a one parameter fourth order family of iterative methods for nonlinear equations abstract in this paper we present a new one parameter fourth order family of iterative methods for solving nonlinear equations the new family requires two evaluations of the given function and one of its first derivative per iteration the well known traub ostrowski s fourth order method is shown to be part of the family several numerical examples are given to illustrate the efficiency and performance of the presented methods

choosing the most stable members of kou s family of iterative methods abstract in this manuscript we analyze the dynamical anomalies of a parametric family of iterative schemes designed by kou et al it is known that its order of convergence is three for any arbitrary value of the parameter but it has order four and it is optimal in the sense of kung traub s conjecture when a specific value is selected among all the elements of this family one can choose this fourth order element or any of the infinite members of third order of convergence if only the speed of convergence is considered however the stability of the methods plays an important role in their reliability when they are applied on different problems this is the reason why we analyze in this paper the dynamical behavior on quadratic polynomials of the mentioned family the study of fixed points and their stability joint with the critical points and their associated parameter planes show the richness of the class and allow us to find members of it with excellent numerical properties as well as other ones with very unstable behavior some test functions are analyzed for confirming the theoretical results

convergence of a class of efficient quadrature based predictor corrector methods for root finding in this paper we analyze a class of predictor corrector techniques for root finding that are derived from quadrature methods they are found to have a rate of convergence of 1 2 regardless of the degree of precision for the quadrature technique from which they are derived provided it is at least one by using previously evaluated quantities in the predictor step they require fewer functional evaluations than the standard class of techniques this class is found to be superior to the standard class provided that the quantity of knots from the quadrature is 1 m 3 with the optimal method being that derived from the midpoint method

on the construction of iterative methods with at least cubic convergence using the iteration formulas of order two for solving nonlinear equations we present a basic tool for deriving new higher order iterative methods that do not require the computation of the second order or higher order derivatives the presented convergence analysis shows that the order of convergence of the obtained iterative methods are three or higher the comparison with other methods is given

some third order families of iterative methods for solving nonlinear equations abstract in this paper we present a convenient third order iteration formula improving newton s method for solving nonlinear equations with any two iteration functions of order two the formula provides one parameter third order family of methods each family member is free from second derivatives and per iteration it requires three evaluations of the given function and its derivative several numerical examples are given to illustrate the efficiency and performance of some of the presented methods

eighth order family of iterative methods for nonlinear equations and their basins of attraction abstract we present a new family of eighth order methods for solving nonlinear equations the order of convergence of the considered methods is proved and corresponding asymptotic error constants are expressed in terms of four parameters numerical examples obtained using mathematica with high precision arithmetic demonstrate convergence and efficacy of our family of methods for some combinations of parameter values the new eighth order methods produce very good results on tested examples compared to the results produced by some of the eighth order methods existing in the related literature an exploration of the relevant dynamics of the proposed methods is presented along with illustrative basins of attraction for various polynomials

an iterative method for computing the approximate inverse of a square matrix and the moore penrose inverse of a non square matrix in this paper an iterative scheme is proposed to find the roots of a nonlinear equation it is shown that this iterative method has fourth order convergence in the neighborhood of the root based on this iterative scheme we propose the main contribution of this paper as a new high order computational algorithm for finding an approximate inverse of a square matrix the analytical discussions show that this algorithm has fourth order convergence as well next the iterative method will be extended by theoretical analysis to find the pseudo inverse also known as the moore penrose inverse of a singular or rectangular matrix numerical examples are also made on some practical problems to reveal the efficiency of the new algorithm for computing a robust approximate inverse of a real or complex matrix

iterative methods with fourth order convergence for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations involving only first derive of the function using a new decomposition technique which is due to noor m aslam noor numerical analysis and optimization lecture notes comsats institute of information technology islamabad pakistan 2006 m aslam noor new iterative schemes for nonlinear equations appl math comput in press and noor and noor m aslam noor k inayat noor some iterative schemes for nonlinear equations appl math comput in press we show that this new iterative method has fourth order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

a family of composite fourth order iterative methods for solving nonlinear equations in this paper we present a family of new fourth order iterative methods for solving nonlinear equations per iteration the methods consisting of the family require only two evaluations of the function and one evaluation of its derivative several numerical examples are given to illustrate the efficiency and performance of some of the presented methods

multipoint iterative method with cubic convergence abstract a new third order multipoint method without using second derivative for finding simple zeros of non linear functions permitting f x 0 in the vicinity of the required root is presented in this paper furthermore numerical tests supporting the theory and comparison of the results with respect to the existing classical methods are also given

