constructing higher order methods for obtaining the multiple roots of nonlinear equations this paper concentrates on iterative methods for obtaining the multiple roots of nonlinear equations using the computer algebra system mathematica we construct an iterative scheme and discuss the conditions to obtain fourth order methods from it all the presented fourth order methods require one function and two derivative evaluation per iteration and are optimal higher order iterative methods for obtaining multiple roots we present some special methods from the iterative scheme including some known already numerical examples are also given to show their performance

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

local refinement of analysis suitable t splines we develop a local refinement algorithm for analysis suitable t splines which does not produce excessive propagation of control points we then demonstrate its use as an adaptive framework for isogeometric analysis analysis suitable t splines are a class of t splines which are linearly independent and form a partition of unity these properties coupled with local refinement make this class of t splines appealing as a basis for isogeometric analysis

a hierarchical approach to adaptive local refinement in isogeometric analysis abstract adaptive local refinement is one of the key issues in isogeometric analysis in this article we present an adaptive local refinement technique for isogeometric analysis based on extensions of hierarchical b splines we investigate the theoretical properties of the spline space to ensure fundamental properties like linear independence and partition of unity furthermore we use concepts well established in finite element analysis to fully integrate hierarchical spline spaces into the isogeometric setting this also allows us to access a posteriori error estimation techniques numerical results for several different examples are given and they turn out to be very promising

isogeometric analysis and hierarchical refinement for higher order phase field models abstract while the interest in higher order models in physics and mechanics grows their numerical simulation still poses a challenge especially for arbitrary shaped three dimensional domains this contribution presents the mathematical framework as well as the application to different problems in the field of material science fracture mechanics and diffusion problems all models under consideration require at least c 1 continuity which prevents the application of standard finite element analysis and local mesh refinements introducing isogeometric analysis iga for the discretization in a finite element framework enables us to deal with these requirements moreover a general hierarchical refinement scheme based on a subdivision projection is presented here for one two and three dimensional simulations this technique allows to enhance the approximation space using finer splines on each level but preserves the partition of unity as well as the continuity properties of the original discretization using this mathematical framework the improved convergence of a kuramoto sivashinsky model a mesh adapted thermal diffusion simulation and computations of a priori unknown crack propagation in different fracture modes underline the versatility of the presented hierarchical refinement scheme

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

drinfeld basis of the twisted quantum affine algebra uq a 2 2 from the gauss decomposition of an l operator we establish the algebraic isomorphism between the drinfeld basis of the twisted quantum affine algebra uq a 2 2 and the twisted reshetihkin and semenov tian shansky algebra by using the gauss decomposition technique of ding and frenkel

construction of optimal order nonlinear solvers using inverse interpolation abstract there is a vast literature on finding simple roots of nonlinear equations by iterative methods these methods can be classified by order by the information used or by efficiency there are very few optimal methods that is methods of order 2 m requiring m 1 function evaluations per iteration here we give a general way to construct such methods by using inverse interpolation and any optimal two point method the presented optimal multipoint methods are tested on numerical examples and compared to existing methods of the same order of convergence

hierarchically refined and coarsened splines for moving interface problems with particular application to phase field models of prostate tumor growth abstract moving interface problems are ubiquitous in science and engineering to develop an accurate and efficient methodology for this class of problems we present algorithms for local h adaptivity of hierarchical b splines to be utilized in isogeometric analysis we extend bezier projection an efficient quadrature free local projection technique to the hierarchical setting in this case extraction operators may not be invertible to address this issue we develop a multi level reconstruction operator which maintains the locality properties of the projection we also introduce a balance parameter to control the overlap of hierarchical functions leading to improved numerical conditioning we apply our algorithms to the simulation of localized prostate cancer growth we model this disease using the phase field method and a set of diffusion reaction equations to account for the dynamics of nutrients and a key biomarker termed prostate specific antigen our results include examples on simple 2d and 3d domains and a more compelling tissue scale patient specific simulation which is run over a prostate anatomy extracted from medical images our methods for local h adaptivity efficiently capture the evolving interface between the tumor and the neighboring healthy tissue with remarkable accuracy in all cases

