wave propagation on helices and hyperhelices a fractal regression a hyperhelix of order n is defined to be a selfsimilar object consisting of a thin elastic rod wound into a helix which is itself wound into a larger helix until this process has been repeated n

vibration analysis of shear deformable circular arches by the differential quadrature method the differential quadrature method is applied in the computation of the eigenvalues of the equations of motion governing in plane and out of plane vibration of circular arches based on the bresse timoshenko beam theory in which both rotatory inertia and shear deformation are taken into account fundamental frequencies are calculated for arches of rectangular and circular cross sections under clamped clamped end conditions and the results are compared with numerical solutions by another method the present method gives good accuracy with only a limited number of grid points

the convergence of euler like method for the simultaneous inclusion of polynomial zeros abstract in this paper we give the convergence analysis of the euler like iterative method for the simultaneous inclusion of all simple real or complex zeros of a polynomial the established initial conditions provide the safe convergence of the considered method and the fourth order of convergence these conditions are computationally verifiable which is of practical importance a procedure for the choice of initial inclusion disks is also given

limits of space times in five dimensions and their relation to the segre types a limiting diagram for the segre classification in 5 dimensional space times is obtained extending a recent work on limits of the energy momentum tensor in general relativity some of geroch s results on limits of space times in general relativity are also extended to the context of five dimensional kaluza klein space times

analytical and numerical study on spatial free vibration of non symmetric thin walled curved beams for spatial free vibration of non symmetric thin walled circular curved beams an accurate displacement field is introduced by defining all displacement parameters at the centroidal axis and three total potential energy functionals are consistently derived by degenerating the potential energy for the elastic continuum to that for thin walled curved beams the closed form solutions are newly obtained for in plane and out of plane free vibration analysis of monosymmetric curved beams respectively also two thin walled curved beam elements are developed using the third and fifth order hermitian polynomials in order to illustrate the accuracy and the practical usefulness of the present method analytical and numerical solutions by this study are presented and compared with previously published results or solutions by abaqus the shell element particularly effects of the thickness curvature as well as the inextensional condition are investigated on free vibration of curved beams with monosymmetric and non symmetric cross sections

the root and bell s disk iteration methods are of the same error propagation characteristics in the simultaneous determination of the zeros of a polynomial part ii round off error analysis by use of interval arithmetic in part i ikhile 2008 4 it was established that the root and bell s disk point iteration methods with or without correction term are of the same asymptotic error propagation characteristics in the simultaneous determination of the zeros of a polynomial this concluding part of the investigation is a study in round offs its propagation and its effects on convergence employing interval arithmetic means the purpose is to consequently draw attention on the effects of round off errors introduced from the point arithmetic part on the rate of convergence of the generalized root and bell s simultaneous interval iteration algorithms and its enhanced modifications introduced in part i for the numerical inclusion of all the zeros of a polynomial simultaneously the motivation for studying the effects of round off error propagation comes from the fact that the readily available computing devices at the moment are limited in precision more so that accuracy expected from some programming or computing environments or from these numerical methods are or can be machine dependent in fact a part of the finding is that round off propagation effects beyond a certain controllable order induces overwhelmingly delayed or even a severely retarded convergence speed which manifest glaringly as poor accuracy of these interval iteration methods in the computation of the zeros of a polynomial simultaneously however in this present consideration and even in the presence of overwhelming influence of round offs we give conditions under which convergence is still possible and derive the error round off relations along with the order r order of convergence of these methods with the results extended to similar interval iteration methods for computing the zeros of a polynomial simultaneously especially to bell s interval methods for refinement of zeros that form a cluster our findings are instructive and quite revealing and supported by evidence from numerical experiments the analysis is preferred in circular interval arithmetic

weierstrass formula and zero finding methods classical weierstrass formula 29 has been often the subject of investigation of many authors in this paper we give some further applications of this formula for finding the zeros of polynomials and analytic functions we are concerned with the problems of localization of polynomial zeros and the construction of iterative methods for the simultaneous approximation and inclusion of these zeros conditions for the safe convergence of weierstrass method depending only on initial approximations are given in particular we study polynomials with interval coefficients using an interval version of weierstrass method enclosures in the form of disks for the complex valued set containing all zeros of a polynomial with varying coefficients are obtained we also present weierstrass like algorithm for approximating simultaneously all zeros of a class of analytic functions in a given closed region to demonstrate the proposed algorithms three numerical examples are included