from third to fourth order variant of newton s method for simple roots abstract in this paper we show one way of deriving a fourth order scheme from any third order newton type method without any additional evaluation of the function or its derivatives for this purpose the rectangular rule may be employed in newton s theorem about a special point this special point may be selected from a variant of any third order scheme two such cases are illustrated here the first case leads to a new fourth order scheme while the second case leads to the well known jarratt s method the efficiency index of the proposed scheme is 1 587 in order to compare its performance with some of the existing third and fourth order schemes several numerical examples are furnished here

a note on some recent methods for solving nonlinear equations abstract in this note we present some comments on the recent results concerning iterative methods for solving nonlinear equations in the first part we compare a new method n ujevic a method for solving nonlinear equations appl math comput 174 2006 1416 1426 with the newton and ostrowski method including an extensive analysis of numerical results together with the choice of initial approximations and the computational efficiency of the considered methods in the second part we give a list of recently derived root finding methods and we study the question of priority namely we find out that all reviewed methods were already derived at the beginning of the 60s of the last century one of them dates from the 18th century some remarks on the comparison analysis and the application of iteration methods are included

some multi step iterative methods for solving nonlinear equations in this paper we develop some new iterative methods for solving nonlinear equations by using the techniques introduced in golbabai and javidi 2007 1 and rafiq and rafiullah 2008 20 we establish the convergence analysis of the proposed methods and then demonstrate their efficiency by taking some test problems

third order iterative methods free from second derivatives for nonlinear equation in this paper we suggest and analyze a new two step iterative method for solving nonlinear equations which is called the modified householder method without second derivatives for nonlinear equation we also prove that the modified method has cubic convergence several examples are given to illustrate the efficiency and the performance of the new method new method can be considered as an alternative to the present cubic convergent methods for solving nonlinear equations

improved iterative methods for solving nonlinear equations in this paper we use the decomposition technique of noor m aslam noor numerical analysis and optimization lecture notes comsats institute of information technology islamabad pakistan 2006 to suggest and analyze some new iterative methods for solving nonlinear equations our method of developing these iterative methods is very simple as compared with other methods several numerical examples are given to illustrate the efficiency and performance of the new method our method can be considered as an improvement of the existing methods

on modified newton methods with cubic convergence abstract in this paper we present two new modified newton methods for solving a non linear equation permitting f x 0 in some points these new methods are showed to be cubically convergent from the practical application we show that these new methods are vast superior and possible in global convergence

modified newton s method with third order convergence and multiple roots in recent papers appl math comput 140 2003 419 426 appl math lett 13 2000 87 93 a new modification of the newton s method mnm which produces iterative methods with order of convergence three have been proposed here we study the order of convergence of such methods when we have multiple roots we prove that the order of convergence of the mnm go down to one but when the multiplicity p is known it may be rised up to two by using two different types of correction when p is unknown we show that the two most efficient methods in the family of the mnm converge faster than the classical newton s method

a cubically convergent newton type method under weak conditions under weak conditions we present an iteration formula to improve newton s method for solving nonlinear equations the method is free from second derivatives permitting f x 0 in some points and per iteration it requires two evaluations of the given function and one evaluation of its derivative analysis of convergence demonstrates that the new method is cubically convergent some numerical examples illustrate that the algorithm is more efficient and performs better than classical newton s method

modified secant type methods for unconstrained optimization for solving nonlinear univariate and unconstrained optimization problems newton method is an important and basic method which convergences quadratically in this paper we suggest a family of three new modifications of the classical secant method where the iteration formula including an approximation of f x k is satisfied by a recursive scheme the efficiencies of the new methods are analyzed in terms of the most popular and widely used criterion the number of iterations in comparison with the newton and secant methods using six test functions

new family of iterative methods for nonlinear equations in this paper we suggest and analyze a new family of iterative methods for solving nonlinear equations using the system of coupled equations coupled with decomposition technique several numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

means based modifications of newton s method for solving nonlinear equations in this paper we consider a family of six sets of means based modifications of newton s method for solving nonlinear equations each set is a parametric class of methods some well known methods belong to our family for example the arithmetic mean newton s method s weerakoon t g i fernando a variant of newton s method with accelerated third order convergence appl math lett 13 2000 87 93 the harmonic mean newton s method a y ozban some new variants of newton s method appl math lett 17 2004 677 682 the geometric mean newton s method t lukic n m ralevic geometric mean newton s method for simple and multiple roots appl math lett 21 2008 30 36 the power mean newton s method x zhou a class of newton s methods with third order convergence appl math lett 20 2007 1026 1030 the convergence analysis shows third order of our family comparison of the family members shows that there are no big differences between them twelve numerical examples were tested and two characteristic ones are presented

