The q-gradient method used a Yuan step size for odd steps, and geometric recursion as an even (q-GY). This study aimed to accelerate convergence minimum point by minimizing the number of iterations, dilating parameter q independent variable then comparing results with three algorithms namely, classical steepest descent (SD) method, Steps (SDY), (q-G). numerical were presented in tables graphs. ...

We consider the special case of the restarted Arnoldi method for approximating the product of a function of a Hermitian matrix with a vector which results when the restart length is set to one. When applied to the solution of a linear system of equations, this approach coincides with the method of steepest descent. We show that the method is equivalent to an interpolation process in which the n...

The negative gradient direction to find local minimizers has been associated with the classical steepest descent method which behaves poorly except for very well conditioned problems. We stress out that the poor behavior of the steepest descent methods is due to the optimal Cauchy choice of steplength and not to the choice of the search direction. We discuss over and under relaxation of the opt...

The propose of this article is to consider the strong convergence of an iterative sequences for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of the variational inequalities for inverse strongly monotone mappings, and the set of solutions of system of equilibrium problems in Hilbert spaces by using a hybrid steepest desc...

The steepest descent (SD) method is well-known as the simplest in optimization. In this paper, we propose a new SD search direction for solving system of linear equations Ax = b. We also prove that proposed with exact line satisfies condition and possesses global convergence properties. This motivated by previous work on Zubai’ah-Mustafa-Rivaie-Ismail (ZMRI)[2]. Numerical comparisons classical ...

Surface networks capture the topological relations between passes of a continuous surface, the paths of steepest descent and ascent starting at the passes, and the pits and peaks where the steepest paths end. This paper extends the topology of the network in three ways. Objects at the edge of the surface model are introduced. Horizontal areas may represent passes, pits, or peaks, and therefore ...