performance characteristics of the median lms adaptive filter the median least mean square mlms adaptive filter alleviates the problem of degradation of performance when inputs are corrupted by impulsive noise by protecting the filter coefficients from the impact of the impulses mlms is obtained from the least mean square lms by applying a median operation to the raw gradient estimates of the mean squared error performance surface the algorithm is analyzed for the class of independent and identically distributed inputs establishing exponential convergence the rate of convergence is shown to depend on order statistics of the input but shows little dependence on characteristics of the impulsive interference analysis of the steady state performance indicates a significantly improved performance for mlms compared to lms analytic predictions for both convergence and steady state behavior are supported by simulations

on developing fourth order optimal families of methods for multiple roots and their dynamics there are few optimal fourth order methods for solving nonlinear equations when the multiplicity m of the required root is known in advance therefore the first focus of this paper is on developing new fourth order optimal families of iterative methods by a simple and elegant way computational and theoretical properties are fully studied along with a main theorem describing the convergence analysis another main focus of this paper is the dynamical analysis of the rational map associated with our proposed class for multiple roots as far as we know there are no deep study of this kind on iterative methods for multiple roots further using mathematica with its high precision compatibility a variety of concrete numerical experiments and relevant results are extensively treated to confirm the theoretical development

third degree anomalies of traub s method traub s method is a tough competitor of newton s scheme for solving nonlinear equations as well as nonlinear systems due to its third order convergence and its low computational cost it is a good procedure to be applied on complicated multidimensional problems in order to better understand its behavior the stability of the method is analyzed on cubic polynomials showing the existence of very small regions with unstable behavior finally the performance of the method on cubic matrix equations arising in control theory is presented showing a good performance

adaptive lms l filters for noise suppression in images several adaptive least mean squares lms l filters both constrained and unconstrained ones are developed for noise suppression in images and compared in this paper first the location invariant lms l filter for a nonconstant signal corrupted by zero mean additive white noise is derived it is demonstrated that the location invariant lms l filter can be described in terms of the generalized linearly constrained adaptive processing structure proposed by griffiths and jim 1982 subsequently the normalized and the signed error lms l filters are studied a modified lms l filter with nonhomogeneous step sizes is also proposed in order to accelerate the rate of convergence of the adaptive l filter finally a signal dependent adaptive filter structure is developed to allow a separate treatment of the pixels that are close to the edges from the pixels that belong to homogeneous image regions

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

min max and min max regret versions of combinatorial optimization problems a survey abstract min max and min max regret criteria are commonly used to define robust solutions after motivating the use of these criteria we present general results then we survey complexity results for the min max and min max regret versions of some combinatorial optimization problems shortest path spanning tree assignment min cut min s t cut knapsack since most of these problems are np hard we also investigate the approximability of these problems furthermore we present algorithms to solve these problems to optimality

dynamics of a family of chebyshev halley type methods in this paper the dynamics of the chebyshev halley family is studied on quadratic polynomials a singular set that we call cat set appears in the parameter space associated to the family this set has interesting similarities with the mandelbrot set the parameter space has allowed us to find different elements of the family which have bad convergence properties since periodic orbits and attractive strange fixed points appear in the dynamical plane of the corresponding method

dynamical analysis on cubic polynomials of damped traub s method for approximating multiple roots abstract in this paper the performance of a parametric family including newton s and traub s schemes on multiple roots is analyzed the local order of convergence on nonlinear equations with multiple roots is studied as well as the dynamical behavior in terms of the damping parameter on cubic polynomials with multiple roots the fixed and critical points and the associated parameter plane are some of the characteristic dynamical features of the family which are obtained in this work from the analysis of these elements we identify members of the family of methods with good numerical properties in terms of stability and efficiency both for finding the simple and multiple roots and also other ones with very unstable behavior

