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

some variants of king s fourth order family of methods for nonlinear equations abstract in this paper we present fourth order families of new variants of king s fourth order family of methods for solving nonlinear equations per iteration the obtained methods require two evaluations of the given function and one of its first derivative the classical traub ostrowski method is obtained as a special variant of king s method several numerical examples are given to illustrate the efficiency and performance of the presented methods

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

a classification of the face numbers of buchsbaum simplicial posets the family of buchsbaum simplicial posets generalizes the family of simplicial cell manifolds the h vector of a simplicial complex or simplicial poset encodes the combinatorial and topological data of its face numbers and the reduced betti numbers of its geometric realization novik and swartz showed that the h vector of a buchsbaum simplicial poset satisfies certain simple inequalities in this paper we show that these necessary conditions are in fact sufficient to characterize the h vectors of buchsbaum simplicial posets with prescribed betti numbers

avoiding the computation of the second fre chet derivative in the convex acceleration of newton s method we introduce a new two step method to approximate a solution of a nonlinear operator equation in a banach space an existence uniqueness theorem and error estimates are provided for this iteration using newton kantorovich type assumptions and a technique based on a new system of recurrence relations for a special choice of the parameter involved we use our method is of fourth order

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

a note on the halley method in banach spaces abstract we provide a convergence theorem under the usual ostrowski kantorovich conditions for an equivalent form of the halley method in banach spaces the best possible upper error bound for the method is obtained some applications to the solution of quadratic operator equations are provided

ext and local cohomology modules of face rings of simplicial posets abstract there are a large number of theorems detailing the homological properties of the stanley reisner ring of a simplicial complex here we attempt to generalize some of these results to the case of a simplicial poset by investigating the combinatorics of certain modules associated with the face ring of a simplicial poset from a topological viewpoint we extend some results of miyazaki and grabe to a wider setting

stationary min stable stochastic processes we consider the class of stationary stochastic processes whose margins are jointly min stable we show how the scalar elements can be generated by a single realization of a standard homogeneous poisson process on the upper half strip 0 1 x r and a group of l1 isometries we include a dobrushin like result for the realizations in continuous time

dependence modelling for spatial extremes current dependence models for spatial extremes are based upon max stable processes within this class there are few inferentially viable models available and we propose one further model more problematic are the restrictive assumptions that must be made when using max stable processes to model dependence for spatial extremes it must be assumed that the dependence structure of the observed extremes is compatible with a limiting model that holds for all events more extreme than those that have already occurred this problem has long been acknowledged in the context of finite dimensional multivariate extremes in particular when data display dependence at observable levels but are independent in the limit we propose a flexible class of models that is suitable for such data in a spatial context in addition we consider the situation where the extremal dependence structure may vary with distance we apply our models to spatially referenced significant wave height data from the north sea finding evidence that their extremal structure is not compatible with a limiting dependence model

a biparametric extension of king s fourth order methods and their dynamics a class of two point quartic order simple zero finders and their dynamics are investigated in this paper by extending king s fourth order family of methods with the introduction of an error corrector having a weight function dependent on a function to function ratio higher order convergence is obtained through a variety of test equations numerical experiments strongly support the theory developed in this paper in addition relevant dynamics of the proposed methods is successfully explored for a prototype quadratic polynomial as well as parameter spaces and dynamical planes

fourth order iterative methods free from second derivative in this paper we present a family of new iterative methods with order of convergence four for solving non linear equations per iteration these methods require one evaluation of the function and two of its first derivative analysis of efficiency in term of function evaluations shows that this family of methods has great superiority which is also demonstrated by numerical examples

h vectors of gorenstein simplicial posets abstract as is well known h vectors of simplicial convex polytopes are characterized those h vectors satisfy dehn sommerville equations and some inequalities conjectured by p mcmullen and first proved by r stanley using toric geometry the boundary of a simplicial convex polytope determines a gorenstein simplicial poset but there are many gorenstein simplicial posets which do not arise this way however it is known that h vectors of gorenstein simplicial posets still satisfy dehn sommerville equations and that every component in the h vectors is non negative in this paper we prove that h vectors of gorenstein simplicial posets must satisfy one more subtle condition conjectured by r stanley and complete the characterization of h vectors of gorenstein simplicial posets our proof is purely algebraic but the idea of the proof stems from topology