a note on some recent methods for solving nonlinear equations abstract in this note we present some comments on the recent results concerning iterative methods for solving nonlinear equations in the first part we compare a new method n ujevic a method for solving nonlinear equations appl math comput 174 2006 1416 1426 with the newton and ostrowski method including an extensive analysis of numerical results together with the choice of initial approximations and the computational efficiency of the considered methods in the second part we give a list of recently derived root finding methods and we study the question of priority namely we find out that all reviewed methods were already derived at the beginning of the 60s of the last century one of them dates from the 18th century some remarks on the comparison analysis and the application of iteration methods are included

influence of centerline extensibility on the in plane free vibrations of loaded circular arches free vibrations of circular arches about a prestressed static equilibrium state are investigated the equations of motion for the small amplitude free vibrations about the initial equilibrium state attained under distributed tangential and normal loading derived in a previous paper and specialized to constant curvature are used particular attention is given to the influence of centerline stretching during the vibratory motion the vanishing of the loaded free vibration frequencies signals static buckling and the load intensities at which the frequencies go to zero correspond to the static buckling loads free vibrations with no initial loading is treated as a special case of the problem considered it is shown that exact numerical values for the frequencies can be obtained in this case in general the presence of distributed initial loading precludes the possibility of obtaining closed form analytical solutions barring a few simple loading situations such as uniform constant directional pressure as the governing differential equations have variable coefficients in the present work numerical results are obtained for uniform arches subjected to gravity loading the galerkin method with polynomial trial functions that satisfy the geometric boundary conditions is employed in obtaining accurate values of free vibration frequencies convergence of the method with increasing number of terms in the assumed expansion representing the true solution is demonstrated arches with pinned and clamped end support conditions are considered considerably different frequencies are found depending upon whether one includes or ignores the influence of centerline stretching during the vibratory motion

free vibration of a beam subjected to large static deflection abstract considered in this paper is the problem of free vibration of a beam that has undergone a large static deflection the nonlinear equations of motion for the beam are derived first the equations are then decomposed into a set of nonlinear differential equations for the static deflection and a set of linear differential equations for the vibrational motion of the beam the coefficients of the vibration equations consist of the beam s static deflection the nonlinear differential equations are solved analytically to obtain the static deflection the vibration equations are solved by expanding the displacements in a power series coefficients of the power series are constructed analytically through a recursive relationship the natural frequencies of the beam under large static bending are determined by solving a 3 3 eigenvalue problem substitution of the eigenvalues and eigenvectors into the power series expansion of the displacements yields the corresponding modes of vibration several numerical examples are given to illustrate the solution procedure

on the determination of the safe initial approximation for the durand kerner algorithm abstract in this paper applying the majorant function method we present a new proof of the convergence of the durand kerner method and obtain a greater computable radius estimation of safe initial discs this result is an improvement of all results now available furthermore combining the kuhn algorithm for solving all zeros of polynomials we obtain a discriminant to get safe initial discs finally we compare the complexity between the durand kerner algorithm and several known results and the numerical results show the superiority of our result

dynamic stiffness analysis for in plane vibrations of arches with variable curvature this paper provides a systematic approach to solve in plane free vibrations of arches with variable curvature the proposed approach basically introduces the concept of dynamic stiffness matrix into a series solution for in plane vibrations of arches with variable curvature an arch is decomposed into as many elements as needed for accuracy of solution in each element a series solution is formulated in terms of polynomials the coefficients of which are related to each other through recurrence formulas as a result in order to have an accurate solution one does not need a lot of terms in series solution and in taylor expansion series for the variable coefficients of the governing equations due to the consideration of variable curvature finally a dynamic stiffness matrix is formed such that it can be applied to solve more complicated systems such as multiple span arches in the whole analysis the effects of rotary inertia and shear deformation have been taken into account

inclusion of the roots of a polynomial based on gerschgorin s theorem in this note a new companion matrix is presented which can be interpreted as a product of werner s companion matrices 13 gerschgorin s theorem yields an inclusion of the roots of a polynomial which is best in the sense of 4 and generalizes a result of l elsner 5 this inclusion is better than the one due to w borsch supan in 1

a convergence analysis of a fourth order method for computing all zeros of a polynomial simultaneously in 2011 petkovi rani and miloevi petkovi etal 2011 introduced and studied a new fourth order iterative method for finding all zeros of a polynomial simultaneously they obtained a semilocal convergence theorem for their method with computationally verifiable initial conditions which is of practical importance in this paper we provide new local as well as semilocal convergence results for this method over an algebraically closed normed field our semilocal results improve and complement the result of petkovi rani and miloevi in several directions the main advantage of the new semilocal results are weaker sufficient convergence conditions computationally verifiable a posteriori error estimates and computationally verifiable sufficient conditions for all zeros of a polynomial to be simple furthermore several numerical examples are provided to show some practical applications of our semilocal results