thermodynamically consistent phase field models of fracture variational principles and multi field fe implementations the computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies this can be overcome by a diffusive crack modeling based on the introduction of a crack phase field in this paper we outline a thermodynamically consistent framework for phase field models of crack propagation in elastic solids develop incremental variational principles and consider their numerical implementations by multi field finite element methods we start our investigation with an intuitive and descriptive derivation of a regularized crack surface functional that converges for vanishing length scale parameter to a sharp crack topology functional this functional provides the basis for the definition of suitable convex dissipation functions that govern the evolution of the crack phase field here we propose alternative rate independent and viscous over force models that ensure the local growth of the phase field next we define an energy storage function whose positive tensile part degrades with increasing phase field with these constitutive functionals at hand we derive the coupled balances of quasi static stress equilibrium and gradient type phase field evolution in the solid from the argument of virtual power here we consider a canonical two field setting for rate independent response and a time regularized three field formulation with viscous over force response it is then shown that these balances follow as the euler equations of incremental variational principles that govern the multi field problems these principles make the proposed formulation extremely compact and provide a perfect base for the finite element implementation including features such as the symmetry of the monolithic tangent matrices we demonstrate the performance of the proposed phase field formulations of fracture by means of representative numerical examples copyright 2010 john wiley sons ltd

x m for symmetric powers author s schilling anne shimozono mark abstract the x m conjecture of hatayama et al asserts the equality between the one dimensional configuration sum x expressed as the generating function of crystal paths with energy statistics and the fermionic formula m for all affine kac moody algebra in this paper we prove the x m conjecture for tensor products of kirillov reshetikhin crystals b 1 s associated to symmetric powers for all nonexceptional affine algebras

combinatorial structure of kirillov reshetikhin crystals of type dn 1 bn 1 a2n 1 2 abstract we provide the explicit combinatorial structure of the kirillov reshetikhin crystals b r s of type d n 1 b n 1 and a 2 n 1 2 this is achieved by constructing the crystal analogue of the automorphism of the d n 1 respectively b n 1 or a 2 n 1 2 dynkin diagram that interchanges the 0 and 1 node the involution is defined in terms of new diagrams that govern the d n to d n 1 respectively b n to b n 1 or c n to c n 1 branching it is also shown that the crystal b r s is perfect these crystals have been implemented in mupad combinat the implementation is discussed in terms of many examples

letter to the editor new higher order methods for solving nonlinear equations with multiple roots for a nonlinear equation f x 0 having a multiple root we consider steffensen s transformation t using the transformation say f q x t qf x for integer q 2 repeatedly we develop higher order iterative methods which require neither derivatives of f x nor the multiplicity of the root it is proved that the convergence order of the proposed iterative method is 1 2 q 2 for any equation having a multiple root of multiplicity m 2 the efficiency of the new method is shown by the results for some numerical examples

a subdivision based implementation of the hierarchical b spline finite element method abstract a novel technique is presented to facilitate the implementation of hierarchical b splines and their interfacing with conventional finite element implementations the discrete interpretation of the two scale relation as common in subdivision schemes is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b spline basis the subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same level basis functions their subsequent multiplication with subdivision matrices projects them during the assembly stage to the correct levels of the hierarchical b spline basis the proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one two and three space dimensions

vertex operators for twisted quantum affine algebras we construct explicitly the q vertex operators intertwining operators for the level one modules v i of the classical quantum affine algebras of twisted types using interacting bosons where i 0 1 for a 2 n 1 i 0 for d 3 i 0 n for d 2 1 and i n for a 2 n a perfect crystal graph for d 3 4 is constructed as a by product