minmax regret location allocation problem on a network under uncertainty abstract we consider a robust location allocation problem with uncertainty in demand coefficients specifically for each demand point only an interval estimate of its demand is known and we consider the problem of determining where to locate a new service when a given fraction of these demand points must be served by the utility the optimal solution of this problem is determined by the minimax regret location i e the point that minimizes the worst case loss in the objective function that may occur because a decision is made without knowing which state of nature will take place for the case where the demand points are vertices of a network we show that the robust location allocation problem can be solved in o min p n p n 3 m time where n is the number of demand points p p n is the fixed number of demand points that must be served by the new service and m is the number of edges of the network

on signal recovery with adaptive order statistic filters adaptive order statistic filters are used to estimate a constant amplitude signal embedded in noise with unknown statistics iterative algorithms are proposed which adapt the order statistic filter to minimize the mean square estimation error both with and without an unbiasedness constraint for each case the algorithm used is shown to achieve convergence in the mean to the optimal filter properties of the convergence rates are discussed and conditions for convergence in mean square are noted

a study of dynamics via mobius conjugacy map on a family of sixth order modified newton like multiple zero finders with bivariate polynomial weight functions abstract a generic family of sixth order modified newton like multiple zero finders have been proposed in geum et al 2016 among them we select a specific family of iterative methods with uniparametric bivariate polynomial weight functions and study their dynamics by investigating the relevant parameter spaces and dynamical planes via mobius conjugacy map applied to a prototype polynomial of the form z a m z b m the resulting dynamics is best illustrated through a variety of parameter spaces as well as dynamical planes

on combinatorial optimization problems on matroids with uncertain weights in this paper the combinatorial optimization problem on weighted matroid is considered it is assumed that the weights in the problem are ill known and they are modeled as fuzzy intervals the optimality of solutions and the optimality of elements are characterized this characterization is performed in the setting of possibility theory a method of choosing a solution under uncertainty is also proposed

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

ordered weighted average optimization in multiobjective spanning tree problem abstract multiobjective spanning tree problems are studied in this paper the ordered median objective function is used as an averaging operator to aggregate the vector of objective values of feasible solutions this leads to the ordered weighted average spanning tree problem a nonlinear combinatorial optimization problem different mixed integer linear programs are proposed based on the most relevant minimum cost spanning tree models in the literature these formulations are analyzed and several enhancements presented their empirical performance is tested over a set of randomly generated benchmark instances the results of the computational experiments show that the choice of an appropriate formulation allows to solve larger instances with more objectives than those previously solved in the literature

adaptive trimmed mean filters for image restoration an adaptive smoothing filter is proposed for reducing noise in digital signals of any dimensionality the adaptive procedure is based on the selection of an appropriate inner or outer trimmed mean filter according to local measurements of the tail behavior impulsivity of the noise process the set of trimmed means used provides robustness against a wide range of noise possibilities ranging from very shallow tailed to very heavy tailed a monte carlo analysis using a family of generalized exponential distributions supports the choice of the trimmed mean selected for measured values of an impulsivity statistic the assumption underlying the definition of the filter is that the signal to be filtered is locally smoothly varying and that the noise process is uncorrelated and derives from an unknown unimodal symmetric distribution for image processing applications a second statistic is used to mark the location of abrupt intensity changes or edges in the vicinity of an edge the trend preserving median filter is used since the impulsivity and edge statistics used in defining the adaptive filter are both functions of order statistics the extra computation required for their calculation is minimal examples are provided of the filter as applied to images corrupted by a variety of noises

minimax regret spanning arborescences under uncertain costs abstract the paper considers a classical optimization problem on a network whose arc costs are partially known it is assumed that an interval estimate is given for each arc cost and no further information about the statistical distribution of the truth value of the arc cost is known in this context given a spanning arborescence in the network its cost can take on different values according to the choice of each individual arc cost that is according to the different cost scenarios we analyze the problem of finding which spanning arborescence better approaches the optimal one under each possible scenario the minimax regret criterion is proposed in order to obtain such a robust solution to the problem in the paper it is shown that a greedy type algorithm can compute an optimal solution of this problem on acyclic networks for general networks the problem becomes np hard in this case the special structure of the optimization problem allows us to design a bounding process for the optimum value that will result in a heuristic algorithm described at the end of the paper

a multidimensional dynamical approach to iterative methods with memory a dynamical approach on the dynamics of iterative methods with memory for solving nonlinear equations is made we have designed new methods with memory from steffensen or traub s schemes as well as from a parametric family of iterative procedures of third and fourth order of convergence we study the local order of convergence of the new iterative methods with memory we define each iterative method with memory as a discrete dynamical system and we analyze the stability of the fixed points of its rational operator associated on quadratic polynomials as far as we know there is no dynamical study on iterative methods with memory and the techniques of complex dynamics used in schemes without memory are not useful in this context so we adapt real multidimensional dynamical tools to afford this task the dynamical behavior of secant method and the versions of steffensen and traub s schemes with memory applied on quadratic polynomials are analyzed different kinds of behavior occur being in general very stable but pathologic cases as attracting strange fixed points are also found finally a modified parametric family of order four applied on quadratic polynomials is also studied showing the bifurcations diagrams and the appearance of chaos

a construction of attracting periodic orbits for some classical third order iterative methods we use a family of root finding iterative methods for finding roots of nonlinear equations we present a procedure for constructing polynomials so that superattracting periodic orbits of any prescribed period occur when these methods are applied this family includes chebyshev s method halley s method the super halley method and the c methods as particular cases

possibilistic minmax regret sequencing problems with fuzzy parameters in this paper a class of sequencing problems with uncertain parameters is discussed the uncertainty is modeled by the usage of fuzzy intervals whose membership functions are regarded as possibility distributions for the values of unknown parameters it is shown how to use possibility theory to find robust solutions under fuzzy parameters this paper presents a general framework together with applications to some classical sequencing problems first the interval sequencing problems with the minmax regret criterion are discussed the state of the art in this area is recalled next the fuzzy sequencing problems in which the classical intervals are replaced with fuzzy ones are investigated a possibilistic interpretation of such problems solution concepts and algorithms for the computation of a solution are described in particular it is shown that every fuzzy problem can be efficiently solved if a polynomial algorithm for the corresponding interval problem with the minmax regret criterion is known some methods to deal with np hard problems are also proposed and the efficiency of these methods is explored

a probabilistic model for minmax regret in combinatorial optimization in this paper we propose a new probabilistic model for minimizing the anticipated regret in combinatorial optimization problems with distributional uncertainty in the objective coefficients the interval uncertainty representation of data is supplemented with information on the marginal distributions as a decision criterion we minimize the worst case conditional value at risk of regret the proposed model includes the interval data minmax regret model as a special case for the class of combinatorial optimization problems with a compact convex hull representation a polynomial sized mixed integer linear program is formulated when a the range and mean are known and b the range mean and mean absolute deviation are known and a mixed integer second order cone program is formulated when c the range mean and standard deviation are known for the subset selection problem of choosing k elements of maximum total weight out of a set of n elements the probabilistic regret model is shown to be solvable in polynomial time in the instances a and b above this extends the current known polynomial complexity result for minmax regret subset selection with range information only

dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension abstract this paper deals with the real dynamical analysis of iterative methods for solving nonlinear systems on vectorial quadratic polynomials we use the extended concept of critical point and propose an easy test to determine the stability of fixed points to multivariate rational functions moreover an scaling theorem for different known methods is satisfied we use these tools to analyze the dynamics of the operator associated to known iterative methods on vectorial quadratic polynomials of two variables the dynamical behavior of newton s method is very similar to the obtained in the scalar case but this is not the case for other schemes some procedures of different orders of convergence have been analyzed under this point of view and some dangerous numerical behavior have been found as attracting strange fixed points or periodic orbits

complex dynamics of derivative free methods for nonlinear equations the dynamical behavior of two iterative derivative free schemes steffensen and m4 methods is studied in case of quadratic and cubic polynomials the parameter plane is analyzed for both procedures on quadratic polynomials different dynamical planes are showed when the mentioned methods are applied on particular cubic polynomials with real or complex coefficients the property of immersion of the basins of attraction in all cases is analyzed

a new tool to study real dynamics in this paper the author presents a graphical tool that allows to study the real dynamics of iterative methods whose iterations depends on one parameter in an easy and compact way this tool gives the information as previous tools such as feigenbaum diagrams and lyapunov exponents for every initial point the convergence plane can be used inter alia to find the elements of a family that have good convergence properties to see how the basins of attraction changes along the elements of the family to study two point methods such as secant method or even to study two parameter families of iterative methods to show the applicability of the tool an example of the dynamics of the damped newton s method applied to a cubic polynomial is presented in this paper

extending the convergence domain of the secant and moser method in banach space we present a new semilocal convergence analysis for the secant and the moser method in order to approximate a solution of an equation in a banach space setting using the method of recurrent relations and weaker sufficient convergence criteria than in earlier studies such as amat et al 2014 hernandez and rubio 2007 hernandez and rubio 1999 and hernandez and rubio 2002 we increase the convergence domain of these methods the advantages are also obtained under less computational cost than in amat et al 2014 hernandez and rubio 2007 hernandez and rubio 1999 and hernandez and rubio 2002 numerical examples where the older convergence criteria are not satisfied but the new convergence criteria are satisfied are also provided in this study

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

stability analysis of a parametric family of iterative methods for solving nonlinear models a one parametric family of fourth order iterative methods for solving nonlinear systems is presented proving the fourth order of convergence of all members in this family except one of them whose order is five the methods in our family are numerically compared with other known methods in terms of the classical efficiency index order of convergence and number of functional evaluations and in terms of the operational efficiency index which also takes into account the total number of product quotients per iteration in order to analyze its stability and its dynamical properties the parameter space for quadratic polynomials is shown the stability of the strange fixed points is studied in this case we note that even for this particular case the family presents a very interesting dynamical behavior the analysis of the parameter plane allows us to find values for the involved parameter with good stability properties as well as other values with bad numerical behavior finally amongst the first ones there is a special value of the parameter related to a fifth order method in the family

an efficient optimal family of sixteenth order methods for nonlinear models abstract the principle aim of this manuscript is to propose a general scheme that can be applied to any optimal iteration function of order eight whose first substep employ newton s method to further develop new interesting optimal scheme of order sixteen this scheme requires four evaluations of the involved function and one evaluation of its first order derivative at each step so it is being optimally consistent with the conjecture of kung traub in addition theoretical and computational properties are fully investigated along with a main theorem describing the order of convergence moreover the conjugacy maps and the strange fixed points of some iterative methods are discussed their basins of attractions are also given to show their dynamical behavior around the simple roots from the numerical experiments we find that our methods perform better than the existing ones when we checked the performance on a concrete variety of nonlinear equations

on the complexity of a class of combinatorial optimization problems with uncertainty we consider a robust minmax regret version of the problem of selecting p elements of minimum total weight out of a set of m elements with uncertainty in weights of the elements we present a polynomial algorithm with the order of complexity o min p m p 2m for the case where uncertainty is represented by means of interval estimates for the weights we show that the problem is np hard in the case of an arbitrary finite set of possible scenarios even if there are only two possible scenarios this is the first known example of a robust combinatorial optimization problem that is np hard in the case of scenario represented uncertainty but is polynomially solvable in the case of the interval representation of uncertainty