improvement of a convergence condition for the durand kerner iteration abstract the durand kerner iteration is a well known simultaneous method for approximation of simple zeros of a polynomial by relating weierstrass correction and the minimal distance between approximations practical conditions for convergence have been obtained these conditions also ensure the existence of isolating discs for the polynomial roots i e each iteration step gives a refined set of inclusion discs in this paper refined conditions of convergence are given

on the convergence order of accelerated root iterations a gauss seidel procedure for accelerating the convergence of the generalized method of the root iterations type of the k 2 th order k n for finding polynomial complex zeros given in 7 is considered in this paper it is shown that ther order of convergence of the accelerated method is at leastk 1 n k where n k 1 is the unique positive root of the equation n k 1 0 andn is the degree of the polynomial the examples of algebraic equations in ordinary and circular arithmetic are given

point estimation of simultaneous methods for solving polynomial equations a survey ii the construction of computationally verifiable initial conditions which provide both the guaranteed and fast convergence of the numerical root finding algorithm is one of the most important problems in solving nonlinear equations smale s point estimation theory from 1981 was a great advance in this topic it treats convergence conditions and the domain of convergence in solving an equation f z 0 using only the information of f at the initial point z 0 the study of a general problem of the construction of initial conditions of practical interest providing guaranteed convergence is very difficult even in the case of algebraic polynomials in the light of smale s point estimation theory an efficient approach based on some results concerning localization of polynomial zeros and convergent sequences is applied in this paper to iterative methods for the simultaneous determination of simple zeros of polynomials we state new improved initial conditions which provide the guaranteed convergence of frequently used simultaneous methods for solving algebraic equations ehrlich aberth s method ehrlich aberth s method with newton s correction borsch supan s method with weierstrass correction and halley like or wang zheng method the introduced concept offers not only a clear insight into the convergence analysis of sequences generated by the considered methods but also explicitly gives their order of convergence the stated initial conditions are of significant practical importance since they are computationally verifiable they depend only on the coefficients of a given polynomial its degree n and initial approximations to polynomial zeros

interval versions of some procedures for the simultaneous estimation of complex polynomial zeros an idea due to neumaier is used to construct interval versions of point iterative procedures for the estimation of simple zeros of analytic functions in particular interval versions of some point iterative procedures for the simultaneous estimation of simple complex polynomial zeros are described some numerical results are presented

exact dynamic and static stiffness matrices of shear deformable thin walled beam columns abstract total potential energy of non symmetric thin walled beam columns in the general form is presented by introducing the displacement field based on semitangential rotations and deriving transformation equations between displacement and force parameters defined at the arbitrary axis and the centroid shear center axis respectively next governing equations and force deformation relations are derived from the total potential energy for a shear deformable uniform beam element and a system of linear eigenproblem with non symmetric matrices is constructed based on 14 displacement parameters and then explicit expressions for displacement parameters are derived and exact dynamic stiffness matrices are determined using force deformatin relationships in addition the modified numerical method to eliminate multiple zero eigenvalues and to evaluate the exact static stiffness matrix is developed for spatial stability analysis finally in order to demonstrate the validity and the accuracy of this study the spatially coupled natural frequencies and buckling loads are evaluated and compared with analytical solutions or results analyzed by thin walled beam elements and abaqus s shell elements

low frequency mode transition in the free in plane vibration of curved beams the low frequency mode transition in the free in plane vibration of beams with varying curvature and cross section is examined by using perturbation analysis a simplified zeroth order equation for beam vibration in the region of the mode transition is derived this equation shows explicitly which modes undergo a transition for a particular type of beam curvature and cross section analytic approximations for frequency and mode shape are derived by the cases of beam curvature represented by symmetric and antisymmetric polynomials and their validity is illustrated by comparison with numerical solutions many features of mode transition phenomenon are revealed analytically including the effect of beam curvature on mode shape during the transition stage the similarities and distinctions between the low mode and the high mode number transitions are discussed

exact natural frequencies of plane structures composed of slender elastic curved members abstract exact finite elements form the basis of a new and convenient procedure for converging with certainty upon the required natural frequencies of any plane structure composed of slender elastic curved members of constant radius solution of the inherent transcendental eigenvalue problem is achieved through a variation on the powerful wittrick williams algorithm two illustrative examples are included

a bibliography on roots of polynomials abstract a categorized bibliography on roots of polynomials is presented covering the period from the earliest times until late 1990 the actual bibliography is on a computer diskette accompanying this issue together with programs designed to print parts of the main work such as entries belonging to a certain category

a family of simultaneous zero finding methods abstract applying hansen patrick s formula for solving the single equation f z 0 to a suitable function appearing in the classical weierstrass method two one parameter families of interation functions for the simultaneous approximation of all simple and multiple zeros of a polynomial are derived it is shown that all the methods of these families have fourth order of convergence some computational aspects of the proposed methods and numerical examples are given

interval analysis theory and applications we give an overview on applications of interval arithmetic among others we discuss verification methods for linear systems of equations nonlinear systems the algebraic eigenvalue problem initial value problems for odes and boundary value problems for elliptic pdes of second order we also consider the item software in this field and give some historical remarks