a higher order phase field model for brittle fracture formulation and analysis within the isogeometric analysis framework phase field models based on the variational formulation for brittle fracture have recently been gaining popularity these models have proven capable of accurately and robustly predicting complex crack behavior in both two and three dimensions in this work we propose a fourth order model for the phase field approximation of the variational formulation for brittle fracture we derive the thermodynamically consistent governing equations for the fourth order phase field model by way of a variational principle based on energy balance assumptions the resulting model leads to higher regularity in the exact phase field solution which can be exploited by the smooth spline function spaces utilized in isogeometric analysis this increased regularity improves the convergence rate of the numerical solution and opens the door to higher order convergence rates for fracture problems we present an analysis of our proposed theory and numerical examples that support this claim we also demonstrate the robustness of the model in capturing complex three dimensional crack behavior

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

irreducible finite dimensional representations of equivariant map algebras suppose a finite group acts on a scheme x and a finite dimensional lie algebra g the corresponding equivariant map algebra is the lie algebra m of equivariant regular maps from x to g we classify the irreducible finite dimensional representations of these algebras in particu lar we show that all such representations are tensor products of evaluation representations and one dimensional representations and we establish conditions ensuring that they are all evaluation representations for example this is always the case if m is perfect our results can be applied to multiloop algebras current algebras the onsager algebra and the tetrahedron algebra doing so we easily recover the known classifications of irreducible finite dimensional representations of these algebras moreover we obtain previously unknown classifica tions of irreducible finite dimensional representations of other types of equivariant map algebras such as the generalized onsager algebra

isogeometric spline forests in this paper we present isogeometric spline forests an isogeometric spline forest is a hierarchical spline representation capable of representing surfaces or volumes of arbitrarily complex geometry and topological genus spline forests can accomodate arbitrary degree and smoothness in the underlying hierarchical basis as well as non uniform knot interval configurations we describe adaptive h refinement and coarsening algorithms for isogeometric spline forests and develop a bezier extraction framework which provides a simple and efficient single level finite element description of the complex multi level unstructured hierarchical spline basis we then demonstrate the potential of spline forests as a basis for analysis in the context of transient advection diffusion problems where fully integrated adaptivity is demonstrated for the first time in an isogeometric simulation in all cases the adaptive process remains local even in the case of moving fronts and preserves exact geometry at the coarsest level of the discretization the accuracy and robustness of the approach is demonstrated in all cases

families of third and fourth order methods for multiple roots of nonlinear equations this paper presents two families of higher order iterative methods for solving multiple roots of nonlinear equations one is of order three and the other is of order four the presented iterative families all require two evaluations of the function and one evaluation of its first derivative thus the latter is of optimal order the third order family contains several iterative methods known already and different from the optimal fourth order methods for multiple roots known already the presented fourth order family use the modified newton s method as its first step local convergence analyses and some special cases of the presented families are given we also carry out some numerical examples to show their performance

isogeometric analysis on implicit domains using weighted extended pht splines abstract the urging quest for diminishing the gap between finite element methods and computer aided design is growing every day isogeometric analysis is driving that search a step forward in contrast with traditional finite element methods one of the areas that need more investigation is using isogeometric analysis on domains that contain singularities in this case the parameterization process is occasionally non trivial and some of the inherited basis functions are not well defined producing rough solutions moreover nurbs basis functions are not the best choice to perform local refinement since adaptivity is indispensable in this study a new approach that serves as a generalization for some of the ideas in both the isogeometric analysis and the web method is introduced isogeometric analysis on implicit domains replaces mesh generation with implicit spline weight function generation and construct weighted extended pht splines for analysis the geometry and the analysis both are built starting from the same function space avoiding parameterization the pht splines are adaptive and allow local refinement naturally leading to a higher accuracy while dealing with singularities an illustration with numerical examples demonstrates the efficiency and performance of the proposed method

isogeometric mortar methods the application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically for the lagrange multiplier two choices of uniformly stable spaces are presented both of them are spline spaces but of a different degree in one case we consider an equal order pairing for which a cross point modification based on a local degree reduction is required in the other case the degree of the dual space is reduced by two compared to the primal this pairing is proven to be inf sup stable without any necessary cross point modification several numerical examples confirm the theoretical results and illustrate additional aspects

