backward errors for the inverse eigenvalue problem backward errors for the symmetric matrix inverse eigenvalue problem with respect to an approximate solution are defined and explicit expressions of the backward errors are derived the expressions may be useful for testing the stability of practical algorithms

a numerical study on the solution of the cauchy problem in elasticity this work deals with the cauchy problem in two dimensional linear elasticity the equations of the problem are discretized through a standard fem approach and the resulting ill conditioned discrete problem is solved within the frame of the tikhonov approach the choice of the required regularization parameter is accomplished through the generalized cross validation criterion on this basis a numerical experimentation has been performed and the calculated solutions have been used to highlight the sensitivity to the amount of known data the noise always present in the data the regularity of boundary conditions and the choice of the regularization parameter the aim of the numerical study is to implicitly device some guidelines to be used in the solution of this kind of problems

a note on the backward errors for hermite eigenvalue problems we discuss the backward error analysis of the hermite eigenproblems three kinds of problems are included generalized eigenproblem matrix polynomial eigenproblem and multiparameter eigenproblem in the case of the approximate eigenvalue being real these problems have already been solved by higham and higham siam j matrix anal 20 1998 493 tisseur lin alg appl 309 2002 339 and hachstenbach and plestenjak lin alg appl 375 2003 63 this note as a complement of their results considers the complex case

finite element solution of two dimensional inverse elastic problems using spatial smoothing a finite element method fem is presented for calculating the surface tractions on a body from internal measurements of displacement at discrete sensor locations the solution algorithm employs a sensitivity analysis which minimizes the difference between the calculated and measured displacements at each sensor location spatial regularization is one technique employed to stabilize the minimization process by imposing various degrees of smoothness on the solution it also allows the problem to be solved with fewer sensors than traction boundary nodes as an alternative to spatial regularization a method based on keynodes is introduced which assumes that each component of the boundary traction distribution can be described by a polynomial of specified order the methods are applied to several two dimensional examples including a rolling contact problem the effects of parameters such as the number of sensors the location of the sensors and the error in the sensor displacements are discussed

existence of solutions for impulsive neutral functional differential equations with nonlocal conditions abstract the existence uniqueness and continuous dependence of a mild solution of an impulsive neutral functional differential evolution nonlocal cauchy problem in general banach spaces are studied by using the fixed point technique and semigroup of operators

an iterative method for the cauchy problem in linear elasticity with fading regularization effect in this paper an iterative method for solving the cauchy problem in linear elasticity is introduced this problem consists in recovering missing data displacements and forces on some parts of a domain boundary from the knowledge of overspecified data displacements and forces on the remaining parts the algorithm reads as a least square fitting of the given data with a regularization term whose effect fades as the iterations go on so the algorithm converges to the solution of the cauchy problem numerical simulations using the finite element method highlight the algorithm s efficiency accuracy robustness to noisy data as well as its ability to deblur noisy data

existence results for semilinear differential equations with nonlocal and impulsive conditions abstract this paper is concerned with the existence for impulsive semilinear differential equations with nonlocal conditions using the techniques of approximate solutions and fixed point existence results are obtained for mild solutions when the impulsive functions are only continuous and the nonlocal item is lipschitz in the space of piecewise continuous functions is not lipschitz and not compact is continuous in the space of bochner integrable functions respectively

the minimal error method for the cauchy problem in linear elasticity numerical implementation for two dimensional homogeneous isotropic linear elasticity abstract in this paper yet another iterative procedure namely the minimal error method mem for solving stably the cauchy problem in linear elasticity is introduced and investigated furthermore this method is compared with another two iterative algorithms i e the conjugate gradient cgm and landweber fridman methods lfm previously proposed by marin et al marin l hao d n lesnic d 2002b conjugate gradient boundary element method for the cauchy problem in elasticity quarterly journal of mechanics and applied mathematics 55 227 247 and marin and lesnic marin l lesnic d 2005 boundary element landweber method for the cauchy problem in linear elasticity ima journal of applied mathematics 18 817 825 respectively in the case of two dimensional homogeneous isotropic linear elasticity the inverse problem analysed in this paper is regularized by providing an efficient stopping criterion that ceases the iterative process in order to retrieve stable numerical solutions the numerical implementation of the aforementioned iterative algorithms is realized by employing the boundary element method bem for two dimensional homogeneous isotropic linear elastic materials

on eigenvalue variations of rayleigh quotient matrix pencils of a definite pencil abstract let a b be a definite matrix pencil of order n i e both a and b are n n hermitian and c a b def min xe c n x 2 1 x h a ib x 0 suppose y is an n l matrix with full column rank whose column vectors span an approximate invariant subspace for a b this note investigates the relation between eigenvalues of a b and those of y h ay y h by our result for the spectral norm improves sun s linear algebra appl 139 253 267 1990 we also present bounds in frobenius norms and in general unitarily invariant norms

new perturbation bounds of partitioned generalized hermitian eigenvalue problem abstract in this paper some new absolute perturbation bounds of partitioned generalized hermitian positive definite eigenvalue problem are established by two different ways numerical results show that our bounds are sharper than the ones in the literature

on interval estimates of perturbations of generalized eigenvalues for diagonalizable pairs abstract on generalized eigenvalue perturbation bounds for diagonalizable matrix pairs upper bounds are discussed all the time in this paper we mainly consider not only upper bounds but also lower bounds of perturbation of generalized eigenvalues for diagonalizable matrix pairs sharper upper bounds and sharp lower bounds on perturbation of generalized eigenvalues for diagonalizable matrix pairs are obtained in terms of the distances of two points in grassmann manifold the main results improve the existing results of chen 2007 1 and numerical examples illustrate the efficiency of the theoretical results