adams like techniques for zero finder methods two families of zero finding iterative methods for nonlinear equations are presented we derive them solving an initial value problem using adams like multistep techniques namely adams methods have been used to solve the problem that consists in a differential equation in what appears the inverse function of the one which zero will be computed and the condition given by the value attained by it at the initial approximation performing this procedure several methods of different local orders of convergence have been obtained

a two parameter third order family of methods for solving nonlinear equations in this paper we present a new two parameter family of iterative methods for solving nonlinear equations which includes as a particular case the classical potra and ptak third order method per iteration the new methods require two evaluations of the function and one evaluation of its first derivative it is shown that each family member is cubically convergent several examples are given to illustrate the performance of the family members

some modifications of newton s method with fifth order convergence in this paper we present some new modifications of newton s method for solving non linear equations analysis of convergence shows that these methods have order of convergence five numerical tests verifying the theory are given and based on these methods a class of new multistep iterations is developed

fourth order variants of cauchy s method for solving non linear equations abstract in this paper we present some new variants of cauchy s method in which the second derivative is replaced by a finite difference between the first derivatives analysis of convergence shows that the new methods have fourth order convergence per iteration the new methods require one evaluations of the function and two of its first derivative numerical results show that the new methods are efficient

a bound for the magnitude characteristics of nonlinear output frequency response functions part 1 analysis and computation a bound for the magnitude frequency domain characteristics associated with the outputs of a wide class of nonlinear systems is derived as a relatively simple function of the generalized frequency response functions and properties of the system inputs it is shown how the practical computation of the new bound can be easily performed for nonlinear systems with finite but arbitrary order nonlinearities and worked examples are included the paper is divided into two parts in part 1 an expression for the output magnitude bound is derived properties of the result are discussed and general procedures for the practical computation of the bound are developed in part 2 the practical computations associated with applying the bound to the polynomial nonlinear autoregressive model with exogenous input are discussed

a simply constructed third order modifications of newton s method in this paper we present a simple and easily applicable approach to construct some third order modifications of newton s method for solving nonlinear equations it is shown by way of illustration that existing third order methods can be employed to construct new third order iterative methods the proposed approach is applied to the classical chebyshev halley methods to derive their second derivative free variants numerical examples are given to support that the methods thus obtained can compete with known third order methods

an iterative method with cubic convergence for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations we show that this new iterative method has third order convergence several numerical examples are given to illustrate the efficiency and performance of this new method new method can be viewed as an improvement of the previously known iterative methods

the cubic semilocal convergence on two variants of newton s method in this paper we discuss two variants of newton s method without using any second derivative for solving nonlinear equations by using the majorant function and confirming the majorant sequences we obtain the cubic semilocal convergence and the error estimation in the kantorovich type theorems the numerical examples are presented to support the usefulness and significance

a new modified king werner method for solving nonlinear equations in this paper a new method for solving nonlinear equations f x 0 is presented analysis of the convergence shows that the asymptotic convergence order of this method is 1 3 some numerical results are given to demonstrate its efficiency

adaptive precompensation of wiener systems this article presents an adaptive precompensation technique for the wiener system a class of nonlinear systems that can be represented by the interconnection of a linear dynamic subsystem and a memoryless nonlinear subsystem an adaptive algorithm for adjusting the parameters of the precompensator structured by a hammerstein model is derived using the stochastic gradient method the validity of the proposed algorithm is confirmed in a computer simulation by applying it to known wiener systems

the construction of rational iterative methods for solving nonlinear equations abstract in this paper based on the idea of constructing iterative methods by sharma j r sharma a family of third order methods to solve nonlinear equations appl math comput 184 2007 210 215 jiang and han dongdong jiang danfu han some one parameter families of third order methods for solving nonlinear equations appl math comput 195 2008 392 396 we propose some rational iterative methods by linearizing the quadratic curve equation by analysis of asymptotic errors we prove the new families are all cubically convergent as an example we present a new concrete iterative family with better convergent performance than classic third order methods through the adjustment of parameter n automatically