3 d vibration analysis of circular rings with sectorial cross sections the free vibration characteristics of circular rings with sectorial cross section are studied based on the three dimensional 3 d small strain linear elasticity theory the complete vibration spectrum has been obtained by using the ritz method a set of three dimensional orthogonal coordinates composing of the polar coordinates r at the origin of the sectorial cross section and circumferential coordinate around the ring is developed to describe the variables in the analysis each of the displacement components is taken as a triplicate series two chebyshev polynomial series respectively about the r and coordinates and a trigonometric series about the coordinate frequency parameters and vibration mode shapes are computed by means of the displacement based extremum energy principle upper bound convergence of the first eight frequency parameters accurate to at least five significant figures is presented the effect of radius ratio subtended angle and initial slope angle on frequency parameters is investigated in detail all major modes such as flexural modes thickness shear modes stretching modes and torsional modes etc are presented in the paper the present results may serve as a benchmark reference to validate the accuracy of various approximate theories and other computational techniques for the vibration of circular rings

on the new fourth order methods for the simultaneous approximation of polynomial zeros a new iterative method of the fourth order for the simultaneous determination of polynomial zeros is proposed this method is based on a suitable zero relation derived from the fourth order method for a single zero belonging to the schroder basic sequence one of the most important problems in solving polynomial equations the construction of initial conditions that enable both guaranteed and fast convergence is studied in detail for the proposed method these conditions are computationally verifiable since they depend only on initial approximations the polynomial coefficients and the polynomial degree which is of practical importance the construction of improved methods in ordinary complex arithmetic and complex circular arithmetic is discussed finally numerical examples and the comparison with existing fourth order methods are given

efficient methods for the inclusion of polynomial zeros abstract using a suitable zero relation and the inclusion isotonicity property new interval iterative methods for the simultaneous inclusion of simple complex zeros of a polynomial are derived these methods produce disks in the complex plane that contain the polynomial zeros in each iteration providing in this manner an information about upper error bounds of approximations starting from the basic method of the fourth order two accelerated methods with newton s and halley s corrections having the order of convergence five and six respectively are constructed this increase of the convergence rate is obtained without any additional operations which means that the methods with corrections are very efficient the convergence analysis of the basic method and the methods with corrections is performed under computationally verifiable initial conditions which is of practical importance two numerical examples are presented to demonstrate the convergence behavior of the proposed interval methods

in plane and out of plane free vibrations of curved beams with variable sections we present an approximate method to study the analysis for both the in plane and out of plane free vibration of horizontally curved beams with arbitrary shapes and variable cross sections the characteristic equation for free vibration can be derived by applying the green function which is obtained as a discrete type solution of differential equations governing the flexural behaviour of the curved beam under the action of a concentrated load

some improved inclusion methods for polynomial roots with weierstrass corrections one decade ago the third order method without derivatives for the simultaneous inclusion of simple zeros of a polynomial was proposed in 1 following nourein s idea 2 some modifications of this method with the increased convergence are proposed the acceleration of convergence is attained by using weierstrass corrections without additional calculations which provides a high computational efficiency of the modified methods it is proved that their r orders of convergence are asymptotically greater than 3 5 the presented interval methods are realized in circular complex arithmetic

some simultaneous iterations for finding all zeros of a polynomial with high order convergence in this paper using lagrange interpolation with special nodes we construct some iterations for simultaneously finding all zeros of an algebraic polynomial with high order convergence

on the simultaneous determination of the zeros of an analytic function inside a simple smooth closed contour in the complex plane abstract a family of higher order iterative methods for the simultaneous determination of all simple or multiple zeros of an analytic function inside a simple smooth closed contour is obtained using earlier results of the author with the help of circular arithmetic the interval variant of this family is proposed many parallel iterative methods of the literature are special cases of this family

high order euler like method for the inclusion of polynomial zeros abstract improved iterative method of euler s type for the simultaneous inclusion of polynomial zeros is considered to accelerate the convergence of the basic method of the fourth order we applied borsch supan s correction it is proved that the r order of convergence of the improved euler like method is six the convergence analysis is derived under computationally verifiable initial conditions the proposed algorithm possesses great computational efficiency since the increase of the convergence rate from 4 to 6 is obtained with negligible number of additional calculations in order to demonstrate convergence properties of the suggested method two numerical examples are given

