branch and bound search for experimental designs based on d optimality and other criteria this article presents a branch and bound algorithm that constructs a catalog of all d optimal n point designs for specified design region linear model and number of observations n while the primary design criterion is d optimality the algorithm may also be used to find designs performing well by other secondary criteria if a small sacrifice in ellkiency as measured by d optimahty is accepted finally some designs are supplied for a quadratic response surface model

optimum continuous block designs the incidence matrix of a block design is replaced by a normalized version n in which the entries are non negative numbers whose sum is unity the so called c matrix the information matrix for estimation of treatment contrasts is similarly replaced by the normalized analogue c n we study the set of ordered eigenvalues of all c n and give a complete specification for three treatments rows for any number of treatments we characterize the eigenvalues of an important subclass of designs for which the non zero entries in any given block are equal it is suggested that the natural ordering between designs is upper weak majorization of the eigenvalues using this we show how to improve a given n matrix and this leads to several optimality statements

an optimum design for estimating the first derivative an optimum design of experiment for a class of estimates of the first derivative at 0 used in stochastic approximation and density estimation is shown to be equivalent to the problem of finding a point of minimum of the function gamma defined by gamma x det lbrack 1 x 3 ldots x 2m 1 rbrack det lbrack x x 3 ldots x 2m 1 rbrack on the set of all m dimensional vectors with components satisfying 0 x 1 x 2 cdots 1 m 1 x m and pi x i 1 in the determinants 1 is the column vector with all components 1 and x i has components of x raised to the i th power the minimum of gamma is shown to be m and the point at which the minimum is attained is characterized by chebyshev polynomials of the second kind

extraneous fixed points basin boundaries and chaotic dynamics for schro der and ko nig rational iteration functions the schroder and konig iteration schemes to find the zeros of a polynomial functiong z represent generalizations of newton s method in both schemes iteration functionsf m z are constructed so that sequencesz n 1 f m z n converge locally to a rootz ofg z aso z n z m it is well known that attractive cycles other than the zerosz may exist for newton s method m 2 asm increases the iteration functions add extraneous fixed points and cycles whether attractive or repulsive they affect the julia set basin boundaries the konig functionsk m z appear to minimize such perturbations in the case of two roots e g g z z 2 1 cayley s classical result for the basins of attraction of newton s method is extended for allk m z the existence of chaotic z n sequences is also demonstrated for these iteration methods

new third order nonlinear solvers for multiple roots abstract two third order methods for finding multiple zeros of nonlinear functions are developed one method is based on chebyshev s third order scheme for simple roots and the other is a family based on a variant of chebyshev s which does not require the second derivative two other more efficient methods of lower order are also given these last two methods are variants of chebyshev s and osada s schemes the informational efficiency of the methods is discussed all these methods require the knowledge of the multiplicity

a third order modification of newton s method for multiple roots in this paper we present a new third order modification of newton s method for multiple roots which is based on existing third order multiple root finding methods numerical examples show that the new method is competitive to other methods for multiple roots

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

on the convergence of high order gargantini farmer loizou type iterative methods for simultaneous approximation of polynomial zeros abstract in 1984 kyurkchiev et al constructed an infinite sequence of iterative methods for simultaneous approximation of polynomial zeros with known multiplicity the first member of this sequence of iterative methods is the famous root finding method derived independently by farmer and loizou 1977 and gargantini 1978 for every given positive integer n the nth method of this family has the order of convergence 2 n 1 in this paper we prove two new local convergence results for this family of iterative methods the first one improves the result of kyurkchiev et al 1984 we end the paper with a comparison of the computational efficiency the convergence behavior and the computational order convergence of different methods of the family

new families of nonlinear third order solvers for finding multiple roots in this paper we present two new families of iterative methods for multiple roots of nonlinear equations one of the families require one function and two derivative evaluation per step and the other family requires two function and one derivative evaluation it is shown that both are third order convergent for multiple roots numerical examples suggest that each family member can be competitive to other third order methods and newton s method for multiple roots in fact the second family is even better than the first