a note on convergence radius of osada s method under holder continuous condition abstract in this paper we revise the proofs of the results obtained in convergence radius of osada s method under holder continuous condition 4 because the remainder of the taylor s expansion used for the obtainment of the local convergence radius is not correct so we perform the complete study in order to modify the equation for getting the local convergence radius the uniqueness radius and the error bounds moreover a dynamical study for the third order osada s method is also developed

a generalization of median filtering using linear combinations of order statistics we consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence assuming a constant signal in white noise the coefficients in the linear combination are chosen to minimize the output mse for several noise distributions it is shown that the optimal order statistic filter osf tends toward the median filter as the noise becomes more impulsive the optimal osf is applied to an actual noisy image and is shown to perform well combining properties of both the averaging and median filters a more general design scheme for applications involving nonconstant signals is also given

an efficient high order iterative scheme for large nonlinear systems with dynamics abstract this study suggests a new general scheme of high convergence order for approximating the solutions of nonlinear systems the proposed scheme is the extension of an earlier study of parhi and gupta this method requires two vector function two jacobian matrices two inverse matrices and one frozen inverse matrix per iteration convergence error computational efficiency and numerical experiments are performed to verify the applicability and validity of the proposed methods compared with existing methods finally we discuss the strange fixed points and conjugacy functions on a particular case of our scheme the basins of attractions also demonstrate the dynamical behavior of this special case in the neighborhood of required roots and also assert the theoretical outcomes

dynamics of a new family of iterative processes for quadratic polynomials in this work we show the presence of the well known catalan numbers in the study of the convergence and the dynamical behavior of a family of iterative methods for solving nonlinear equations in fact we introduce a family of methods depending on a parameter m n 0 these methods reach the order of convergence m 2 when they are applied to quadratic polynomials with different roots newton s and chebyshev s methods appear as particular choices of the family appear for m 0 and m 1 respectively we make both analytical and graphical studies of these methods which give rise to rational functions defined in the extended complex plane firstly we prove that the coefficients of the aforementioned family of iterative processes can be written in terms of the catalan numbers secondly we make an incursion into its dynamical behavior in fact we show that the rational maps related to these methods can be written in terms of the entries of the catalan triangle next we analyze its general convergence by including some computer plots showing the intricate structure of the universal julia sets associated with the methods

restricted robust uniform matroid maximization under interval uncertainty for the problem of selecting p items with interval objective function coefficients so as to maximize total profit we introduce the r restricted robust deviation criterion and seek solutions that minimize the r restricted robust deviation this new criterion increases the modeling power of the robust deviation minmax regret criterion by reducing the level of conservatism of the robust solution it is shown that r restricted robust deviation solutions can be computed efficiently results of experiments and comparisons with absolute robustness robust deviation and restricted absolute robustness criteria are reported

robust regret for uncertain linear programs with application to co production models abstract this paper considers the regret optimization criterion for linear programming problems with uncertainty in the data inputs the problems of study are more challenging than those considered in previous works that address only interval objective coefficients and furthermore the uncertainties are allowed to arise from arbitrarily specified polyhedral sets to this end a safe approximation of the regret function is developed so that the maximum regret can be evaluated reasonably efficiently by leveraging on previous established results and solution algorithms the proposed approach is then applied to a two stage co production newsvendor problem that contains uncertainties in both supplies and demands computational experiments demonstrate that the proposed regret approximation is reasonably accurate and the corresponding regret optimization model performs competitively well against other optimization approaches such as worst case and sample average optimization across different performance measures

an improved algorithm for selecting p items with uncertain returns according to the minmax regret criterion we consider the problem of selecting a subset of p investments of maximum total return out of a set of n available investments with uncertain returns where uncertainty is represented by interval estimates for the returns and the minmax regret objective is used we develop an algorithm that solves this problem in o min p n p n time this improves the previously known complexity o min p n p 2n