decomposition of generalized frequency response functions for nonlinear systems using symbolic computation a symbolic manipulation procedure which both computes and automatically decomposes the generalized frequency response functions of nonlinear rational polynomial and integrodifferential equation models into a set of closed form nth order transfer functions is presented the symbolic representation exposes the explicit relationship between the model parameters and the nonlinear transfer functions in the frequency domain and leads to important insights into the characterization of nonlinear systems examples for each model type are included to demonstrate the symbolic transfer function approach

efficient computation of higher order frequency response functions for nonlinear systems with and without a constant term the behaviour of a nonlinear system can be profoundly affected by the presence of a constant or dc term in the system governing equation these changes are reflected in the nonlinear frequency response characteristics of the system which provide a powerful insight into the system s dynamics in this article a new and efficient algorithm is presented for computing the higher order volterra frequency response functions from nonlinear time domain models that may contain a constant term a comparison with previous methods is included to demonstrate the significant gains in computational efficiency that are achieved using the new method the algorithm is applicable to systems modelled by nonlinear differential or difference equations and is easily automated several examples are used to illustrate the method and to highlight the importance of dc terms in nonlinear system analysis

fractal boundaries of basin of attraction of newton raphson method in helicopter trim a key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim particularly when free wake models are used trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero an appropriate initial estimate of the trim state is needed for successful helicopter trim this study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations set of initial guess points from which the nonlinear equations converge it is illustrated that the three main rotor pitch controls of collective pitch longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution trajectories of the newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed it is found that the basins of attraction can have fractal boundaries

iterative methods improving newton s method by the decomposition method in this paper we present a sequence of iterative methods improving newton s method for solving nonlinear equations the adomian decomposition method is applied to an equivalent coupled system to construct the sequence of the methods whose order of convergence increases as it progresses the orders of convergence are derived analytically and then rederived by applying symbolic computation of maple some numerical illustrations are given

certain improvements of newton s method with fourth order convergence in this paper we present two new schemes one is third order and the other is fourth order these are improvements of second order methods for solving nonlinear equations and are based on the method of undetermined coefficients we show that the fourth order method is more efficient than the fifth order method due to kou et al j kou y li x wang some modifications of newton s method with fifth order covergence j comput appl math 209 2007 146 152 numerical examples are given to support that the methods thus obtained can compete with other iterative methods

on newton type methods with cubic convergence recently there has been some progress on newton type methods with cubic convergence that do not require the computation of second derivatives weerakoon and fernando appl math lett 13 2000 87 derived the newton method and a cubically convergent variant by rectangular and trapezoidal approximations to newton s theorem while frontini and sormani j comput appl math 156 2003 345 140 2003 419 derived further cubically convergent variants by using different approximations to newton s theorem homeier j comput appl math 157 2003 227 169 2004 161 independently derived one of the latter variants and extended it to the multivariate case here we show that one can modify the werrakoon fernando approach by using newton s theorem for the inverse function and derive a new class of cubically convergent newton type methods

a one parameter square root family of two step root finders a one parameter family of iterative methods for solving nonlinear equations is constructed all the methods of the proposed family are cubically convergent for a simple root except one particular method which attains the fourth order without the increase of computational cost these methods belong to the class of two step methods and require three function evaluations per iteration the square root structure of the family provides finding a complex zero of real functions in some cases a comparison analysis shows that the presented family generates the methods which are comparable or even superior than the existing two step iterative methods of the third order

bayesian wavelet method for multivariate model assessment of dynamic systems abstract in this paper an energy based bayesian wavelet method is presented for validation assessment of multivariate predictive models under uncertainty using time series data collected from a dynamic system time history data are decomposed into multiple time frequency resolutions using a discrete wavelet packet transform method as a signal feature wavelet packet component energy is computed in terms of the decomposed coefficients the effectiveness of the selected feature is assessed using both cross correlation and cross coherence metrics a generalized likelihood ratio is derived as a quantitative validation metric based on bayes theorem and gaussian distribution assumption of errors of the wavelet packet component energy between validation data and model prediction the multivariate model is then assessed based on the bayesian point and interval hypothesis testing approaches the probability density function of the likelihood ratio is constructed using the statistics of multiple response quantities and monte carlo simulation the proposed methodology is implemented in the validation of a structural dynamics problem using multivariate time series data sets sensitivity analysis is also performed to investigate the effect of parameter selection on the model validation decision

new iterative schemes for nonlinear equations in this paper we suggest and analyze a new iterative method for solving nonlinear equations by using a new decomposition method we also discuss the convergence criteria of these iterative methods several numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

