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

on a higher order secant method in this paper we carry out a modification of the classical secant method our goal is to accelerate the convergence until order two but without using any derivative two convergence theorems are presented finally some numerical experiments are analyzed

autocovariance based plant model mismatch estimation for linear model predictive control abstract in this paper we present autocovariance based estimation as a novel methodology for determining plant model mismatch for multiple input multiple output systems operating under model predictive control considering discrete time linear time invariant systems under reasonable assumptions we derive explicit expressions of the autocovariances of the system inputs and outputs as functions of the plant model mismatch we then formulate the mismatch estimation problem as a global optimization aimed at minimizing the discrepancy between the theoretical autocovariance estimates and the corresponding values computed from historical closed loop operating data practical considerations related to implementing these ideas are discussed and the results are illustrated with a chemical process case study

a family of fourth order steffensen type methods with the applications on solving nonlinear odes abstract in this paper a family of fourth order steffensen type two step methods is constructed to make progress in including ren wu bi s methods h ren q wu w bi a class of two step steffensen type methods with fourth order convergence appl math comput 209 2009 206 210 and liu zheng zhao s method z liu q zheng p zhao a variant of steffensens method of fourth order convergence and its applications appl math comput 216 2010 1978 1983 as its special cases its error equation and asymptotic convergence constant are deduced the family provides the opportunity to obtain derivative free iterative methods varying in different rates and ranges of convergence in the numerical examples the family is not only compared with the related methods for solving nonlinear equations but also applied in the solution of bvps of nonlinear odes by the finite difference method and the multiple shooting method

on chebyshev halley methods with sixth order convergence for solving non linear equations abstract in this paper we present a family of new variants of chebyshev halley methods the new methods have sixth order convergence although they only add one evaluation of the function at the point iterated by chebyshev halley methods the numerical results presented show that the new methods work better not only in order but in efficiency

a new technique to obtain derivative free optimal iterative methods for solving nonlinear equations abstract a new technique to obtain derivative free methods with optimal order of convergence in the sense of the kung traub conjecture for solving nonlinear smooth equations is described the procedure uses steffensen like methods and pade approximants some numerical examples are provided to show the good performance of the new methods

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

attracting cycles for the relaxed newton s method we study the relaxed newton s method applied to polynomials in particular we give a technique such that for any n 2 we may construct a polynomial so that when the method is applied to a polynomial the resulting rational function has an attracting cycle of period n we show that when we use the method to extract radicals the set consisting of the points at which the method fails to converge to the roots of the polynomial p z z m c this set includes the julia set has zero lebesgue measure consequently iterate sequences under the relaxed newton s method converge to the roots of the preceding polynomial with probability one

improving the domain of starting points for secant like methods abstract from the simplified secant method and a family of secant like methods we construct a family of predictor corrector iterative methods for solving a nonlinear equation in banach spaces

a composite third order newton steffensen method for solving nonlinear equations in this paper we suggest a third order method formed by the composition of newton and steffensen methods for finding simple and real roots of a nonlinear equation in single variable per iteration the formula requires two evaluations of the function and single evaluation of the derivative experiments show that the method is suitable in the cases where newton and steffensen methods fail

steffensen type methods for solving non linear equations families of steffensen type methods for solving non linear equations are obtained one family consists of second order method involving no derivatives while other consists of third order methods involving only the first derivatives also a derivative free third order method is provided the theory is supported by an example comparing the existing methods with the present one

modified chebyshev halley methods with sixth order convergence abstract in this paper we present a family of modified chebyshev halley methods the new methods add one evaluation of the function at the point iterated by chebyshev halley methods analysis of convergence shows that these methods have sixth order convergence numerical results show that the new methods can be of practical interest

a linear framework on the distributed model predictive control of positive systems abstract this paper investigates the distributed model predictive control dmpc for positive systems with interval and polytopic uncertainties respectively different from the traditional quadratic dmpc a new linear dmpc framework is established for positive systems first a linear cooperative cost function performance index function is introduced for the dmpc of positive systems accordingly some linear constraint conditions are imposed on the systems then a linear co positive lyapunov function is constructed using the linear lyapunov function the dmpc controllers are designed for interval positive systems and polytopic positive systems respectively the controller of each subsystem contains not only the state information of the subsystem but also the state information of other correlated subsystems linear programming based optimization algorithm is addressed to compute the controller parameters to guarantee the feasibility and stability of the systems a cone invariant set is proposed finally two case studies are provided to illustrate the effectiveness of the theoretical findings