some fourth order iterative methods for solving nonlinear equations abstract in this paper we present some fourth order iterative methods for solving nonlinear equations which contains the well known king s fourth order family as a particular case per iteration the methods require two function and one first derivative evaluations numerical comparisons are made with several other existing methods to show the performance of the presented methods

regional modelling of extreme storms via max stable processes asymptotic models for extremes of random processes often form the basis for estimating the extremal behaviour of environmental phenomena most such phenomena have a spatial dimension and the aim of this paper is to develop a procedure for modelling in continuous space the spatial dependence within extreme events a principal objective in the analysis as with other current research on extremes is to base inference on as much of the available data as possible the modelling procedures are justified on simulated data and subsequently applied to a series of rainfall data

spatial extremes models for the stationary case the aim of this paper is to provide models for spatial extremes in the case of stationarity the spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max stable processes of de haan and pickands probab theory related fields 72 1986 477 492 we propose three one dimensional and three two dimensional models these models depend on just one parameter or a few parameters that measure the strength of tail dependence as a function of the distance between locations we also propose two estimators for this parameter and prove consistency under domain of attraction conditions and asymptotic normality under appropriate extra conditions

on developing a higher order family of double newton methods with a bivariate weighting function a high order family of two point methods costing two derivatives and two functions are developed by introducing a two variable weighting function in the second step of the classical double newton method their theoretical and computational properties are fully investigated along with a main theorem describing the order of convergence and the asymptotic error constant as well as proper choices of special cases a variety of concrete numerical examples and relevant results are extensively treated to verify the underlying theoretical development in addition this paper investigates the dynamics of rational iterative maps associated with the proposed method and an existing method based on illustrated description of basins of attraction for various polynomials

some fourth order modifications of newton s method abstract in this paper we construct some fourth order modifications of newton s method for solving nonlinear equations any two existing fourth order methods can be effectively used to give rise to new fourth order methods per iteration the new methods require two evaluations of the function and one of its first derivative numerical examples are given to show the performance of the presented methods

certain improvements of chebyshev halley methods with accelerated fourth order convergence abstract in this paper we present a new one parameter family of methods which improves the classical chebyshev halley methods with cubic convergence the convergence analysis shows that each method of the family is quartically convergent and per iteration it requires one evaluation of the given function and two of its first derivative the well known jarratt 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

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

a modification of the super halley method under mild differentiability conditions a new two point iteration of order three is introduced to approximate a solution of a nonlinear operator equation in banach spaces under the same assumptions as for newton s method we provide a result on the existence of a unique solution for the nonlinear equation which is based on a technique consisting of a new system of recurrence relations

a family of methods for solving nonlinear equations we present a family of methods for solving nonlinear equations some well known classical methods and their modifications belong to our family for example newton potra ptak chebyshev halley and ostrowski s methods convergence analysis shows that our family contains methods of convergence order from 2 to 4 all our fourth order methods are optimal in terms of the kung and traub conjecture several examples are presented and compared

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

the jarratt method in banach space setting abstract in this note we extend the jarratt method of order four into banach spaces we also establish a kantorovich type convergence theorem see the references and give an explicit expression for the error bound of the method jarratt 1966 1969

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

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

socles of buchsbaum modules complexes and posets abstract the socle of a graded buchsbaum module is studied and is related to its local cohomology modules this algebraic result is then applied to face enumeration of buchsbaum simplicial complexes and posets in particular new necessary conditions on face numbers and betti numbers of such complexes and posets are established these conditions are used to settle in the affirmative kuhnel s conjecture for the maximum value of the euler characteristic of a 2k dimensional simplicial manifold on n vertices as well as kalai s conjecture providing a lower bound on the number of edges of a simplicial manifold in terms of its dimension number of vertices and the first betti number

a new family of methods for single and multiple roots abstract we present a new family of iterative methods for multiple and single roots of nonlinear equations this family contains as a special case the authors family for finding simple roots from herceg and herceg 2015 some well known classical methods for simple roots for example newton potra ptak newton steffensen king and ostrowski s methods belong to this family which implies that our new family contains modifications of these methods suitable for finding multiple roots convergence analysis shows that our family contains methods of convergence order from 2 to 4 the new methods require two function evaluations and one evaluation of the first derivative per iteration so all our fourth order methods are optimal in terms of the kung and traub conjecture several examples are presented and compared through various test equations relevant numerical experiments strongly support the claimed theory in this paper extraneous fixed points of the iterative maps associated with the proposed methods are also investigated their dynamics is explored along with illustrated basins of attraction for various polynomials