a new third order newton type iterative method for solving nonlinear equations in this paper we introduce a new third order iterative method for solving nonlinear equations this method is converging on larger intervals than some other similar known methods a comparison between the new method and other third order methods is presented by using the basins of attraction for the real roots for some test problems the numerical results are also presented

optimal volterra kernel estimation algorithms for a nonlinear communication system for psk and qam inputs a fifth order volterra kernel estimation algorithm which is optimal in the least mean square error sense for a bandpass nonlinear system is derived the algorithm is based on some characteristics of i i d circularly symmetric zero mean complex valued gaussian random variables the proposed algorithm can be used to identify a nonlinear system under uniformly i i d rectangular m qam input and under uniformly i i d m psk input m spl ges 4 with modest modification the same approach has been used to derive an optimal volterra kernel estimation algorithm up to the third order however in some cases a third order model is not of high enough order to capture the nonlinear system characteristics a simulation example is given to show the necessity of deriving a fifth order volterra kernel estimation algorithm and to test for the correctness of the algorithm

some variant of newton s method with third order convergence we present a new modification of the newton s method which produces iterative methods with order of convergence three a general error analysis providing the higher order of convergence is given and the best efficiency in term of function evaluations of two of this new methods is provided

letter to the editor third order modification of newton s method in this paper we present a new modification of newton s method for solving non linear equations analysis of convergence shows that the new method is cubically convergent numerical examples show that the new method can compete with the classical newton s method

geometric constructions of iterative functions to solve nonlinear equations in this paper we present the geometrical interpretation of several iterative methods to solve a nonlinear scalar equation in addition we also review the extension to general banach spaces and some computational aspects of these methods

achieving higher order of convergence for solving systems of nonlinear equations abstract in this paper we develop a class of third order methods which is a generalization of the existing ones and a method of fourth order method then introduce a technique that improves the order of convergence of any given iterative method for solving systems of nonlinear equations based on a given iterative method of order p 2 which uses the extended newton iteration as a predictor a new method of order p 2 is proposed with only one additional evaluation of the function moreover if the given iterative method of order p 3 uses the newton iteration as a predictor then a new method of order p 3 can be developed applying this procedure we obtain some new methods with higher order of convergence moreover computational efficiency is analyzed and comparisons are made between these new methods and the ones from which have been derived finally several numerical tests are performed to show the asymptotic behaviors which confirm the theoretical results

higher order iterative schemes for nonlinear equations using decomposition technique in this paper we suggest and analyze some unique recurrence relations which can generate different classes of iterative methods for solving nonlinear equations using the system of coupled equations together with decomposition technique by using an auxiliary function various numerical examples are given to illustrate the efficiency and performance of the newly suggested methods these new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations

an optimal and efficient general eighth order derivative free scheme for simple roots abstract the main motivation of this study is to present an optimal scheme in a general way that can be applied to any existing optimal multipoint fourth order iterative scheme whose first substep employs steffensen s method or steffensen like method to further produce optimal eighth order iterative schemes a rational function approximation approach is used in the construction of proposed scheme in addition we also discussed the theoretical and computational properties of our scheme each member of the presented scheme satisfies the optimality conjecture for multipoint iterative methods without memory which was given by kung and traub in 1970 finally we also concluded on the basis of obtained numerical results that our methods have faster convergence in contrast to the existing methods of same order because they have minimum residual errors minimum error difference between two consecutive iterations and minimum asymptotic error constants corresponding to the considered test function

some higher order modifications of newton s method for solving nonlinear equations in this paper we consider constructing some higher order modifications of newton s method for solving nonlinear equations which increase the order of convergence of existing iterative methods by one or two or three units this construction can be applied to any iteration formula and per iteration the resulting methods add only one additional function evaluation to increase the order some illustrative examples are provided and several numerical results are given to show the performance of the presented methods

output frequency characteristics of nonlinear systems some interesting properties of output frequencies of volterra type nonlinear systems are particularly investigated these results provide a very novel and useful insight into the super harmonic and inter modulation phenomena in output frequency response of nonlinear systems with consideration of the effects incurred by different nonlinear components in the system the new properties theoretically demonstrate several fundamental output frequency characteristics and unveil clearly the mechanism of the interaction or coupling effects between different harmonic behaviors in system output frequency response incurred by different nonlinear components these results have significance in the analysis and design of nonlinear systems and nonlinear filters in order to achieve a specific output spectrum in a desired frequency band by taking advantage of nonlinearities they can provide an important guidance to modeling identification control and signal processing by using the volterra series theory in practice

