variants of newton s method using fifth order quadrature formulas abstract some variants of newton s method are developed in this work in order to solve nonlinear equations depending on one or several variables based in rules of quadrature of fifth order we prove the third or fifth order of convergence of these methods for dimension one and the second or third order in several variables depending on the behaviour of the second derivative moreover different numeric tests confirm or improve theoretic results and allow us to compare these variants with newton s classical method

quasi linear dynamics in nonlinear schrodinger equation with periodic boundary conditions it is shown that a large subset of initial data with finite energy l2 norm evolves nearly linearly in nonlinear schrodinger equation with periodic boundary conditions these new solutions are not perturbations of the known ones such as solitons semiclassical or weakly linear solutions

ostrowski type methods for solving systems of nonlinear equations abstract four generalized algorithms builded up from ostrowski s method for solving systems of nonlinear equations are written and analyzed a development of an inverse first order divided difference operator for functions of several variables is presented as well as a direct computation of the local order of convergence for these variants of ostrowski s method furthermore a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced

algebraic constructions of optimal frequency hopping sequences frequency hopping fh spread spectrum and direct sequence spread spectrum are two main spread coding technologies frequency hopping sequences are needed in fh code division multiple access cdma systems in this correspondence three classes of optimal frequency hopping sequences are constructed with algebraic methods the three classes are based on perfect nonlinear functions power functions and norm functions respectively both individual optimal frequency hopping sequences and optimal families of frequency hopping sequences are presented

poincare dulac normal form reduction for unconditional well posedness of the periodic cubic nls we implement an infinite iteration scheme of poincare dulac normal form reductions to establish an energy estimate on the one dimensional cubic nonlinear schrodinger equation nls in c tl 2 mathbb t without using any auxiliary function space this allows us to construct weak solutions of nls in c tl 2 mathbb t with initial data in l 2 mathbb t as limits of classical solutions as a consequence of our construction we also prove unconditional well posedness of nls in h s mathbb t for s geq frac 1 6

a new class of methods with higher order of convergence for solving systems of nonlinear equations by studying the commonness of some fifth order methods modified from third order ones for solving systems of nonlinear equations we propose a new class of three step methods of convergence order five by modifying a class of two step methods with cubic convergence next for a given method of order p 2 which uses the extended newton iteration yk xk af xk 1f xk as a predictor a new method of order p 2 is proposed for example we construct a class of m 2 step methods of convergence order 2m 3 by introducing only one evaluation of the function to each of the last m steps for any positive integer m in this paper we mainly focus on the class of fifth order methods when m 1 computational efficiency in the general form is considered several examples for numerical tests are given to show the asymptotic behavior and the computational efficiency of these higher order methods

kepler equation and accelerated newton method we study the efficiency of the accelerated newton method garlach siam rev 36 1994 272 276 for several orders of convergence versus danby s method for the resolution of kepler s equation we find that the cited method of order three is competitive with danby s method and the classical newton s method we also generalize the accelerated newton method for the resolution of system of algebraic equations obtaining a formula of order three and a proof of its convergence its application to several examples shows that its efficiency is greater than newton s method

letter to the editor frozen divided difference scheme for solving systems of nonlinear equations the development of an inverse first order divided difference operator for functions of several variables as well as a direct computation of the local order of convergence of an iterative method is presented a generalized algorithm of the secant method for solving a system of nonlinear equations is studied and the maximum computational efficiency is computed furthermore a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced

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

third order methods from quadrature formulae for solving systems of nonlinear equations we extend to p dimensional problems a modification of the newton method based on quadrature formulas of order at least one which produces iterative methods with order of convergence three a general error analysis providing the higher order of convergence is given these new methods may be more efficient then other third order methods as they do not require the use of the second order frechet derivative

comments on lower bounds on the hamming auto and cross correlations of frequency hopping sequences by d peng and p fan the author points out that several of the results in the paper by d peng and p fan see ibid vol 50 no 9 p 2149 54 sep 2004 have been published previously

multilinear weighted convolution of l 2 functions and applications to nonlinear dispersive equations the x s b spaces as used by beals bourgain kenig ponce vega klainerman machedon and others are fundamental tools to study the low regularity behavior of nonlinear dispersive equations it is of particular interest to obtain bilinear or multilinear estimates involving these spaces by plancherel s theorem and duality these estimates reduce to estimating a weighted convolution integral in terms of the l 2 norms of the component functions in this paper we systematically study weighted convolution estimates on l 2 as a consequence we obtain sharp bilinear estimates for the kdv wave and schrodinger x s b spaces