variational space time elements for large scale systems abstract in this paper we introduce a new galerkin based formulation for transient continuum problems governed by partial differential equations in space and time therefore we aim at a direct finite element discretization of the space time suitable for massive parallel analysis of the arising large scale problem the proposed formulation is applied to thermal mechanical and fluid systems as well as to a kuramoto sivashinsky problem representing the general class of higher order formulations in material science using nurbs based shape functions we verify whenever possible the conservation properties of the formulation finally a series of examples demonstrate the applicability to all systems presented in this paper

convergence radius of the modified newton method for multiple zeros under holder continuous derivative abstract in recent years a lot of iterative methods for finding multiple zeros of nonlinear equations have been presented and analyzed however almost all these studies give no information for the convergence radius of the corresponding method in this paper we give an estimate of the convergence radius of the well known modified newton s method for multiple zeros when the involved function satisfies a holder and center holder continuity condition

stationary dynamical and chaotic states of the two dimensional damped kuramoto sivashinsky equation the long time behavior of the two dimensional damped kuramoto sivashinsky equation is studied numerically in the large aspect ratio limit the equation is shown to lead to three states depending on the magnitude of a damping parameter ensuremath alpha at large intermediate and small values of ensuremath alpha the equation leads respectively to hexagonal breathing hexagonal and disordered states the disordered phase is chaotic in both space and time consistent with spatiotemporal chaos the transitions between these states are examined using standard statistical measures

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

on the crack driving force of phase field models in linearized and finite elasticity abstract the phase field approach to fracture has been proven to be a mathematically sound and easy to implement method for computing crack propagation with arbitrary crack paths hereby crack growth is driven by energy minimization resulting in a variational crack driving force the definition of this force out of a tension related energy functional does however not always agree with the established failure criteria of fracture mechanics in this work different variational formulations for linear and finite elastic materials are discussed and ad hoc driving forces are presented which are motivated by general fracture mechanical considerations the superiority of the generalized approach is demonstrated by a series of numerical examples

hierarchical t splines analysis suitability bezier extraction and application as an adaptive basis for isogeometric analysis abstract in this paper hierarchical analysis suitable t splines hasts are developed the resulting spaces are a superset of both analysis suitable t splines and hierarchical b splines the additional flexibility provided by the hierarchy of t spline spaces results in simple highly localized refinement algorithms which can be utilized in a design or analysis context a detailed theoretical formulation is presented bezier extraction is extended to hasts simplifying the implementation of hasts in existing finite element codes the behavior of a simple hasts refinement algorithm is compared to the local refinement algorithm for analysis suitable t splines demonstrating the superior efficiency and locality of the hasts algorithm finally hasts are utilized as a basis for adaptive isogeometric analysis

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

twisted quantum affine algebras we give a highest weight classification of the finite dimensional irreducible representations of twisted quantum affine algebras as in the untwisted case such representations are in one to one correspondence with n tuples of monic polynomials in one variable but whereas in the untwisted case n is the rank of the underlying finite dimensional complex simple lie algebra in the twisted case n is the rank of the subalgebra of fixed by the diagram automorphism the way in which such an n tuple determines a representation is also more complicated than in the untwisted case

overlapping schwarz methods for isogeometric analysis we construct and analyze an overlapping schwarz preconditioner for elliptic problems discretized with isogeometric analysis the preconditioner is based on partitioning the domain of the problem into overlapping subdomains solving local isogeometric problems on these subdomains and solving an additional coarse isogeometric problem associated with the subdomain mesh we develop an h analysis of the preconditioner showing in particular that the resulting algorithm is scalable and its convergence rate depends linearly on the ratio between subdomain and overlap sizes for fixed polynomial degree p and regularity k of the basis functions numerical results in two and three dimensional tests show the good convergence properties of the preconditioner with respect to the isogeometric discretization parameters h p k number of subdomains n overlap size and also jumps in the coefficients of the elliptic operator

