ITERATIONS FOR APPROXIMATING LIMIT REPRESENTATIONS OF GENERALIZED INVERSES

Our underlying motivation is the iterative method for the implementation of the limit representation of the Moore-Penrose inverse$\lim\limits _{\alpha \to 0} \left( \alpha I+A^*A\right) ^{-1} A^*$ from [\v Zukovski, Lipcer, On recurent computation of normal solutions of linear algebraic equations, \v Z. Vicisl. Mat. i Mat. Fiz. 12 (1972), 843--857] and[\v Zukovski, Lipcer, On computation pseudoinverse matrices, \v Z. Vicisl. Mat. i Mat. Fiz. 15 (1975), 489--492].  The iterative process for the implementation of the general limit formula$\lim\limits _{\alpha \to 0}(\alpha I+R^*S) ^{-1}R^*$was defined in [P.S. Stanimirovi\'c, Limit representations of generalized inverses and related methods, Appl. Math. Comput. 103 (1999), 51--68].In this paper we develop an improvement of this iterative process.The iterative method defined in such a way is able to produce the result in a predefined number of iterative steps. Convergence properties of defined iterations are further investigated

MULTIPLE USE OF BACKTRACKING LINE SEARCH IN UNCONSTRAINED OPTIMIZATION

The gradient method is a very efficient iterative technique for solving unconstrained optimization problems. Motivated by recent modifications of some variants of the SM method, this study proposed two methods that are globally convergent as well as computationally efficient. Each of the methods is globally convergent under the influence of a backtracking line search. Results obtained from the numerical implementation of these methods and performance profiling show that the methods are very competitive with well-known traditional methods

Some Notes on Neville’s Algorithm of Interpolation with Applications to Trigonometric Interpolation

 In this paper is given a description of Neville’s algorithm which is generated from Lagrange interpolation polynomials. Given a summary of the properties of these polynomials with some applications. Then, using the Lagrange polynomials of lower degrees, Neville algorithm allows recursive computation of those of the larger degrees, including the adaption of Neville’s method to trigonometric interpolation. Furthermore, using a software application, such as in our case, Matlab, we will show the numerical experiments comparisons between the Lagrange interpolation and Neville`s interpolation methods and conclude for their advantages or disadvantages

Implementation of ICT in the management of transport vehicles

Fleet Management is a M2M (Machine to Machine) solution for locating, tracking, managing and controlling the shipping fleet, including commercial motor vehicles such as cars, planes, ships, trucks and trains. All vehicles that are subject to monitoring are equipped with GPS devices in which SIM cards are installed, and which help monitor the position and parameters of the vehicle. The survey shows that in addition to monitoring the location and vehicle parameters, the implementation of such a solution in the fleets provides additional benefits such as saving fuel costs, maintenance, time etc. The purpose of this paper is to explore a real implementation of a fleet management solution in a public transportation company. Being part of a wider IT system, the fleet management solution, is associated with a range of different benefits for the transport company and the citizens, as its end users. This paper, furthermore, intents to quantify the perceived advantages and give recommendations for further system extensions that can optimize the operations of the transport company, thus increasing citizen satisfaction

A Novel Value for the Parameter in the Dai-Liao-Type Conjugate Gradient Method

A new rule for calculating the parameter t involved in each iteration of the MHSDL (Dai-Liao) conjugate gradient (CG) method is presented. The new value of the parameter initiates a more efficient and robust variant of the Dai-Liao algorithm. Under proper conditions, theoretical analysis reveals that the proposed method in conjunction with backtracking line search is of global convergence. Numerical experiments are also presented, which confirm the influence of the new value of the parameter t on the behavior of the underlying CG optimization method. Numerical comparisons and the analysis of obtained results considering Dolan and Moré’s performance profile show better performances of the novel method with respect to all three analyzed characteristics: number of iterative steps, number of function evaluations, and CPU time

Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations

This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods in solving single scalar equations. Our strategy is to control the speed of the convergence of gradient methods through the step size value defined using more parameters. As a result, efficient minimization schemes for solving SNE are introduced. Linear global convergence of the proposed iterative method is confirmed by theoretical analysis under standard assumptions. Numerical experiments confirm the significant computational efficiency of proposed methods compared to traditional gradient descent methods for solving SNE