Title :
Convergence theorems of the steepest descent method for accretive mappings
Author :
Wu, Ding-Ping ; Shi, Jin-Wei ; Zheng, Chun-yang
Author_Institution :
Coll. of Math., Chengdu Univ. of Inf. Technol., Chengdu, China
Abstract :
This paper is devoted to prove the generalized Φ-accretive mapping A : D(A) ⊆ E → 2E or generalized Lipschitz and generalized α - accretive with some specific conditions, then sequence {xn} generated by the steepest descent approximation method which converges strongly to a solution x* of the equation Ax = 0, furthermore, the global convergence theorem is proved.
Keywords :
convergence of numerical methods; differential equations; gradient methods; generalized Φ-accretive mapping; generalized Lipschitz equation; global convergence theorem; steepest descent approximation method; Artificial neural networks; Magnetic resonance imaging; Silicon compounds; Φ-strongly accretive; Generalized α-accretive operator; Global convergence theorem; Steepest descent approximation; Strong convergence;
Conference_Titel :
Machine Learning and Cybernetics (ICMLC), 2010 International Conference on
Conference_Location :
Qingdao
Print_ISBN :
978-1-4244-6526-2
DOI :
10.1109/ICMLC.2010.5581071