γ convergence for high order phase field fracture continuum and isogeometric formulations abstract we consider high order phase field functionals introduced in borden et al 2014 and provide a rigorous proof that these functionals converge to a sharp crack brittle fracture energy we take into account three dimensional problems in linear elastic fracture mechanics and functionals defined both in sobolev spaces and in spaces of tensor product b splines in the latter convergence holds when the mesh size vanishes faster than the internal length of the phase field model on the theoretical level this condition is natural since the size of the phase field layer around the crack itself scales like the internal length on the numerical level it should be satisfied by local h refinement technically convergence holds in the sense of convergence with respect to the strong topology of l 1 while the sharp crack energy is defined in g s b d 2 the constraint on the phase field to take values in 0 1 is taken into account both in the sobolev setting and in the iso geometric setting in the latter it requires a special treatment since the projection operator on the space of tensor product b splines is not lagrangian i e interpolatory

a categorification of twisted heisenberg algebras abstract we categorify a quantized twisted heisenberg algebra associated to a finite subgroup of sl 2 c

two parameter twisted quantum affine algebras we establish drinfeld realization for the two parameter twisted quantum affine algebras using a new method the hopf algebra structure for drinfeld generators is given for both untwisted and twisted two parameter quantum affine algebras which include the quantum affine algebras as special cases

equivariant map superalgebras suppose a group gamma acts on a scheme x and a lie superalgebra mathfrak g the corresponding equivariant map superalgebra is the lie superalgebra of equivariant regular maps from x to mathfrak g we classify the irreducible finite dimensional modules for these superalgebras under the assumptions that the coordinate ring of x is finitely generated gamma is finite abelian and acts freely on the rational points of x and mathfrak g is a basic classical lie superalgebra or mathfrak sl n n n ge 1 if gamma is trivial we show that they are all tensor products of generalized evaluation modules and are parameterized by a certain set of equivariant finitely supported maps defined on x furthermore in the case that the even part of mathfrak g is semisimple we show that all such modules are in fact tensor products of evaluation modules on the other hand if the even part of mathfrak g is not semisimple more generally if mathfrak g is of type i we introduce a natural generalization of kac modules and show that all irreducible finite dimensional modules are quotients of these as a special case our results give the first classification of the irreducible finite dimensional modules for twisted loop superalgebras

high order nonlinear solver for multiple roots a method of order four for finding multiple zeros of nonlinear functions is developed the method is based on jarratt s fifth order method for simple roots and it requires one evaluation of the function and three evaluations of the derivative the informational efficiency of the method is the same as previously developed schemes of lower order for the special case of double root we found a family of fourth order methods requiring one less derivative thus this family is more efficient than all others all these methods require the knowledge of the multiplicity

modified newton methods for solving fully monolithic phase field quasi static brittle fracture propagation abstract our goal in this work is to develop and compare modified newton methods for fully monolithic quasi static brittle phase field fracture propagation in variational phase field fracture a smoothed phase field indicator variable denoting the crack path is coupled to elasticity moreover a crack irreversibility condition is incorporated to develop a fully monolithic scheme is an extremely challenging task since the underlying problem is non convex and the jacobian of newton s method is indefinite to split the problem using alternating minimization thus a partitioned approach is a possible resort however there are good reasons to consider monolithic approaches such as for example robustness and efficiency although an error oriented newton method can cope with a larger variety of configurations it appears that this method is not always robust and also not always efficient inspired by nonlinear flow problems as alternative we develop a modified newton scheme in which globalization is based on a dynamic modification of the jacobian matrix rather than utilizing line search or trust region strategies this variation switches smoothly between full newton and newton like steps in several 2d and 3d numerical examples all of them with different characteristic features our modified newton solver is compared to a backtracking line search newton method another line search method monitoring the global energy and allowing for negative curvatures and to already published results of an error oriented version these computations also include further modifications of newton s method and detailed discussions why certain schemes either work or fail revisiting all findings the main outcome of this paper is that the modified newton scheme with jacobian modification is currently the only method that works in a robust and efficient way for all provided examples whereas line search schemes or the error oriented scheme show deficiencies for certain configurations

