-term conjugate gradient algorithm for solving large-scale unstrained optimization problems. The search direction of the algorithms from this class has three terms and is computed as modifications of the classical conjugate gradient algorithms to satisfy both the descent and the conjugacy conditions. An example of three-term conjugate gradient algorithm from this class, as modifications of the classical and well known Hestenes and Stiefel or of the CG_DESCENT by Hager and Zhang conjugate gradient algorithms, satisfying both the descent and the conjugacy conditions is presented. Under mild conditions, we prove that the modified three-term conjugate gradient algorithm with Wolfe type line search is globally convergent. Preliminary numerical results show the proposed method is very promising.Keywords: unconstrained optimization, three-term conjugate gradient, sufficient descent property, line search
Procedia PDF Downloads 370