the guaranteed convergence of laguerre like method abstract the construction of initial conditions that provide a guaranteed convergence of zero finding methods has attracted a great deal of attention for many years in this paper we consider convergent properties of the laguerre like method of the fourth order for the simultaneous approximation of polynomial zeros using a procedure based on smale s point estimation theory and some recent results concerned with localization of complex polynomial zeros we state initial conditions which enable both the guaranteed and fast convergence of this method these conditions are computationally verifiable since they depend only on initial approximations polynomial coefficients and polynomial degree which is of practical importance

free vibrations of arches with variable curvature abstract the equations governing free in plane vibrations of variable curvature arches are derived and solved numerically to obtain frequencies and mode shapes for parabolic sinusoidal and elliptic geometries included are experimental validations of the lowest four predicted frequencies and mode shapes for parabolic arches

computer aided study of a class of riemannian space times the riemannian godel type manifolds are examined in the light of the equivalence problem techniques by using algebraic computing the conditions for space time homogeneity of a riemannian manifold with a godel type metric are derived generalizing previous work on this subject matter a classification of the godel type riemannian manifolds based on the two relevant parameters m and is formulated it is shown that apart from the m2 4 2 case they are all petrov type d with a five parameter group of motions the special m2 4 2 manifold is shown to be conformally flat and to admit a seven parameter group of isometries an algebraic classification of the ricci spinor of all godel type riemannian manifolds is discussed possible sources for these space times are examined a generalization of the reboucas tiomno theorem on godel type manifolds is given

classification of second order symmetric tensors in five dimensional kaluza klein type theories an algebraic classification of second order symmetric tensors in five dimensional kaluza klein type lorentzian spaces is presented by using jordan matrices it is shown that the possible segre types are 1 1111 2111 311 zz111 and the degeneracies thereof a set of canonical forms for each segre type is found the possible continuous groups of symmetry for each canonical form are also studied

convergence analysis of sakurai torii sugiura iterative method for simultaneous approximation of polynomial zeros abstract in 1991 t sakurai t torii and h sugiura presented a fourth order iterative algorithm for finding all zeros of a polynomial simultaneously in this paper we provide a detailed convergence analysis local and semilocal of this method the new results improve and complement existing results due to petkovic et al 2003 and petkovic 2008 numerical examples are given to show the applicability of our semilocal convergence results

improved halley like methods for the inclusion of polynomial zeros improved iterative methods of halley s type for the simultaneous inclusion of all simple complex zeros of a polynomial are proposed the presented convergence analysis which uses the concept of the r order of convergence of mutually dependent sequences shows that the convergence rate of the basic fourth order method is increased to 5 and 6 using newton s and halley s corrections respectively the proposed inclusion methods possess a high computational efficiency since the increase of the convergence is attained without additional calculations this advantage together with very fast convergence make that the presented methods are ranking among the most powerful inclusion methods for polynomial zeros in order to demonstrate convergence properties of the proposed methods two numerical examples are given

improved methods for the simultaneous inclusion of multiple polynomial zeros using a new fixed point relation the interval methods for the simultaneous inclusion of complex multiple zeros in circular complex arithmetic are constructed using the concept of the r order of convergence of mutually dependent sequences we present the convergence analysis for the total step and the single step methods with schroder s and halley like corrections under computationally verifiable initial conditions the suggested algorithms possess a great computational efficiency since the increase of the convergence rate is attained without additional calculations two numerical examples are given to demonstrate convergence characteristics of the proposed method

on iteration methods without derivatives for the simultaneous determination of polynomial zeros carstensen c and m s petkovic on iteration methods without derivatives for the simultaneous determination of polynomial zeros journal of computational and applied mathematics 45 1993 251 266 several algorithms for simultaneously approximating simple complex zeros of a polynomial are presented these algorithms use weierstrass corrections and do not require any polynomial derivatives it is shown that nourein s method is actually regula falsi for weierstrass corrections convergence analysis and computational efficiency are given for the considered methods in complex and circular arithmetic special attention is paid to hybrid methods that combine the efficiency of floating point arithmetic and the inclusion property of interval arithmetic

a parallel algorithm for simple roots for polynomials abstract a method for finding simple roots of arbitrary polynomials based on divided differences is discussed theoretical background is presented for the case of simple roots numerical results are presented which show the algorithm finds simple and multiple zeros to an accuracy usually limited by the accuracy of polynomial evaluation the method is designed for a simd parallel computer the algorithm is compared to two other frequently used polynomial root finders the jenkins traub algorithm and laguerre s method