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

on the regularization mechanism for the periodic korteweg de vries equation in this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic korteweg de vries kdv equation in the homogeneous sobolev spaces s for s 0 specifically we prove the global existence uniqueness and lipschitz continuous dependence on the initial data of the solutions of the periodic kdv for the case where the initial data is in l2 we also show the lipschitz continuous dependence of these solutions with respect to the initial data as maps from s to s for s 1 0 2010 wiley periodicals inc

a fourth order method from quadrature formulae to solve systems of nonlinear equations in this paper we obtain a fourth order convergence method to solve systems of nonlinear equations this method is based on a quadrature formulae a general error analysis providing the fourth order of convergence is given numerical examples show the fourth order convergence this method does not use the second order frechet derivative

nearly linear dynamics of nonlinear dispersive waves abstract dispersive averaging effects are used to show that the korteweg de vries kdv equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly numerical simulations are presented which indicate the high accuracy of this approximation furthermore this result is applied to shallow water wave dynamics in the limit of kdv approximation which is obtained by asymptotic analysis in combination with numerical simulations of kdv

on the computational efficiency index and some iterative methods for solving systems of nonlinear equations in this paper two new iterative methods are built up and analyzed a generalization of the efficiency index used in the scalar case to several variables in iterative methods for solving systems of nonlinear equations is revisited analytic proofs of the local order of convergence based on developments of multilineal functions and numerical concepts that will be used to illustrate the analytic results are given an approximation of the computational order of convergence is computed independently of the knowledge of the root and the necessary time to get one correct decimal is studied in our examples

an efficient fifth order method for solving systems of nonlinear equations in this paper we present a three step iterative method of convergence order five for solving systems of nonlinear equations the methodology is based on the two step homeier s method with cubic convergence homeier 2004 computational efficiency in its general form is discussed and a comparison between the efficiency of proposed technique and existing ones is made the performance is tested through numerical examples moreover theoretical results concerning order of convergence and computational efficiency are verified in the examples it is shown that the present method has an edge over existing methods particularly when applied to large systems of equations

an improved newton traub composition for solving systems of nonlinear equations in this paper we present a modified newton traub composition with increasing order of convergence for solving systems of nonlinear equations the idea is based on the recent development by sharma et al 2015 analysis of convergence shows that the presented method has sixth order of convergence computational efficiency of the new method is considered and compared with some well known existing methods numerical tests are performed on some problems of different nature which confirm robust and efficient convergence behavior of the proposed method moreover theoretical results concerning order of convergence and computational efficiency are verified in the numerical problems the basins of attraction of existing methods and the presented method are given to demonstrate their performance

optimal frequency hopping sequences a combinatorial approach frequency hopping multiple access fhma spread spectrum communication systems employing multiple frequency shift keying mfsk as data modulation technique are investigated from a combinatorial approach a correspondence between optimal frequency hopping fh sequences and partition type difference packings is first established by virtue of this correspondence fhma systems with a single optimal fh sequence each are constructed from various combinatorial structures such as affine geometries cyclic designs and difference families combinatorial recursive constructions are also presented many new infinite series of optimal fh sequences are thus obtained these new fh sequences are also useful in ultra wideband uwb communication systems

normal form approach to near linear dynamics of modified kdv equation abstract in this paper we implement normal form reduction to the periodic modified korteweg de vries mkdv equation to investigate the behavior of a solution when a subtle high frequency initial data is given we use differentiation by parts to decompose the equation into resonant and non resonant parts and provide some nonlinear estimates for each term if a subtle high frequency initial data is given a solution of the mkdv equation can be approximated by a solution of the linearized mkdv equation for large times

quasi invariant gaussian measures for the cubic fourth order nonlinear schrodinger equation we consider the cubic fourth order nonlinear schrodinger equation on the circle in particular we prove that the mean zero gaussian measures on sobolev spaces h s mathbb t s frac 3 4 are quasi invariant under the flow

optimal frequency hopping sequences auto and cross correlation properties frequency hopping fh sequences play a key role in frequency hopping spread spectrum communication systems in order to evaluate the performance of fh sequences lempel and greenberger 1974 and peng and fan 2004 derived lower bounds on their hamming auto and cross correlations in this paper we construct families of fh sequences with hamming correlations meeting those bounds by combinatorial and algebraic techniques we first construct optimal families consisting of a single fh sequence with maximum hamming correlation equal to 2 from a combinatorial approach then we investigate families consisting of multiple fh sequences we provide a combinatorial characterization for such families and present a recursive method to construct them by means of this characterization we also describe two algebraic constructions for such families of fh sequences generalizing those of ding moisio and yuan 2007 as a consequence many new optimal families of fh sequences are obtained

some iterative methods for solving a system of nonlinear equations in this paper we suggest and analyze two new two step iterative methods for solving the system of nonlinear equations using quadrature formulas we prove that these new methods have cubic convergence several numerical examples are given to illustrate the efficiency and the performance of the new iterative methods these new iterative methods may be viewed as an extension and generalizations of the existing methods for solving the system of nonlinear equations

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