quantum group symmetries and non local currents in 2d qft we construct and study the implications of some new non local conserved currents that exist is a wide variety of massive integrable quantum field theories in 2 dimensions including the sine gordon theory and its generalization to affine toda theory these non local currents provide a non perturbative formulation of the theories the symmetry algebras correspond to the quantum affine kac moody algebras thes matrices are completely characterized by these symmetries formals matrices for the imaginary coupling affine toda theories are thereby derived the application of theses matrices to perturbed coset conformal field theory is studied non local charges generating the finite dimensional quantum group in the liouville theory are briefly presented the formalism based on non local charges we describe provides an algernative to the quantum inverse scattering method for solving integrable quantum field theories in 2d

convergence radius of halley s method for multiple roots under center holder continuous condition recently a new treatment based on taylor s expansion to give the estimate of the convergence radius of iterative method for multiple roots has been presented it has been successfully applied to enlarge the convergence radius of the modified newton s method and osada s method for multiple roots this paper re investigates the convergence radius of halley s method under the condition that the derivative f m 1 of function f satisfies the center holder continuous condition we show that our result can be obtained under much weaker condition and has a wider range of application than that given by bi et al 2011 21

twisted vertex representations of quantum affine algebras recent interests in quantum groups are stimulated by their marvelous relations with quantum yang baxter equations conformal field theory invariants of links and knots and q hypergeometric series besides understanding the reason of the appearance of quantum groups in both mathematics and theoretical physics there is a natural problem of finding q deformations or quantum analogues of known structures quantum groups were first defined by drinfeld 2 and jimbo 9 also see 4 as a q deformation of the universal enveloping algebras of the kacmoody algebras in the work of trigonometric solutions of yang baxter equations in the same spirit it was shown in 13 14 that there exists a 1 1 correspondence between the integrable highest weight representations of symmetrizable kac moody algebras and those of the corresponding quantum groups where both spaces have the same dimension in the case of generic q i e q is not a root of unity moreover one can be very explicit in the case of quantum gl n to write down the irreducible highest weight representations quantum affine algebras are the quantum groups associated to affine lie algebras following drinfeld s realization 3 of q analog of loop algebras the vertex representation of untwisted simply laced quantum affine algebras was constructed in frenkel jing 6 which is a q deformation of frenkel kac 7 and segal 15 construction in the theory of affine lie algebras subsequently the same was done for the quantum affine algebra of type b in 1 in the present work we construct vertex representations of quantum affine algebras twisted by an automorphism of the dynkin diagram which generalizes certain important cases in the ordinary twisted vertex operator calculus 5

numerical simulation of asymptotic states of the damped kuramoto sivashinsky equation the damped kuramoto sivashinsky equation has emerged as a fundamental tool for the understanding of the onset and evolution of secondary instabilities in a wide range of physical phenomena most existing studies about this equation deal with its asymptotic states on one dimensional settings or on periodic square domains we utilize a large scale numerical simulation to investigate the asymptotic states of the damped kuramoto sivashinsky equation on annular two dimensional geometries and three dimensional domains to this end we propose an accurate efficient and robust algorithm based on a recently introduced numerical methodology namely isogeometric analysis we compared our two dimensional results with several experiments of directed percolation on square and annular geometries and found qualitative agreement

convergence radius of osada s method under center holder continuous condition recently a new treatment based on taylor s expansion to give the estimate of the convergence radius of iterative method for multiple roots has been presented it has been successfully applied to enlarge the estimate of the convergence radius of the modified newton s method for multiple roots using the similarly treatment this paper investigates the convergence radius of the osada s method under the condition that the derivative f m 1 of function f satisfies the center holder continuous condition by some examples we show the treatment is simpler and efficient once again the uniqueness ball of solution is also discussed