on an iterative method for simultaneous inclusion of polynomial complex zeros abstract starting from disjoint discs which contain polynomial complex zeros the iterative interval method of the third order for the simultaneous finding inclusive discs for complex zeros is formulated the lagrangean interpolation formula and complex circular arithmetic are used the convergence theorem and the conditions for convergence are considered the proposed method has been applied for solving an algebraic equation

on a simultaneous method of newton weierstrass type for finding all zeros of a polynomial combining a suitable two point iterative method for solving nonlinear equations and weierstrass correction a new iterative method for simultaneous finding all zeros of a polynomial is derived it is proved that the proposed method possesses a cubic convergence locally numerical examples demonstrate a good convergence behavior of this method in a global sense it is shown that its computational efficiency is higher than the existing derivative free methods

a family of root finding methods with accelerated convergence a parametric family of iterative methods for the simultaneous determination of simple complex zeros of a polynomial is considered the convergence of the basic method of the fourth order is accelerated using newton s and halley s corrections thus generating total step methods of orders five and six further improvements are obtained by applying the gauss seidel approach accelerated convergence of all proposed methods is attained at the cost of a negligible number of additional operations detailed convergence analysis and two numerical examples are given

acceleration of convergence of interval sequences abstract let s n be a sequence of intervals we give a definition of linearity and acceleration of convergence when the stationary index of the sequence is finite or infinite for the aitken 2 process the property of acceleration is described for two cases

vibrations of beams and helices with arbitrarily large uniform curvature an analytical numerical and experimental study of the vibrational modes of beams with constant curvature ranging from small values up to helices with large numbers of turns is presented it is shown that after an initial stage at low curvature in which extensional symmetrical modes hybridize so as to become inextensional all modes show a decrease in frequency with increasing beam curvature the frequency reaches a minimum at a value of the curvature which is a function of mode number and successive minima are separated by steps of in the opening angle of the beam for large values of curvature it is shown that for both symmetric and antisymmetric modes there are two types of vibrational modes with comparable frequencies modes develop into one or the other of these types in a way that is precisely defined but that has the appearance of being random physical descriptions of the processes involved are given and the modes of the two types are described

the theory of smale s point estimation and its applications abstract the main result of this paper is that we exact smale s point estimation theory i e without assuming k p z 1 p k z k k 2 being bounded by the point estimation convergence theorem of the ne method is set up by making use of the majorizing method the proof of the theorem is simple and precise while the required point estimation conditions are weaker than all those of known point estimation convergence theorems another result of this paper is an application of the above new theory to the durand kerner method we compare the point estimation conditions for the durand kerner method with other known point estimation conditions numerical results show that our results have evident advantages

a posteriori error bound methods for the inclusion of polynomial zeros using carstensen s results from 1991 we state a theorem concerning the localization of polynomial zeros and derive two a posteriori error bound methods with the convergence order 3 and 4 these methods possess useful property of inclusion methods to produce disks containing all simple zeros of a polynomial we establish computationally verifiable initial conditions that guarantee the convergence of these methods some computational aspects and the possibility of implementation on parallel computers are considered including two numerical examples a comparison of a posteriori error bound methods with the corresponding circular interval methods regarding the computational costs and sizes of produced inclusion disks were given

notes on a class of homogeneous space times the breakdown of causality in homogeneous godel type space time manifolds is examined an extension of reboucas tiomno rt and accioly goncalves studies is made the existence of noncausal curves is also investigated under two different conditions on the energy momentum tensor an integral representation of the infinitesimal generators of isometries is obtained extending previous works on the rt geometry

laguerre like inclusion method for polynomial zeros a new method of the fourth order for the simultaneous inclusion of simple polynomial zeros is proposed the presented method is based on the fixed point relation of laguerre s type and realized in circular complex interval arithmetic the established initial conditions guarantee the convergence of the considered method and the fourth order of convergence these conditions are computationally verifiable which is of practical importance the presented iteration formula is suitable for the construction of modified interval methods with improved convergence rate with negligible additional operations convergence analysis and numerical results are given

asymptotic analysis of the free in plane vibrations of beams with arbitrarily varying curvature and cross section abstract an asymptotic analysis is carried out for the equations of free vibrations of a beam having varying curvature and cross section the effect of splitting the asymptotic limit for eigen values into two families is revealed and its connection with boundary conditions is discussed the analysis of the properties of the asymptotic solution explains the phenomenon of transformation of mode shape with change in curvature and provides a method for predicting the spectrum of curved beams the asymptotic solution obtained also gives a simple approximation for high mode number extensional vibrations of curved beams which are difficult to analyse by other means the asymptotic behaviour of the solution is illustrated numerically for different types of curvature including antisymmetric curvature an experimental verification of the asymptotic behaviour of mode frequencies is presented