dynamics and local convergence of a family of derivative free iterative processes abstract in this paper we establish the construction of a family of free derivative of point to point iterative processes with quadratic convergence from two known data in each previous iteration besides we study the accessibility of this family by means of the basins of attraction and the convergence balls we provide a local convergence analysis for the family of iterative processes free of derivatives when the operator f is not necessarily frechet differentiable the sufficient convergence conditions are weaker and more flexible than in earlier studies an application is provided involving mixed hammerstein nonlinear integral equation with application in real world problems finally we show also a dynamical study and the convergence regions of some members of the family

basin attractors for various methods for multiple roots abstract there are several methods for approximating the multiple zeros of a nonlinear function when the multiplicity is known the methods are classified by the order informational efficiency and efficiency index here we consider other criteria namely the basin of attraction of the method and its dependence on the order we discuss all known methods of orders two to four and present the basin of attraction for several examples

a stable family with high order of convergence for solving nonlinear equations recently li et al 2014 have published a new family of iterative methods without memory with order of convergence five or six which are not optimal in the sense of kung and traub s conjecture therefore we attempt to modify this suggested family in such a way that it becomes optimal to this end we consider the same two first steps of the mentioned family and furthermore we introduce a better approximation for f z in the third step based on interpolation idea as opposed to the taylor s series used in the work of li et al theoretical dynamical and numerical aspects of the new family are described and investigated in details

compromise solutions for robust combinatorial optimization with variable sized uncertainty in classic robust optimization it is assumed that a set of possible parameter realizations the uncertainty set is modeled in a previous step and part of the input as recent work has shown finding the most suitable uncertainty set is in itself already a difficult task we consider robust problems where the uncertainty set is not completely defined only the shape is known but not its size such a setting is known as variable sized uncertainty in this work we present an approach how to find a single robust solution that performs well on average over all possible uncertainty set sizes we demonstrate that this approach can be solved efficiently for min max robust optimization but is more involved in the case of min max regret where positive and negative complexity results for the selection problem the minimum spanning tree problem and the shortest path problem are provided we introduce an iterative solution procedure and evaluate its performance in an experimental comparison

on the comparison of inventory replenishment policies with time varying stochastic demand for the paper industry the aim of this paper is the development of a mathematical model to compute the optimal inventory mix to face stochastic demand at minimum cost in a two level supply chain the paper addresses a multi product dynamic lot sizing problem under stochastic demand subject to capacity and service level constraints this model is executed to compare a make to order mto strategy to a vendor managed inventory vmi partnership between the supplier and their customers both strategies provide the demand order to be produced a schedule of production orders is determined over the planning horizon in order to minimize the inventory holding costs of the supply chain taking into consideration that the supplier is also responsible of initiating the replenishment orders and deliveries of their customers according to the vmi partnership the simulation model is illustrated empirically using a real case study a paper manufacturing company that pursues to improve customer service level and supply chain inventory costs through a proper production planning of their paper machines and a suitable vmi order replenishment schedule

a sixth order family of three point modified newton like multiple root finders and the dynamics behind their extraneous fixed points a class of three point sixth order multiple root finders and the dynamics behind their extraneous fixed points are investigated by extending modified newton like methods with the introduction of the multivariate weight functions in the intermediate steps the multivariate weight functions dependent on function to function ratios play a key role in constructing higher order iterative methods extensive investigation of extraneous fixed points of the proposed iterative methods is carried out for the study of the dynamics associated with corresponding basins of attraction numerical experiments applied to a number of test equations strongly support the underlying theory pursued in this paper relevant dynamics of the proposed methods is well presented with a variety of illustrative basins of attraction applied to various test polynomials

stability analysis of a parametric family of seventh order iterative methods for solving nonlinear systems abstract in this paper a parametric family of seventh order of iterative method to solve systems of nonlinear equations is presented its local convergence is studied and quadratic polynomials are used to investigate its dynamical behavior the study of the fixed and critical points of the rational function associated to this class allows us to obtain regions of the complex plane where the method is stable by depicting parameter planes and dynamical planes we obtain complementary information of the analytical results these results are used to solve some nonlinear problems