a geometric construction of iterative functions of order three to solve nonlinear equations in this paper we consider a geometric construction of iteration functions of order three to develop cubically convergent iterative methods for solving nonlinear equations this construction can be applied to any iteration function of order two to develop an iteration function of order three some examples are given of deriving several third order iteration methods and several numerical results follow to illustrate the performance of the derived methods

a digital technique to estimate second order distortion using higher order coherence spectra a digital spectral method for evaluating second order distortion of a nonlinear system which can be represented by volterra kernels up to second order and which is subjected to a random noise input is discussed the importance of departures from the commonly assumed gaussian excitation is investigated the hinich test is shown to be an appropriate test for orthogonality in the system identification tests for gaussianity of two important sources which are commonly used for gaussian inputs in nonlinear system identification are presented 1 commercial software routines for simulation experiments and 2 noise generators for practical experiments the deleterious effects of assuming a gaussian input when it is not are demonstrated the random input method for evaluating the second order distortion of a nonlinear system is compared with the sine wave input method using both simulation and experimental data the approach is applied to a loudspeaker in the low frequency band

a new modified secant like method for solving nonlinear equations in this paper we present a new secant like method for solving nonlinear equations analysis of the convergence shows that the asymptotic convergence order of this method is 1 3 some numerical results are given to demonstrate its efficiency

construction of third order modifications of newton s method abstract in this paper an approach for constructing third order modifications of newton s method using second order iteration formulas is presented several numerical examples are given to compare some of the newly obtained methods with the other third order methods

a modified newton method for rootfinding with cubic convergence we consider a modification of the newton method for finding a zero of a univariate function the case of multiple roots is not treated it is proven that the modification converges cubically per iteration it requires one evaluation of the function and two evaluations of its derivative thus the modification is suitable if the calculation of the derivative has a similar or lower cost than that of the function itself classes of such functions are sketched and a numerical example is given

the improvements of modified newton s method abstract in this paper we improve some third order modifications of newton s method and obtain many new methods for solving non linear equations the new methods have the order of convergence five or six per iteration these methods require two evaluations of the function and two evaluations of its first derivative and therefore the efficiency of the new methods may also be improved these methods can compete with newton s method as we show in some examples

some variants of chebyshev halley methods free from second derivative abstract in this paper we present some new modifications of chebyshev halley methods free from second derivative the convergence analysis shows that the new methods are third order convergent and require one function and two first derivative evaluations per iteration several numerical examples are given to illustrate the performance of the presented methods

a digital method of modeling quadratically nonlinear systems with a general random input without assuming particular statistics of the input a practical digital method of estimating linear and quadratic transfer functions of a nonlinear time invariant system that can be described by volterra series of up to second order is presented the method is tested and validated by analyzing input output data of a known quadratically nonlinear system it is used when there is little knowledge about the input statistics or the input is non gaussian it is also noted that the ordinary coherence functions cannot be used in explaining the input output power transfer relationship of a quadratic system excited by a non gaussian input signal with respect to the practical application of the method the relationship between the mean square errors involved in the transfer function estimates and the number of averages taken from the spectral estimation is qualitatively discussed

the improvements of chebyshev halley methods with fifth order convergence abstract in this paper we present a family of new fifth order methods which improves the classical chebyshev halley methods with cubic convergence the new methods add one evaluation of the function at the point iterated by chebyshev halley methods analysis of efficiency shows that the new methods can be of practical interest which is also corroborated by numerical tests

output frequency response characteristics of nonlinear systems part i general multi tone inputs a systematic algorithm for determining the output frequencies generated by a nonlinear system subject to a general multi tone input including a bias input is presented the algorithm is very efficient and circumvents many of the difficulties of duplicate frequencies that are often generated using previous methods the inclusion of the dc bias component in the analysis is also important because of the significant effect that non zero mean inputs can have on nonlinear system response the algorithm is straightforward to implement on a computer and the results are illustrated by means of an example

extension of the fdtd huygens subgridding algorithm to two dimensions this paper extends to two dimensions the finite difference time domain huygens subgridding algorithm previously published in the one dimensional case the algorithm is described in detail and several numerical experiments are provided to illustrate its possibilities and to demonstrate its effectiveness