the root and bell s disk iteration methods are of the same error propagation characteristics in the simultaneous determination of the zeros of a polynomial part i correction methods in this paper we consider the error propagation of the root and bell s disk iteration methods enhanced by incorporating a correction term and a choice of a disk inversion formula in the methods for the simultaneous computation of the zeros of a polynomial the asymptotic error propagation is proved to be the same in both methods this result is important considering the fact that these methods are in popular usage in the simultaneous computation of the zeros of a polynomial the proof of the results herein follows the ideas of m s petkovic c carstensen some improved inclusion methods for polynomial roots with weierstrass corrections comput math appl 25 3 1993 59 67 when the refinement process of correction is efficient it is this mode of correction we have desired to propose

an analytic model for the free in plane vibration of beams of variable curvature and depth in this study a flexible and powerful model is presented for the in plane vibration of a beam whose curvature and depth are arbitrary constrained only to such smoothness as can be accommodated by a quartic polynomial in the centerline arc length the model includes the effects of shear deformation rotary inertia and centerline extensibility the equations of motion are solved by an extension of the classic galerkin method wherein the effect of boundary residuals is included timoshenko models are compared to other theoretical models and to experimental results the comparisons are done for a variety of support schemes a detailed study of a cantilever beam of variable curvature and depth is done and finally the utility and flexibility of the model is demonstrated for an arch whose shape is given only by a scale drawing devoid of any other information except material properties

exact dynamic stiffness matrix of non symmetric thin walled curved beams subjected to initial axial force abstract an improved numerical method to exactly evaluate the dynamic element stiffness matrix is proposed for the spatially coupled free vibration analysis of non symmetric thin walled curved beams subjected to uniform axial force for this purpose firstly equations of motion boundary conditions and force deformation relations are rigorously derived from the total potential energy for a curved beam element next systems of linear algebraic equations with non symmetric matrices are constructed by introducing 14 displacement parameters and transforming the fourth order simultaneous differential equations into the first order simultaneous equations and then explicit expressions for displacement parameters are numerically evaluated via eigensolutions and the exact 14 14 element stiffness matrix is determined using force deformation relations in order to demonstrate the validity and the accuracy of this study the spatially coupled natural frequencies of non symmetric thin walled curved beams subjected to uniform compressive and tensile forces are evaluated and compared with analytical and finite element solutions using hermitian curved beam elements or abaqus s shell element in addition some results by the parametric study are reported

computational efficiency of some combined methods for polynomial equations abstract the iterative methods for the simultaneous determination of all simple complex zeros of algebraic polynomials based on the fixed point relation of ehrlich s type are considered using the iterative correction appearing in the jarratt method of the fourth order it is proved that the convergence rate of the modified ehrlich method is increased from 3 to 6 this acceleration of the convergence is obtained with few additional numerical operations which means that the proposed combined method possesses very high computational efficiency moreover the convergence rate can be further accelerated using the gauss siedel approach single step or serial mode a great part of the paper is devoted to the computational aspects of the discussed methods including numerical examples a comparison procedure shows that the new iterative method is more efficient than existing methods in the considered class

a new higher order family of inclusion zero finding methods starting from a suitable fixed point relation a new one parameter family of iterative methods for the simultaneous inclusion of complex zeros in circular complex arithmetic is constructed it is proved that the order of convergence of this family is four the convergence analysis is performed under computationally verifiable initial conditions an approach for the construction of accelerated methods with negligible number of additional operations is discussed to demonstrate convergence properties of the proposed family of methods two numerical examples results are given

iterative methods for solving nonlinear equations with finitely many roots in an interval in this paper we consider a nonlinear equation f x 0 having finitely many roots in a bounded interval based on the so called numerical integration method b i yun a non iterative method for solving non linear equations appl math comput 198 2008 691 699 without any initial guess we propose iterative methods to obtain all the roots of the nonlinear equation in the result an algorithm to find all of the simple roots and multiple ones as well as the extrema of f x is developed moreover criteria for distinguishing zeros and extrema are included in the algorithm availability of the proposed method is demonstrated by some numerical examples

the numerical stability of the generalised root iterations for polynomial zeros abstract the generalised root iterations for simultaneous finding polynomial complex zeros with the convergence order k 2 k n was formulated in 6 in terms of circular regions the method produces the disks which contain the exact zeros giving error bounds automatically for each approximation this paper investigates the numerical stability of this algorithm in the presence of rounding errors the conditions for preserving the convergence rate are established the presented analysis contains the results given in 3 and 4