l1 induced norm and controller synthesis of positive systems in this paper the problem of 1 1 induced controller design for discrete time positive systems is investigated with the use of linear lyapunov function an analytical method to compute the exact value of 1 1 induced norm is first presented then a novel characterization for stability and 1 1 induced performance is proposed based on the characterization a necessary and sufficient condition for the existence of desired controllers is derived and an iterative convex optimization approach is developed to solve the condition in addition the synthesis of the state feedback controller for single input multiple output simo positive systems is investigated for this special case an analytic solution is established to show how the optimal 1 1 induced controller can be designed and some links to the spectral radius of the closed loop systems are provided finally the theoretical results are illustrated through a numerical example

hadamard type operators on spaces of real analytic functions in several variables abstract we consider multipliers on the space of real analytic functions of several variables a r d open i e linear continuous operators for which all monomials are eigenvectors if zero belongs to these operators are just multipliers on the sequences of taylor coefficients at zero in particular euler differential operators of arbitrary order are multipliers we represent all multipliers via a kind of multiplicative convolution with analytic functionals and characterize the corresponding sequences of eigenvalues as moments of suitable analytic functionals moreover we represent multipliers via suitable holomorphic functions with laurent coefficients equal to the eigenvalues of the operator we identify in some standard cases what topology should be put on the suitable space of analytic functionals in order that the above mentioned isomorphism becomes a topological one when the space of multipliers inherits the topology of uniform convergence on bounded sets from the space of all endomorphisms on a we also characterize in the same cases when the discovered topology coincides with the classical topology of bounded convergence on the space of analytic functionals we provide several examples of multipliers and show surjectivity results for multipliers on a if r d

secant like methods for solving nonlinear integral equations of the hammerstein type we consider a one parametric family of secant type iterations for solving nonlinear equations in banach spaces we establish a semilocal convergence result for these iterations by means of a technique based on a new system of recurrence relations this result is then applied to obtain existence and uniqueness results for nonlinear integral equations of the hammerstein type we also present a numerical example where the solution of a particular hammerstein integral equation is approximated by different secant type methods

families of rational maps and iterative root finding algorithms in this paper we develop a rigidity theorem for algebraic families of rational maps and apply it to the study of iterative root finding algorithms we answer a question of smale s by showing there is no generally convergent algorithm for finding the roots of a polynomial of degree 4 or more we settle the case of degree 3 by exhibiting a generally convergent algorithm for cubics and we give a classification of all such algorithms in the context of conformal dynamics our main result is the following a stable algebraic family of rational maps is either trivial all its members are conjugate by mobius transformations or affine its members are obtained as quotients of iterated addition on a family of complex tori our classification of generally convergent algorithms follows easily from this result as another consequence of rigidity we observe that the eigenvalues of a nonaffine rational map at its periodic points determine the map up to finitely many choices this implies that bounded analytic functions nearly separate points on the moduli space of a rational map

a modified chebyshev s iterative method with at least sixth order of convergence this paper is devoted to the construction and analysis of a high order variant of the classical chebyshev method the method has order of convergence at least six for simple roots the extension to system of equations and its semilocal convergence for nonlinear equations are presented finally an application to well known algebraic riccati equation is considered

optimal steffensen type methods with eighth order of convergence this paper proposes two classes of three step without memory iterations based on the well known second order method of steffensen per computing step the methods from the developed classes reach the order of convergence eight using only four evaluations while they are totally free from derivative evaluation hence they agree with the optimality conjecture of kung traub for providing multi point iterations without memory as things develop numerical examples are employed to support the underlying theory developed for the contributed classes of optimal steffensen type eighth order methods

on the semilocal convergence of efficient chebyshev secant type methods we introduce a three step chebyshev secant type method cstm with high efficiency index for solving nonlinear equations in a banach space setting we provide a semilocal convergence analysis for cstm using recurrence relations numerical examples validating our theoretical results are also provided in this study