adaptive filters based on order statistics an adaptive filter structure which is based on linear combinations of order statistics is proposed an efficient method to update the filter coefficients is presented which is based on the minimal mean square error criterion and which is similar to the widrow algorithm for the linear adaptive filters another method for coefficient update is presented which is similar to the recursive least squares rls algorithm and which has faster convergence properties the proposed filter can adapt well to a variety of noise probability distributions including impulsive noise it also performs well in the case of nonstationary signals and therefore it is suitable for image processing applications

on the convergence of a higher order family of methods and its dynamics in this paper we present the study of the local convergence of a higher order family of methods moreover the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied some anomalies are found in this family by means of studying the associated rational function parameter spaces are shown and the study of the stability of all the fixed points is presented

construction of stable and globally convergent schemes for the matrix sign function abstract in this paper we propose a dynamics based approach to develop efficient matrix iterations for computing the matrix sign function considering an iterative method with unknown weight functions our approach constructs a double sequence of weight functions so that for a quadratic polynomial with distinct roots the julia set of the method associated with each term of the sequence is the perpendicular bisector of the line segment from one root to another based on the sequence generated methods we introduce a double sequence of matrix iterations for computing the matrix sign function and perform precise convergence and stability analyses of these iterations we show that our matrix iterations contain the well known globally convergent principal pade family and its reciprocal as special cases based on the result of the numerical experiments we found several of our methods that do not belong to the principal pade family and its reciprocal which are more efficient in computing the matrix sign function

highly efficient family of iterative methods for solving nonlinear models abstract in this study we present a new highly efficient sixth order family of iterative methods for solving nonlinear equations along with convergence properties further we extend this family to the multidimensional case preserving the same order of convergence in order to illustrate the applicability of our methods we choose some real world problems namely kinematic syntheses boundary value bratu s 2d fisher s and hammerstein integral problems in the case of nonlinear systems see farhane et al 2017 1 kaur and arora 2017 2 for more applications in addition numerical comparisons are made to show the performance of our iterative techniques with the existing ones moreover we find that our techniques perform better as compared to the existing ones of same order in terms of residual error and the errors between two consecutive iterations finally the stability analysis of our methods also support this to great extent

chaotic dynamics of a third order newton type method the dynamics of a classical third order newton type iterative method is studied when it is applied to degrees two and three polynomials the method is free of second derivatives which is the main limitation of the classical third order iterative schemes for systems moreover each iteration consists only in two steps of newton s method having the same derivative with these two properties the scheme becomes a real alternative to the classical newton method affine conjugacy class of the method when is applied to a differentiable function is given chaotic dynamics have been investigated in several examples applying the root finding method to a family of degree three polynomials we have find a bifurcation diagram as those that appear in the bifurcation of the logistic map in the interval

a class of order statistic lms algorithms conventional gradient based adaptive filters as typified by the well known lms algorithm use an instantaneous estimate of the error surface gradient to update the filter coefficients such a strategy leaves the algorithm extremely vulnerable to impulsive interference a class of adaptive algorithms employing order statistic filtering of the sampled gradient estimates is presented these algorithms dubbed order statistic least mean squares oslms are designed to facilitate adaptive filter performance close to the least squares optimum across a wide range of input environments from gaussian to highly impulsive three specific oslms filters are defined the median lms the average lms and the trimmed mean lms the properties of these algorithms are investigated and the potential for improvement demonstrated finally a general adaptive oslms scheme in which the nature of the order statistic operator is also adapted in response to the statistics of the input signal is presented it is shown that this can facilitate performance gains over a wide range of input data types

an analysis of a khattri s 4th order family of methods in this paper we analyze an optimal fourth order family of methods suggested by khattri and babajee 2013 we analyze the family using the information on the extraneous fixed points two measures of closeness to the imaginary axis of the set of extraneous points are considered and applied to the members of the family to find its best performer the results are compared to three best members of king s family of methods

