A Rapid Numerical Algorithm to Compute Matrix Inversion

The aim of the present work is to suggest and establish a numerical algorithm based on matrix multiplications for computing approximate inverses. It is shown theoretically that the scheme possesses seventh-order convergence, and thus it rapidly converges. Some discussions on the choice of the initial value to preserve the convergence rate are given, and it is also shown in numerical examples that the proposed scheme can easily be taken into account to provide robust preconditioners

Finding the solution of nonlinear equations by a class of optimal methods

AbstractThis paper is devoted to the study of an iterative class for numerically approximating the solution of nonlinear equations. In fact, a general class of iterations using two evaluations of the first order derivative and one evaluation of the function per computing step is presented. It is also proven that the class reaches the fourth-order convergence. Therefore, the novel methods from the class are Jarratt-type iterations, which agree with the optimality hypothesis of Kung–Traub. The derived class is further extended for multiple roots. That is to say, a general optimal quartic class of iterations for multiple roots is contributed, when the multiplicity of the roots is available. Numerical experiments are employed to support the theory developed in this work

Computing Simple Roots by an Optimal Sixteenth-Order Class

The problem considered in this paper is to approximate the simple zeros of the function by iterative processes. An optimal 16th order class is constructed. The class is built by considering any of the optimal three-step derivative-involved methods in the first three steps of a four-step cycle in which the first derivative of the function at the fourth step is estimated by a combination of already known values. Per iteration, each method of the class reaches the efficiency index , by carrying out four evaluations of the function and one evaluation of the first derivative. The error equation for one technique of the class is furnished analytically. Some methods of the class are tested by challenging the existing high-order methods. The interval Newton's method is given as a tool for extracting enough accurate initial approximations to start such high-order methods. The obtained numerical results show that the derived methods are accurate and efficient

Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index

Steffensen-type methods are practical in solving nonlinear equations. Since, such schemes do not need derivative evaluation per iteration. Hence, this work contributes two new multistep classes of Steffensen-type methods for finding the solution of the nonlinear equation ()=0. New techniques can be taken into account as the generalizations of the one-step method of Steffensen. Theoretical proofs of the main theorems are furnished to reveal the eighth-order convergence. Per computing step, the derived methods require only four function evaluations. Experimental results are also given to add more supports on the underlying theory of this paper as well as lead us to draw a conclusion on the efficiency of the developed classes

Factors influencing verbal intelligence and spoken language in children with phenylketonuria

Objectives: To determine verbal intelligence and spoken language of children with phenylketonuria and to study the effect of age at diagnosis and phenylalanine plasma level on these abilities. Design: Cross-sectional. Setting: Children with phenylketonuria were recruited from pediatric hospitals in 2012. Normal control subjects were recruited from kindergartens in Tehran. Participants: 30 phenylketonuria and 42 control subjects aged 4- 6.5 years. Skills were compared between 3 phenylketonuria groups categorized by age at diagnosis/treatment, and between the phenylketonuria and control groups. Main outcome measures: Scores on Wechsler Preschool and Primary Scale of Intelligence for verbal and total intelligence, and Test of Language Development-Primary, third edition for spoken language, listening, speaking, semantics, syntax, and organization. Results: The performance of control subjects was significantly better than that of early-treated subjects for all composite quotients from Test of Language Development and verbal intelligence (P >0.001). Early-treated subjects scored significantly higher than the two groups of late-treated subjects for spoken language (P =0.01), speaking (P =0.04), syntax (P =0.02), and verbal intelligence (P =0.019). There was a negative correlation between phenylalanine level and verbal intelligence (r= �0.79) in early-treated subjects and between phenylalanine level and spoken language (r= �0.71), organization (r= �0.82) and semantics (r= �0.82) for late-treated subjects diagnosed before the age one year. Conclusion: The study confirmed that diagnosis of newborns and control of blood phenylalanine concentration improves verbal intelligence and spoken language scores in phenylketonuria subjects. © 2015, Indian Academy of Pediatrics

Self-Organizing Traffic Flow Prediction with an Optimized Deep Belief Network for Internet of Vehicles

To assist in the broadcasting of time-critical traffic information in an Internet of Vehicles (IoV) and vehicular sensor networks (VSN), fast network connectivity is needed. Accurate traffic information prediction can improve traffic congestion and operation efficiency, which helps to reduce commute times, noise and carbon emissions. In this study, we present a novel approach for predicting the traffic flow volume by using traffic data in self-organizing vehicular networks. The proposed method is based on using a probabilistic generative neural network techniques called deep belief network (DBN) that includes multiple layers of restricted Boltzmann machine (RBM) auto-encoders. Time series data generated from the roadside units (RSUs) for five highway links are used by a three layer DBN to extract and learn key input features for constructing a model to predict traffic flow. Back-propagation is utilized as a general learning algorithm for fine-tuning the weight parameters among the visible and hidden layers of RBMs. During the training process the firefly algorithm (FFA) is applied for optimizing the DBN topology and learning rate parameter. Monte Carlo simulations are used to assess the accuracy of the prediction model. The results show that the proposed model achieves superior performance accuracy for predicting traffic flow in comparison with other approaches applied in the literature. The proposed approach can help to solve the problem of traffic congestion, and provide guidance and advice for road users and traffic regulators

The effect of the magnetically dead layer on the magnetization and the magnetic anisotropy of the dextran-coated magnetite nanoparticles

We present a study on the magnetic behavior of dextran-coated magnetite nanoparticles (DM NPs) with sizes between 3 and 19 nm, synthesized by hydrothermal-assisted co-precipitation method. The decrease of saturation magnetization (M-s) with decreasing particle size has been modeled by assuming the existence of a spin-disordered layer at the particle surface, which is magnetically dead. Based on this core-shell model and taking into account the weight contribution of non-magnetic coating layer (dextran) to the whole magnetization, the dead layer thickness (t) and saturation magnetization M-s of the magnetic cores in our samples were estimated to be t = 6.8 angstrom and M-s = 98.8 emu/g, respectively. The data of M-s were analyzed using a law of approach to saturation, indicating an increase in effective magnetic anisotropy (K-eff) with decreasing the particle size as expected from the increased surface/volume ratio in small MNPs. The obtained K-eff values were successfully modeled by including an extra contribution of dipolar interactions due to the formation of chain-like clusters of MNPs. The surface magnetic anisotropy (K-s) was estimated to be about K-s = 1.04x10(5) J/m(3). Our method provides a simple and accurate way to obtain the M-s core values in surface-disordered MNPs, a relevant parameter required for magnetic modeling in many applications. GRAPHICS]

A New High-Order Stable Numerical Method for Matrix Inversion

A stable numerical method is proposed for matrix inversion. The new method is accompanied by theoretical proof to illustrate twelfth-order convergence. A discussion of how to achieve the convergence using an appropriate initial value is presented. The application of the new scheme for finding Moore-Penrose inverse will also be pointed out analytically. The efficiency of the contributed iterative method is clarified on solving some numerical examples