accelerating generators of iterative methods for finding multiple roots of nonlinear equations two accelerating generators that produce iterative root finding methods of arbitrary order of convergence are presented primary attention is paid to algorithms for finding multiple roots of nonlinear functions and in particular of algebraic polynomials first two classes of algorithms for solving nonlinear equations are studied those with a known order of multiplicity and others with no information on multiplicity we also demonstrate the acceleration of iterative methods for the simultaneous approximations of multiple roots of algebraic polynomials a discussion about the computational efficiency of the root solvers considered and three numerical examples are given

construction of zero finding methods by weierstrass functions abstract in this paper we present a simple and elegant procedure for the construction of iterative methods for the simultaneous determination of simple or multiple zeros of an algebraic polynomial this procedure is based on the application of a special type of functions called weierstrass functions to suitable zero finding methods for a single zero for demonstration using this approach we derive many known iterative methods in a simpler way compared with original derivations as well as some new methods aside from the presented methodology in developing zero finding methods the paper offers a short review of simultaneous methods including some historical notes

enclosing all zeros of an analytic function a rigorous approach we present a method to find all zeros of an analytic function in a rectangular domain the approach is based on finding guaranteed enclosures rather than approximations of the zeros well isolated simple zeros are determined fast and with high accuracy clusters of zeros can in many cases be distinguished from multiple zeros by applying the argument principle to sufficiently high order derivatives of the function we illustrate the proposed method through five examples of varying levels of complexity

on rediscovered methods for solving equations abstract in the recent papers of gerlach siam rev 36 1994 272 276 and ford and pennline siam rev 38 1996 658 659 a class of iterative methods for solving a single equation f x 0 with arbitrary rate of convergence has been presented in this paper we show that this class is equivalent to five other classes of iterative methods derived earlier in various ways and expressed in different forms the proofs of equivalence of all considered iteration formulas are given

on schroder s families of root finding methods schroder s methods of the first and second kind for solving a nonlinear equation f x 0 originally derived in 1870 are of great importance in the theory and practice of iteration processes they were rediscovered several times and expressed in different forms during the last 130 years it was proved in the paper of petkovic and herceg 1999 7 that even seven families of iteration methods for solving nonlinear equations are mutually equivalent in this paper we show that these families are also equivalent to another four families of iteration methods and find that all of them have the origin in schroder s generalized method of the second kind presented in 1870 in the continuation we consider smale s open problem from 1994 about possible link between schroder s methods of the first and second kind and state the link in a simple way

the usefulness of optimum experimental designs optimum experimental designs were originally developed by kiefer mainly for response surface models this survey of recent developments emphasizes potential or actual usefulness for linear models the construction of exact designs particularly over irregular design regions is stressed as is the blocking of response surface designs other important areas include systematic designs that are robust against trend and designs for mixtures with irregular design regions several industrial examples are mentioned both d and c optimum designs are found for a non linear model of the economic response of cereal production to fertilizer level the c optimum design being for the conditions of maximum economic return locally optimum and bayesian designs are both described similar results for generalized linear models lead to designs for the ld 95 in a logistic model in which male and female subjects respond differently designs with structure in the variance suggest alternatives to the potentially wasteful product designs of taguchi designs for sequential clinical trials to include random balance are presented the last section outlines some applications including life testing and models in which time is a factor

jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing abstract a new lattice hydrodynamic model is proposed by considering the interruption probability effect on traffic flow with passing and analyzed both theoretically and numerically from linear and non linear stability analysis the effect of interruption probability on the phase diagram is investigated and the condition of existence for kink antikink soliton solution of mkdv equation is derived the stable region is enhanced with interruption probability and the jamming transition occurs from uniform flow to kink flow through chaotic flow for higher and intermediate values of non interruption effect of passing it is also observed that there exists conventional jamming transition between uniform flow and kink flow for lower values of non interruption effect of passing numerical simulations are carried out and found in accordance with the theoretical findings which confirm that the effect of interruption probability plays an important role in stabilizing traffic flow when passing is allowed

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality