The main objective of this study is to present new method on the basis of genetic algorithms for attenuation relationship determination of horizontal peak ground acceleration and spectral acceleration. The proposed method employs the optimization capabilities of genetic algorithm to determine the coefficients of attenuation relationships of peak ground and spectral accelerations. This method ha...

The purpose of the present study is the damage detection in the thin plates in terms of the wide application of such structures in various branches of engineering such as structural, mechanical, aerospace, shipbuilding, etc. using gradient-based second-order numerical optimization techniques. The technique used for optimization in this study is the second-order Levenberg-Marquardt algorithm (SO...

Inertial navigation systems and gravimeters are now routinely used to map the regional gravitational quantities from an aircraft with mGal accuracy and a spatial resolution of a few kilometers. However, airborne gravimeter of this kind is limited by the inaccuracy of the inertial sensor performance, the integrated navigation technique and the kinematic acceleration determination. As the GPS tec...

The aim of this paper is to present an acceleration procedure based on projection and preconditioning for iterative methods for solving systems of linear equations. A cycling strategy leads to a new iterative method. These procedures are closely related to Richardson’s method and acceleration. Numerical examples illustrate the purpose. For solving the system of linear equations Ax = b, we consi...

This paper concerns an acceleration method for fixed-point iterations that originated in work of D. G. Anderson [Iterative procedures for nonlinear integral equations, J. Assoc. Comput. Machinery, 12 (1965), 547-560], which we accordingly call Anderson acceleration here. This method has enjoyed considerable success and wide usage in electronic structure computations, where it is known as Anders...

In this study, we use a convex acceleration of Newton's method (or super-Halley method) to approximate solutions of nonlinear equations. We provide sufficient convergence conditions for this method in three space settings: real line, complex plane, and Banach space. Several applications of our results are also provided.

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if it is hard to approximate the Hessian well and efficiently. As far as we know, there is no effective way to handle this problem. In this paper, we resort to N...

In this paper the design of a time varying switching plane for the sliding mode control of the third order system subject to the velocity and acceleration constraints is considered. Initially the plane passes through the system representative point in the error state space and then it moves with a constant velocity to the origin of the space. Having reached the origin the plane stops and remain...