graphical representations for the homogeneous bivariate newton s method in this paper we propose a new and effective strategy to apply newton s method to the problem of finding the intersections of two real algebraic curves that is the roots of a pair of real bivariate polynomials the use of adequate homogeneous coordinates and the extension of the domain where the iteration function is defined allow us to avoid some numerical difficulties such as divisions by values close to zero in fact we consider an iteration map defined on a real augmented projective plane so we obtain a global description of the basins of attraction of the fixed points associated to the intersection of the curves as an application of our techniques we can plot the basins of attraction of the roots in the following geometric models hemisphere hemicube mobius band square and disk we can also give local graphical representations on any rectangle of the plane

choosing robust solutions in discrete optimization problems with fuzzy costs in this paper a wide class of discrete optimization problems which can be formulated as a 0 1 linear programming problem is discussed it is assumed that the objective function costs are not precisely known this uncertainty is modeled by specifying a finite set of fuzzy scenarios under every fuzzy scenario the costs are given as fuzzy intervals possibility theory is then applied to chose a solution in such a problem and mixed integer linear programming models are proposed to compute this solution

basin attractors for various methods abstract there are many methods for the solution of a nonlinear algebraic equation the methods are classified by the order informational efficiency and efficiency index here we consider other criteria namely the basin of attraction of the method and its dependence on the order we discuss several methods of various orders and present the basin of attraction for several examples it can be seen that not all higher order methods were created equal newton s halley s murakami s and neta johnson s methods are consistently better than the others in two of the examples neta s 16th order scheme was also as good

different anomalies in a jarratt family of iterative root finding methods abstract in this paper the behavior of a jarratt family of iterative methods applied to quadratic polynomials is studied some anomalies are found in this family be means of studying the dynamical behavior of this fourth order family of methods parameter spaces are shown and the study of the stability of all the fixed points is presented dynamical planes for members with good and bad dynamical behavior are also provided

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

complex analytic dynamics on the riemann sphere dichotomie dynamique de fatou et julia points periodiques consequences du theoreme de montel l ensemble de julia est la fermeture de l ensemble des points periodiques repulseurs resultats classiques sur l ensemble de fatou classification de sullivan de l ensemble de fatou une condition pour le developpement sur l ensemble de julia la dynamique des polynomes l ensemble de mandelbrot et le travail de douady et hubbard le theoreme d application de riemann mesurable et la dynamique analytique

on recoverable and two stage robust selection problems with budgeted uncertainty in this paper the problem of selecting p out of n available items is discussed such that their total cost is minimized we assume that costs are not known exactly but stem from a set of possible outcomes robust recoverable and two stage models of this selection problem are analyzed in the two stage problem up to p items is chosen in the first stage and the solution is completed once the scenario becomes revealed in the second stage in the recoverable problem a set of p items is selected in the first stage and can be modified by exchanging up to k items in the second stage after a scenario reveals we assume that uncertain costs are modeled through bounded uncertainty sets i e the interval uncertainty sets with an additional linear budget constraint in their discrete and continuous variants polynomial algorithms for recoverable and two stage selection problems with continuous bounded uncertainty and compact mixed integer formulations in the case of discrete bounded uncertainty are constructed

constructing a family of optimal eighth order modified newton type multiple zero finders along with the dynamics behind their purely imaginary extraneous fixed points abstract an optimal family of eighth order multiple zero finders and the dynamics behind their basins of attraction are proposed by considering modified newton type methods with multivariate weight functions extensive investigation of purely imaginary extraneous fixed points of the proposed iterative methods is carried out for the study of the dynamics associated with corresponding basins of attraction numerical experiments strongly support the underlying theory pursued in this paper an exploration of the relevant dynamics of the proposed methods is presented along with illustrative basins of attraction for various polynomials

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