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

a class of steffensen type methods with optimal order of convergence abstract in this paper a family of steffensen type methods of fourth order convergence for solving nonlinear smooth equations is suggested in the proposed methods a linear combination of divided differences is used to get a better approximation to the derivative of the given function each derivative free member of the family requires only three evaluations of the given function per iteration therefore this class of methods has efficiency index equal to 1 587 kung and traub conjectured that the order of convergence of any multipoint method without memory cannot exceed the bound 2 d 1 where d is the number of functional evaluations per step the new class of methods agrees with this conjecture for the case d 3 numerical examples are made to show the performance of the presented methods on smooth and nonsmooth equations and to compare with other ones

cooperative distributed model predictive control abstract in this paper we propose a cooperative distributed linear model predictive control strategy applicable to any finite number of subsystems satisfying a stabilizability condition the control strategy has the following features hard input constraints are satisfied terminating the iteration of the distributed controllers prior to convergence retains closed loop stability in the limit of iterating to convergence the control feedback is plantwide pareto optimal and equivalent to the centralized control solution no coordination layer is employed we provide guidance in how to partition the subsystems within the plant we first establish exponential stability of suboptimal model predictive control and show that the proposed cooperative control strategy is in this class we also establish that under perturbation from a stable state estimator the origin remains exponentially stable for plants with sparsely coupled input constraints we provide an extension in which the decision variable space of each suboptimization is augmented to achieve pareto optimality we conclude with a simple example showing the performance advantage of cooperative control compared to noncooperative and decentralized control strategies

variants of steffensen secant method and applications abstract in this paper a parametric variant of steffensen secant method and three fast variants of steffensen secant method for solving nonlinear equations are suggested they achieve cubic convergence or super cubic convergence for finding simple roots by only using three evaluations of the function per step their error equations and asymptotic convergence constants are deduced modified steffensen s method and modified parametric variant of steffensen secant method for finding multiple roots are also discussed in the numerical examples the suggested methods are supported by the solution of nonlinear equations and systems of nonlinear equations and the application in the multiple shooting method

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

bilateral approximations for some aitken steffensen hermite type methods of order three abstract we study the local convergence of some aitken steffensen hermite type methods of order three we obtain that under some reasonable conditions on the monotony and convexity of the nonlinear function the iterations offer bilateral approximations for the solution which can be efficiently used as a posteriori estimations

derivative free two point methods with and without memory for solving nonlinear equations abstract two families of derivative free two point iterative methods for solving nonlinear equations are constructed these methods use a suitable parametric function and an arbitrary real parameter it is proved that the first family has the convergence order four requiring only three function evaluations per iteration in this way it is demonstrated that the proposed family without memory supports the kung traub hypothesis 1974 on the upper bound 2n of the order of multipoint methods based on n 1 function evaluations further acceleration of the convergence rate is attained by varying a free parameter from step to step using information available from the previous step this approach leads to a family of two step self accelerating methods with memory whose order of convergence is at least 2 5 4 236 and even 2 6 4 449 in special cases the increase of convergence order is attained without any additional calculations so that the family of methods with memory possesses a very high computational efficiency numerical examples are included to demonstrate exceptional convergence speed of the proposed methods using only few function evaluations

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

positivity for non metzler systems and its applications to stability of time varying delay systems abstract in 1950 wazewski obtained the following necessary and sufficient condition for positivity of linear systems of ordinary differential equations the matrix of coefficients is metzler i e off diagonal elements in the matrix of coefficients are nonnegative no results on the positivity of solutions to delay systems in the case where the matrix is non metzler were expected to be obtained it was demonstrated that for delay systems the wazewski condition is not a necessary one we prove results on positivity of solutions for non metzler systems of delay differential equations new explicit tests for exponential stability are obtained as applications of results on positivity for non metzler systems examples demonstrate possible applications of our theorems to stabilization for instance in view of our results the implicit requirement on dominance of the main diagonal can be skipped our approach is based on nonoscillation of solutions and positivity of the cauchy functions of scalar diagonal delay differential equations