semilocal convergence of chebyshev like root finding method for simultaneous approximation of polynomial zeros abstract in this paper we present convergence results for the chebyshev like method for the simultaneous computation of all zeros of a polynomial f over a complete normed field our results generalize improve and complement the result of petkovic and petkovic 2001 10 the new results give weaker sufficient convergence conditions a priori and a posteriori error estimates as well as information on the location of the zeros another important aspect of this work is that we do not assume neither simplicity nor existence of the zeros of f furthermore several numerical examples are provided to show some practical applications of our results

in plane vibrations of non circular arcs of non uniform cross section abstract the title problem is solved by using polynomial co ordinate functions and the ritz method to generate the frequency equation symmetric and unsymmetric structural systems are considered the agreement with results available in the literature or with eigenvalues determined by means of a finite element code is good from an engineering viewpoint

letter to the editor comments on some recent methods for the simultaneous determination of polynomial zeros in this note we give some comments on the recent results concerning a simultaneous method of the fourth order for finding complex zeros in circular interval arithmetic the main discussion is directed to a rediscovered iterative formula and its modification presented recently in sun and kosmol j comput appl math 130 2001 293 the presented comments include some critical parts of the papers jpn j indust appl math 15 1998 295 and sun and kosmol 2001 which treat the same subject

spatial free vibration of shear deformable circular curved beams with non symmetric thin walled sections abstract for spatial free vibration of shear deformable circular curved beams with non symmetric thin walled cross sections an improved vibration theory is proposed the elastic strain and kinetic energies are first derived by considering constant curvature effects and shear deformation effects due to shear forces and restrained warping torsion next equilibrium equations and force deformation relations are obtained using a stationary condition of total potential energy and then the closed form solution for out of plane vibration of curved beam is newly derived in addition f e procedures are developed by using isoparametric curved beam element with arbitrary thin walled sections in order to illustrate the accuracy and the practical usefulness of this study closed form and numerical solutions for spatial free vibration are compared with results by available references and abaqus s shell element particularly not only shear deformation and thickness curvature effects on vibration behaviors of curved beams but also mode transition and crossover phenomena with change in curvatures and the length of beams are parametrically investigated

the self validated method for polynomial zeros of high efficiency the improved iterative method of newton s type for the simultaneous inclusion of all simple complex zeros of a polynomial is proposed the presented convergence analysis which uses the concept of the r order of convergence of mutually dependent sequences shows that the convergence rate of the basic third order method is increased from 3 to 6 using ostrowski s corrections the new inclusion method with ostrowski s corrections is more efficient compared to all existing methods belonging to the same class to demonstrate the convergence properties of the proposed method two numerical examples are given

symmetries of bianchi i space times all diagonal proper bianchi i space times are determined which admit certain important symmetries it is shown that for homothetic motions conformal motions and kinematic self similarities the resulting space times are defined explicitly in terms of a set of parameters whereas affine collineations ricci collineations and curvature collineations if they are admitted they determine the metric modulo certain algebraic conditions in all cases the symmetry vectors are explicitly computed the physical and the geometrical consequences of the results are discussed and a new anisotropic fluid physically valid solution which admits a proper conformal killing vector is given

on an efficient inclusion method for finding polynomial zeros new efficient iterative method of halley s type for the simultaneous inclusion of all simple complex zeros of a polynomial is proposed the presented convergence analysis which uses the concept of the r order of convergence of mutually dependent sequences shows that the convergence rate of the basic fourth order method is increased from 4 to 9 using a two point correction the proposed inclusion method possesses high computational efficiency since the increase of convergence is attained with only one additional function evaluation per sought zero further acceleration of the proposed method is carried out using the gauss seidel procedure some computational aspects and three numerical examples are given in order to demonstrate high computational efficiency and the convergence properties of the proposed methods

on halley like algorithms for simultaneous approximation of polynomial complex zeros let p z be a polynomial of degree n with n distinct zeros iterative methods for the simultaneous inclusion of k leqq n simple or multiple zeros are given the iterative formulas presented can be regarded as an interval version of halley s iterative formula for multiple zeros realized in circular arithmetic the convergence analysis is done in the presence of multiplicity the convergence order is three for k n and four if k n applying the gauss seidel approach to the basic iterative formula the single step method with accelerated convergence is stated and the lower bound of the r order of convergence of this method is obtained the dependence of convergence rate of the basic methods on the rounding errors is also studied some numerical examples illustrate the theoretical results

homogeneous space times with seven isometries a new homogeneous space time with seven isometries is derived by means of a complex transformation it is shown that it is conformally flat and its weyl flat form is exhibited its killing vector fields and the corresponding lie algebra are also presented an integral representation of these vector fields is found sources for the new space time geometry are obtained by combining synge s approach to einstein s equations with energy conditions and segre classification of the energy momentum tensors a comparison with other rare space times possessing a g7 of motions is made by using a suite of computer algebra programs