random and pseudorandom inputs for volterra filter identification this paper studies input signals for the identification of nonlinear discrete time systems modeled via a truncated volterra series representation a kronecker product representation of the truncated volterra series is used to study the persistence of excitation pe conditions for this model it is shown that i i d sequences and deterministic pseudorandom multilevel sequences prms s are pe for a truncated volterra series with nonlinearities of polynomial degree n if and only if the sequences take on n 1 or more distinct levels it is well known that polynomial regression models such as the volterra series suffer from severe ill conditioning if the degree of the polynomial is large the condition number of the data matrix corresponding to the truncated volterra series for both prms and i i d inputs is characterized in terms of the system memory length and order of nonlinearity hence the trade off between model complexity and ill conditioning is described mathematically a computationally efficient least squares identification algorithm based on prms or i i d inputs is developed that avoids directly computing the inverse of the correlation matrix in many applications short data records are used in which case it is demonstrated that volterra filter identification is much more accurate using prms inputs rather than gaussian white noise inputs

a class of efficient quadrature based predictor corrector methods for solving nonlinear systems we extend a class of quadrature based predictor corrector techniques for root finding to multivariate systems they are found to have a rate of convergence of 1 2 regardless of the degree of precision for the quadrature technique from which they are derived provided it is at least one by reusing the linear system from the previous iterate this class incorporates a significant improvement in computational time relative to the standard class through the inclusion of an lu decomposition during the iteration complexity is equivalent to newton s method as they only require knowledge of f x and f x

a third order newton type method to solve systems of nonlinear equations in this paper we present a third order newton type method to solve systems of nonlinear equations in the first we present theoretical preliminaries of the method secondly we solve some systems of nonlinear equations all test problems show the third order convergence of our method

three step iterative methods for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations we show that this new iterative method has third order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

a mixed domain method for identification of quadratically nonlinear systems a new mixed domain method for identifying volterra transfer functions of a nonlinear system which can be represented by a second order truncated volterra series is presented in this paper this method is built on a discrete mixed domain volterra model derived from analyzing both discrete time and frequency domain volterra models of quadratically nonlinear systems it is shown that the conventional discrete frequency domain volterra model can be derived from the discrete mixed domain volterra model by making certain approximations in this sense the frequency domain model can be considered to be a cough version of the mixed domain model and thus cannot outperform the mixed domain model in terms of modeling capability in addition the new method is shown to be able to properly identify the volterra transfer functions even when the output of the quadratically nonlinear system is aliased based on this insight a new anti aliasing frequency domain method which is immune from the output aliasing problem is developed the superiority of these new methods over the conventional method is demonstrated by using them to analyze known quadratically nonlinear systems

construction of newton like iteration methods for solving nonlinear equations in this paper we present a simple and yet powerful and easily applicable scheme in constructing the newton like iteration formulae for the computation of the solutions of nonlinear equations the new scheme is based on the homotopy analysis method applied to equations in general form equivalent to the nonlinear equations it provides a tool to develop new newton like iteration methods or to improve the existing iteration methods which contains the well known newton iteration formula in logic those all improve the newton method the orders of convergence and corresponding error equations of the obtained iteration formulae are derived analytically or with the help of maple some numerical tests are given to support the theory developed in this paper

zero finder methods derived using runge kutta techniques abstract in this paper some families of zero finding iterative methods for nonlinear equations are presented the key idea to derive them is to solve an initial value problem applying runge kutta techniques more explicitly these methods are used to solve the problem that consists in a differential equation in what appears the inverse function of the one which zero will be computed and the condition given by the value attained by it at the initial approximation carrying out this procedure several families of different orders of local convergence are obtained furthermore the efficiency of these families are computed and two new families using like newton s methods that improve the most efficient one are also given

analysis of a uwb hemispherical antenna array in fdtd with a time domain huygens method electromagnetic modeling is needed in a wide variety of large and complex situations existing numerical techniques such as finite difference time domain fdtd can in principle solve any problem no matter how large or complicated given a sufficiently powerful computer however in practice there remain problems which require more computer power than is available recently the time domain huygens tdh approach has been shown to be effective for enabling large problems such as propagation on body area networks bans to be modeled in fdtd in this paper it is shown that the much larger problem of the conformal antenna array which is used in the maria breast cancer tumor detection system is also very amenable to this technique with even greater savings in computer resources accurate results are obtained using less that a tenth of the resources needed to solve the same problem using existing advanced fdtd tools the details of how this method is applied and the choices which need to be made are discussed