basins of attraction for several methods to find simple roots of nonlinear equations there are many methods for solving 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 third and fourth order methods to find simple zeros the relationship between the basins of attraction and the corresponding conjugacy maps will be discussed in numerical experiments the effect of the extraneous roots on the basins is also discussed

cost to travel functions a new perspective on optimal and model predictive control abstract this paper concerns a class of functions named cost to travel functions which find applications in model based control for a given potentially nonlinear control system the cost to travel function associates with any given start and end point in the state space and any given travel duration the minimum economic cost of the associated point to point motion cost to travel functions are a generalization of cost to go functions which are often used in the context of dynamic programming as well as model predictive control we discuss the properties of cost to travel functions their relations to existing concepts in control such as dissipativity but also a variety of control theoretic applications of this function class in particular we discuss how cost to travel functions can be used to analyze the properties of economic model predictive control with return constraints

convergence of the variants of the chebyshev halley iteration family under the holder condition of the first derivative the present paper is concerned with the convergence problem of the variants of the chebyshev halley iteration family with parameters for solving nonlinear operator equations in banach spaces under the assumption that the first derivative of the operator satisfies the holder condition of order p a convergence criterion of order 1 p for the iteration family is established an application to a nonlinear hammerstein integral equation of the second kind is provided

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

convergence analysis of some algorithms for solving nonsmooth equations this paper presents convergence analysis of some algorithms for solving systems of nonlinear equations defined by locally lipschitzian functions for the directional derivative based and the generalized jacobian based newton methods both the iterates and the corresponding function values are locally superlinearly convergent globally a limiting point of the iterate sequence generated by the damped directional derivative based newton method is a zero of the system if and only if the iterate sequence converges to this point and the stepsize eventually becomes one provided that the system is strongly bd regular and semismooth at this point in this case the convergence is superlinear a general attraction theorem is presented which can be applied to two algorithms proposed by han pang and rangaraj a hybrid method which is both globally convergent in the sense of finding a stationary point of the norm function of the system and locally quadratically convergent is also presented

a two step steffensen s method under modified convergence conditions a simplification of a third order iterative method is proposed the main advantage of this method is that it does not need to evaluate neither any frechet derivative nor any bilinear operator a semilocal convergence theorem in banach spaces under modified kantorovich conditions is analyzed a local convergence analysis is also performed finally some numerical results are presented

increasing the applicability of steffensen s method abstract we present an original alternative to the majorant principle of kantorovich to study the semilocal convergence of steffensen s method when it is applied to solve nonlinear systems which are differentiable this alternative allows choosing starting points from which the convergence of steffensen s method is guaranteed but it is not from the majorant principle moreover this study extends the applicability of steffensen s method to the solution of nonlinear systems which are nondifferentiable and improves a previous result given by the authors

on the dynamics of the euler iterative function abstract the dynamics of euler s third order iterative method which is used to find roots of non linear equations applied to complex polynomials of degrees three and four is studied the conjugacy classes of this method are found explicitly

equilibria stability and reachability of leslie systems with nonnegative inputs leslie systems a particular class of positive systems used in population dynamics and control are defined and analyzed a simple property relating sign and stability of their equilibria and some geometric characteristics of their reachability set in cases of bounded and unbounded inputs are proved all the properties do not hold in general in other classes of positive systems it is shown that leslie systems have strictly positive equilibria if and only if they are asymptotically stable their reachability set in the case of unbounded inputs is the positive cone generated by the reachability vectors while in the case of bounded inputs it is a polyhedron whose vertices can be easily computed all of these properties follow from the nonpositiveness of the coefficients of the characteristic polynomial of the system

steffensen type methods for solving nonlinear equations in the present paper by approximating the derivatives in the well known fourth order ostrowski s method and in a sixth order improved ostrowski s method by central difference quotients we obtain new modifications of these methods free from derivatives we prove the important fact that the methods obtained preserve their convergence orders 4 and 6 respectively without calculating any derivatives finally numerical tests confirm the theoretical results and allow us to compare these variants with the corresponding methods that make use of derivatives and with the classical newton s method

interpolation of holomorphic functions and surjectivity of taylor coefficient multipliers abstract we prove criteria for global analytic solvability for some euler type partial differential equations a class of linear partial differential equations with variable polynomial coefficients this is based on a very general mellin type theory developed in the present paper which is valid for analytic functionals in particular distributions of compact support substituting the classical mellin transform as a consequence we get a characterization of moment sequences of analytic functionals by interpolation of holomorphic functions satisfying some restrictive growth conditions this allows to study the so called hadamard type multipliers on real analytic functions of several variables i e operators for which monomials are eigenvectors we characterize multiplier sequences i e sequences of eigenvalues of multipliers by interpolation and describe the image of some multipliers especially the image of the principal examples of hadamard multipliers euler type partial differential operators we also get some results showing that the image remains unchanged after some perturbation of the original hadamard type operator

modified chebyshev halley methods free from second derivative abstract in this paper we present some variants of chebyshev halley methods free from second derivative it is shown that the order of convergence of the proposed methods is three at least there are two functions and one first derivative evaluations per iteration several numerical examples are given to demonstrate the performance of the presented methods by comparing with some other methods

a variant of steffensen s method of fourth order convergence and its applications in this paper a variant of steffensen s method of fourth order convergence for solving nonlinear equations is suggested its error equation and asymptotic convergence constant are proven theoretically and demonstrated numerically the derivative free method only uses three evaluations of the function per iteration to achieve fourth order convergence its applications on systems of nonlinear equations and boundary value problems of nonlinear odes are showed as well in the numerical examples

a variant of steffensen king s type family with accelerated sixth order convergence and high efficiency index first it is attempted to derive an optimal derivative free steffensen king s type family without memory for computing a simple zero of a nonlinear function with efficiency index 4 1 3 1 587 next since our without memory family includes a parameter in which it is still possible to increase the convergence order without any new function evaluations therefore we extract a new method with memory so that the convergence order rises to six without any new function evaluation and therefore reaches efficiency index 6 1 3 1 817 consequently derivative free and high efficiency index would be the substantial contributions of this work as opposed to the classical steffensen s and king s methods finally we compare some of the convergence planes with different weight functions in order to show which are the best ones

on a robust aitken newton method based on the hermite polynomial we introduce an aitken newton iterative method for nonlinear equations which is obtained by using the hermite inverse interpolation polynomial of degree 2 with two nodes given by the newton method the local convergence of these iterates is shown to be 8 and the efficiency index is 8 5 1 51 which is not optimal in the sense of kung and traub however we show that under supplementary conditions sometimes easy to verify the inner and outer iterates converge monotonically to the solution this aspect allows an improved control of the iteration stopping avoiding divisions by zero and offer an alternative way to the estimation of radius of attraction balls in ensuring the convergence of the iterates numerical examples show that this method may become competitive and in certain circumstances even more robust than certain optimal methods of same convergence order

hadamard multipliers on spaces of real analytic functions abstract we consider multipliers on spaces of real analytic functions of one variable i e maps for which monomials are eigenvectors we characterize sequences of complex numbers which are sequences of eigenvalues for some multiplier we characterize invertible multipliers in particular we find which euler differential operators of infinite order have global analytic solutions on the real line we present a number of examples where our theory applies in some cases we give algorithms for solving the respective equations perturbation results for solvability are presented

on a new class parametrized newton like method for semismooth equations an extension of some smooth parametrized newton like method to the semismooth case is presented in this paper thus the problems due to the fact the b differential is singular are solved these methods are shown to be superlinear convergence some numerical experiments are given

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

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

secant methods for semismooth equations some generalizations of the secant method to semismooth equations are presented in the one dimensional case the superlinear convergence of the classical secant method for general semismooth equations is proved moreover a new quadratically convergent method is proposed that requires two function values per iteration for the n dimensional cases we discuss secant methods for two classes of composite semismooth equations most often studied semismooth equations are of such form

a class of two step steffensen type methods with fourth order convergence abstract based on steffensen s method we derive a one parameter class of fourth order methods for solving nonlinear equations in the proposed methods an interpolating polynomial is used to get a better approximation to the derivative of the given function each member of the class requires three evaluations of the given function per iteration therefore this class of methods has efficiency index which equals 1 587 kung and traub conjectured an iteration using n evaluations of f or its derivatives without memory is of convergence order at most 2 n 1 the new class of fourth order methods agrees with the conjecture of kung traub for the case n 3 numerical comparisons are made to show the performance of the presented methods

an optimal steffensen type family for solving nonlinear equations abstract in this paper a general family of steffensen type methods with optimal order of convergence for solving nonlinear equations is constructed by using newton s iteration for the direct newtonian interpolation it satisfies the conjecture proposed by kung and traub h t kung j f traub optimal order of one point and multipoint iteration j assoc comput math 21 1974 634 651 that an iterative method based on m evaluations per iteration without memory would arrive at the optimal convergence of order 2 m 1 its error equations and asymptotic convergence constants are obtained finally it is compared with the related methods for solving nonlinear equations in the numerical examples

chebyshev halley methods for analytic functions two modifications of the family of chebyshev halley methods are given the first is to improve the rate of convergence to a multiple zero of an analytic function the second is to find simultaneously all distinct zeros of a polynomial

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

a generalized steffensen s method for matrix sign function a direct generalized steffensen s method is proposed for solving the quadratic matrix equation f x x2 i 0 in this way when the matrix a is nonsingular we derive a new numerical scheme for finding matrix sign function the local and global convergence of the proposed generalization is brought up via the concept of basins of attraction we also report some numerical results of the proposed method which show its applicability

interval state estimation for a class of nonlinear systems the goal of this technical note is to design interval observers for a class of nonlinear continuous time systems the first part of this work shows that it is usually possible to design an interval observer for linear systems by means of linear time invariant changes of coordinates even if the system is not cooperative this result is extended to a class of nonlinear systems using partial exact linearisations the proposed observers guarantee to enclose the set of system states that is consistent with the model the disturbances and the measurement noise moreover it is only assumed that the measurement noise and the disturbances are bounded without any additional information such as stationarity uncorrelation or type of distribution the proposed observer is illustrated through numerical simulations

a steffensen s type method in banach spaces with applications on boundary value problems in this paper a modified steffensen s type iterative scheme for the numerical solution of a system of nonlinear equations is studied two convergence theorems are presented the numerical solution of boundary value problems by the multiple shooting method using the proposed iterative scheme is analyzed

preserving the order of convergence low complexity jacobian free iterative schemes for solving nonlinear systems abstract in this paper a new technique to construct a family of divided differences for designing derivative free iterative methods for solving nonlinear systems is proposed by using these divided differences any kind of iterative methods containing a jacobian matrix in its iterative expression can be transformed into a jacobian free scheme preserving the order of convergence this procedure is applied on different schemes showing theoretically their order and error equation numerical experiments confirm the theoretical results and show the efficiency and performance of the new jacobian free schemes

on steffensen s method on banach spaces we present a modification of steffensen s method as a predictor corrector iterative method so that we can use steffensen s method to approximate a solution of a nonlinear equation in banach spaces from the same starting points from which newton s method converges we study the semilocal convergence of the predictor corrector method by using the majorant principle we illustrate the method with an application to a discrete problem

surjectivity of euler operators on temperate distributions abstract euler operators are partial differential operators of the form p where p is a polynomial and j x j x j we show that every non trivial euler operator is surjective on the space of temperate distributions on r d this is in sharp contrast to the behaviour of such operators when acting on spaces of differentiable or analytic functions

a steffensen type method of two steps in banach spaces with applications this paper is devoted to the analysis of a steffensen type of two steps with order of convergence at least three the main advantage of this method is that it does not need to evaluate any frechet derivative or any bilinear operator the method includes extra parameters in the divided difference in order to ensure a good approximation to the first derivative in each iteration we prove using recurrence relations a semilocal convergence result in banach spaces and do a detailed study of the domain of parameters associated to this result finally some numerical results including differentiable and nondifferentiable operators are presented special attention is paid in the approximation of solutions of boundary problems using the multiple shooting method and in the approximation of a nonlinear model related with image processing