stationary max stable fields associated to negative definite functions let wi i be independent copies of a zero mean gaussian process w t t d with stationary increments and variance 2 t independently of wi let i 1 ui be a poisson point process on the real line with intensity e y dy we show that the law of the random family of functions vi i where vi t ui wi t 2 t 2 is translation invariant in particular the process t i 1 vi t is a stationary max stable process with standard gumbel margins the process arises as a limit of a suitably normalized and rescaled pointwise maximum of n i i d stationary gaussian processes as n if and only if w is a nonisotropic fractional brownian motion on d under suitable conditions on w the process has a mixed moving maxima representation

a dependence measure for multivariate and spatial extreme values properties and inference we present properties of a dependence measure that arises in the study of extreme values in multivariate and spatial problems for multivariate problems the dependence measure characterises dependence at the bivariate level for all pairs and all higher orders up to and including the dimension of the variable necessary and sufficient conditions are given for subsets of dependence measures to be self consistent that is to guarantee the existence of a distribution with such a subset of values for the dependence measure for pairwise dependence these conditions are given in terms of positive semidefinite matrices and non differentiable positive definite functions we construct new nonparametric estimators for the dependence measure which unlike all naive nonparametric estimators impose these self consistency properties as the new estimators provide an improvement on the naive methods both in terms of the inferential and interpretability properties their use in exploratory extreme value analyses should aid the identification of appropriate dependence models the methods are illustrated through an analysis of simulated multivariate data which shows that a lack of self consistency is frequently a problem with the existing estimators and by a spatial analysis of daily rainfall extremes in south west england which finds a smooth decay in extremal dependence with distance

chebyshev s approximation algorithms and applications abstract we introduce a new family of multipoint methods to approximate a solution of a nonlinear operator equation in banach spaces an existence uniqueness theorem and error estimates are provided for these iterations using a technique based on a new system of recurrence relations to finish we apply the results obtained to some nonlinear integral equations of the fredholm type

on halley type iterations with free second derivative in this paper we relax the convergence conditions required in ezquerro and hernandez int j pure appl math 6 1 2003 103 for a multipoint third order iteration of halley type where the conditions provided are the known ones for methods of order three

an acceleration of newton s method super halley method from a study of the convexity we give an acceleration for newton s method and obtain a new third order method then we use this method for solving non linear equations in banach spaces establishing conditions on convergence existence and uniqueness of solution as well as error estimates

on the dynamics of a triparametric family of optimal fourth order multiple zero finders with a weight function of the principal mth root of a function to function ratio abstract under the assumption of known root multiplicity m n a triparametric family of two point optimal quartic order methods locating multiple zeros are investigated in this paper by introducing a weight function dependent on a function to function ratio special cases of weight functions with selected free parameters are considered and studied through various test equations and numerical experiments to support the theory developed in this paper in addition we explore the relevant dynamics of proposed methods via mobius conjugacy map when applied to a prototype polynomial z a m z b m the results of such dynamics are visually illustrated through a variety of parameter spaces as well as dynamical planes

centrally symmetric manifolds with few vertices abstract a centrally symmetric 2 d vertex combinatorial triangulation of the product of spheres s i s d 2 i is constructed for all pairs of nonnegative integers i and d with 0 i d 2 for the case of i d 2 i the existence of such a triangulation was conjectured by sparla the constructed complex admits a vertex transitive action by a group of order 4 d the crux of this construction is a definition of a certain full dimensional subcomplex b i d of the boundary complex of the d dimensional cross polytope this complex b i d is a combinatorial manifold with boundary and its boundary provides a required triangulation of s i s d i 2 enumerative characteristics of b i d and its boundary and connections to another conjecture of sparla are also discussed

on optimal fourth order iterative methods free from second derivative and their dynamics in this paper new fourth order optimal root finding methods for solving nonlinear equations are proposed the classical jarratt s family of fourth order methods are obtained as special cases we then present results which describe the conjugacy classes and dynamics of the presented optimal method for complex polynomials of degree two and three the basins of attraction of existing optimal methods and our method are presented and compared to illustrate their performance

on the likelihood function of gaussian max stable processes summary wederiveaclosedformexpressionforthelikelihoodfunctionofagaussianmax stableprocessindexed by r d at p d 1 sites d 1 we demonstrate the gain in efficiency in the maximum composite likelihood estimators of the covariance matrix from p 2t op 3 sites in r 2 by means of a monte carlo