an analysis of the properties of the variants of newton s method with third order convergence for the last five years the variants of the newton s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non linear equations these methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives in this paper we investigate about the relationship between these methods which are in fact based on the approximation of the second order derivative present in the third order limited taylor expansion we also prove that they are different forms of the halley method and are all contractive iterative methods in a common neighbourhood we extend some of these variants to multivariate cases and prove their respective local cubic convergence from their corresponding linear models

a steffensen like method and its higher order variants for solving nonlinear equations we suggest a second order parametric steffensen like method which is derivative free and only uses two evaluations of the function in one step we also suggest a variant of the steffensen like method which is still derivative free and uses four evaluations of the function to achieve cubic convergence moreover a fast steffensen like method with super quadratic convergence and a fast variant of the steffensen like method with super cubic convergence are proposed by using a parameter estimation the error equations and asymptotic convergence constants are obtained for the discussed methods the numerical results and the basins of attraction support the proposed methods

some modification of newton s method by the method of undetermined coefficients in this paper we construct some modifications of newton s method for solving nonlinear equations which is based on the method of undetermined coefficients it is shown by way of illustration that the method of undetermined coefficients is a promising tool for developing new methods and reveals its wide applicability by obtaining some existing methods as special cases two new sixth order methods are developed numerical examples are given to support that the methods thus obtained can compete with other iterative methods

a modification of newton method with third order convergence in this paper we present a new modification of newton method for solving non linear equations analysis of convergence shows that the new method is cubically convergent per iteration the new method requires two evaluations of the function and one evaluation of its first derivative thus the new method is preferable if the computational costs of the first derivative are equal or more than those of the function itself its practical utility is demonstrated by numerical examples

derivative free iterative methods for nonlinear systems in this work we introduce a new operator of divided differences that preserves the convergence order when it is used for approximating the jacobian matrix in iterative method for solving nonlinear systems we obtain derivative free iterative methods with lower computational cost than the corresponding ones with different operators of divided differences we also study the global convergence of these methods by analyzing their dynamical behavior

third order modifications of newton s method based on stolarsky and gini means in this paper we consider third order modifications of newton s method for solving nonlinear equations considered methods are based on stolarsky and gini means stolarsky 1975 13 stolarsky 1980 14 chen 2008 12 and depend on two parameters some known methods are special cases of our methods for example the power mean newton s method zhou 2007 10 the arithmetic mean newton s method weerakoon and fernando 2000 5 the harmonic mean newton s method ozban 2004 8 and the geometric mean newton s method lukic and ralevic 2008 9 third order convergence of the considered methods is proved and corresponding asymptotic error constants are expressed in terms of two parameters numerical examples obtained using mathematica with high precision arithmetic support the theoretical results some numerical tests were performed and it was shown that our methods yield better numerical results i e a smaller error x email protected when compared to halley euler hansen patrick ostrowski and inverse interpolation methods

a modified newton method with cubic convergence the multivariate case recently a modification of the newton method for finding a zero of a univariate function with local cubic convergence has been introduced here we extend this modification to the multi dimensional case i e we introduce a modified newton method for vector functions that converges locally cubically without the need to compute higher derivatives the case of multiple roots is not treated per iteration the method requires one evaluation of the function vector and solving two linear systems with the jacobian as coefficient matrix where the jacobian has to be evaluated twice since the additional computational effort is nearly that of an additional newton step the proposed method is useful especially in difficult cases where the number of iterations can be reduced by a factor of two in comparison to the newton method this much better convergence is indeed possible as shown by a numerical example also the modified newton method can be advantageous in cases where the evaluation of the function is more expensive than solving a linear system with the jacobian as coefficient matrix an example for this is given where numerical quadrature is involved finally we discuss shortly possible extensions of the method to make it globally convergent

an infinite family of one step iterators for solving nonlinear equations to increase the order of convergence and a new algorithm of global convergence in this paper we present an infinite family of one step iterative formulas for solving nonlinear equations present method one from now on pmi that can be expressed as x n 1 f m x n with email protected m 1 we will prove that the corresponding iteration formula of the family x n 1 f m 0 x n has an order of convergence m 0 1 the increment of the velocity of convergence of the sequence of the iterator family x n 1 f m 1 x n with respect to the previous one x n 1 f m x n is attained at the expense of one derivative evaluation more besides we introduce a new algorithm present method two from now on pmii that plays the role of seeker for an initial value to guarantee the local convergence of the pmi both of them can be combined as an algorithm of global convergence included the case of singular roots that does not depend on the chosen initial value and that allows to find all the roots in a feasible interval in a general and complete way these are in my opinion the main results of this work