on a two step optimal steffensen type method relaxed local and semi local convergence analysis and dynamical stability abstract in this paper we study on the local and semi local convergence and dynamic of an iterative optimal two step steffensen s method we study local convergence by using lipschitz conditions and continuity of differentiable function f we also obtain semi local convergence by using majorizing sequences by this approach we can obtain the convergence of the method by minimum of auxiliary sequences and few initial conditions moreover we analyze the stability of the method via julia sets and parameter planes that is a novelty for steffensen type methods we extend this method for obtaining the sign function of a matrix numerical examples are given to confirm our theoretical results

linear copositive lyapunov functions for continuous time positive switched systems continuous time positive systems switching among p subsystems are introduced and a complete characterization for the existence of a common linear copositive lyapunov function for all the subsystems is provided when the subsystems are obtained by applying different feedback control laws to the same continuous time single input positive system the above characterization leads to a very easy checking procedure

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

brief paper a linear programming approach to routing control in networks of constrained linear positive systems we study routing control in dynamic continuous time networks in which each node is described by a linear internally positive system we derive a linear programming lp characterization of optimal constant routing policies for the infinite horizon routing problem under weighted l 1 constraints and objective for finite horizon problems with piecewise constant state constraints we provide sufficient feasibility conditions which also take the form of an lp problem we illustrate the solution for the finite horizon problem in an application example

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

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

state estimation on positive markovian jump systems with time varying delay and uncertain transition probabilities investigate the positive discrete time mjs with disturbance input time varying delay and uncertain transition probabilities together for the first time where the transition probability matrix is described by a polytope set provide a necessary and sufficient condition of stochastic stability with regard to the resulting error dynamic system present the exact computation of l gain index for the resulting stochastically stable error dynamic systems firstly and derive a necessary and sufficient condition of the l gain performance correspondingly provide a sufficient condition on the existence of a desired observer to solve the state estimation problem such that the error dynamic system is stochastically stable with a prescribed l gain performance all the proposed conditions are expressed in linear programming forms which can be solved effectively by using some existing softwares and the observer gain matrices can be directly obtained by an effective algorithm this paper is concerned with the state estimation problem based on an l observer for a class of positive discrete time markovian jump systems mjss the system under consideration consists of time varying delay and uncertain transition probabilities where the transition probability matrix is described by a polytope set necessary and sufficient conditions are presented in linear programming lp form for the resulting error dynamic system to be stochastically stable and stochastically stable with an l gain performance respectively furthermore an l observer design scheme is presented to solve the state estimation problem such that the resulting error dynamic system is stochastically stable and achieves a prescribed l gain performance all the proposed conditions are solvable in terms of lp with additional parameters finally some examples are given to demonstrate the validity of the developed technique

brief an improved approach for constrained robust model predictive control in this paper we present a new technique to address constrained robust model predictive control the main advantage of this new approach with respect to other well known techniques is the reduced conservativeness specifically the technique described in this paper can be applied to polytopic uncertain systems and is based on the use of several lyapunov functions each one corresponding to a different vertex of the uncertainty s polytope

third order family of methods in banach spaces recently parida and gupta p k parida d k gupta recurrence relations for a newton like method in banach spaces j comput appl math 206 2007 873 877 used rall s recurrence relation approach from 1961 to approximate roots of nonlinear equations by developing several methods the latest of which is free of second derivative and it is of third order in this paper we use an idea of kou and li j s kou y t li modified chebyshev s method free from second derivative for non linear equations appl math comput 187 2007 1027 1032 and modify the approach of parida and gupta obtaining yet another third order method to approximate a solution of a nonlinear equation in a banach space we give several applications to our method

a class of quasi newton generalized steffensen methods on banach spaces we consider a class of generalized steffensen iterations procedure for solving nonlinear equations on banach spaces without any derivative we establish the convergence under the kantarovich ostrowski s conditions the majorizing sequence will be a newton s type sequence thus the convergence can have better properties finally a numerical comparation with the classical methods is presented

on a steffensen s type method and its behavior for semismooth equations abstract a generalization of steffensen s method is proposed our goal is to obtain similar convergence as newton s method but without to evaluate any derivative and without to have stability problems convergence analysis and numerical results for semismooth equations are presented