a fast multilevel algorithm for the solution of nonlinear systems of conductive radiative heat transfer equations in this paper we describe and analyze a fast multilevel algorithm for the solution of a system of nonlinear integro differential equations that model steady state combined conductive radiative heat transfer this system of equations for radiative intensity and temperature can be formulated as a compact fixed point problem in temperature alone with a fixed point map that requires both a solution of the linear transport equation and the linear heat equation for its evaluation we obtain an efficient evaluation of the fixed point map by coupling a finite element diffusion solver with a fast transport solver developed by the second author as a solver we apply a modification of the atkinson brakhage method with newton gmres as the coarse mesh solver to the full nonlinear system we compare our discretization solver pair with newton gmres and the classical atkinson brakhage algorithm

non iterative regularized mfs solution of inverse boundary value problems in linear elasticity numerical reconstruction of the missing boundary data in 2d and 3d linear elasticity noisy over prescribed data are available on the remaining accessible boundary the inverse problem is solved by a meshless method i e the method of fundamental solutions mfs stabilization is achieved via several svd based regularization methods the regularization parameter is selected via the criteria used for inverse problems the numerical reconstruction of the missing dirichlet and neumann data on an inaccessible part of the boundary in the case of two and three dimensional linear isotropic elastic materials from the knowledge of over prescribed noisy measurements taken on the remaining accessible boundary part is investigated this inverse problem is solved using the method of fundamental solutions mfs whilst its stabilization is achieved through several singular value decomposition svd based regularization methods such as the tikhonov regularization method 48 the damped svd and the truncated svd 18 the regularization parameter is selected according to the discrepancy principle 40 generalized cross validation criterion 14 and hansen s l curve method 20

existence of solutions for a class of neutral partial differential equations with nonlocal conditions in the α norm abstract this paper is concerned with the existence of mild and strong solutions for some neutral partial differential equations with nonlocal conditions in the norm the linear part of the equations is assumed to generate a compact analytic semigroup of uniformly bounded linear operators and the nonlinear part satisfies some lipschitz conditions with respect to the norm by using a fixed point theorem of sadovskii we establish some existence results which generalize the recent conclusions on this issue in the end the obtained results will be applied to a class of partial differential equations with nonlocal conditions

determination of an optimal regularization factor in system identification with tikhonov regularization for linear elastic continua this paper presents a geometric mean scheme gms to determine an optimal regularization factor for tikhonov regularization technique in the system identification problems of linear elastic continua the characteristics of non linear inverse problems and the role of the regularization are investigated by the singular value decomposition of a sensitivity matrix of responses it is shown that the regularization results in a solution of a generalized average between the a priori estimates and the a posteriori solution based on this observation the optimal regularization factor is defined as the geometric mean between the maximum singular value and the minimum singular value of the sensitivity matrix of responses the validity of the gms is demonstrated through two numerical examples with measurement errors and modelling errors copyright 2001 john wiley sons ltd

numerical solution of cauchy problems in linear elasticity in axisymmetric situations abstract an iterative method for solving axisymmetric cauchy problems in linear elasticity is presented this kind of problem consists in recovering missing displacements and forces data on one part of a domain boundary from the knowledge of overspecified displacements and forces data on another part of this boundary numerical simulations using the finite element method highlight the algorithm s efficiency accuracy and robustness to noisy data as well as its ability to deblur noisy data an application of the inverse technique to the identification of a friction coefficient is also presented

on some perturbation inequalities for operators abstract an estimate for the norm of the solution to the equation ax xb s obtained by r bhatia c davis and a mcintosh for normal operators a and b is shown to be valid for a larger class some other inequalities in the same spirit are obtained including a sin theorem for singular vectors some inequalities concerning the continuity of the map a ita obtained recently by kittaneh and kosaki are extended using these ideas

on the local convergence of an iterative approach for inverse singular value problems the purpose of this paper is to provide the convergence theory for the iterative approach given by m t chu numerical methods for inverse singular value problems siam j numer anal 29 1992 pp 885 903 in the context of solving inverse singular value problems we provide a detailed convergence analysis and show that the ultimate rate of convergence is quadratic in the root sense numerical results which confirm our theory are presented it is still an open issue to prove that the method is q quadratic convergent as claimed by m t chu

a new spatial regularization scheme for the identification of the geometric shape of an inclusion in a finite body this paper presents a system identification scheme to determine the geometric shape of an inclusion in a finite body the proposed algorithm is based on the minimization of the least squared errors between the measured displacement field and calculated displacement field by the finite element model the domain parameterization technique is adopted to manipulate the shape variation of an inclusion to stabilize the optimization process a new regularization function defined by the length of the boundary curve of an inclusion is added to the error function a variable regularization factor scheme is proposed for a consistent regularization effect the modified newton method with the active set method is adopted for optimization copyright 1999 john wiley sons ltd

a note on stewart s theorem for definite matrix pairs abstract let a and b be n n hermitian matrices the matrix pair a b is called definite pair and the corresponding eigenvalue problem ax bx is definite if c a b inf x 1 h a ib x 0 in this note we develop a uniform upper bound for differences of corresponding eigenvalues of two definite pairs and so improve a result which is obtained by g w stewart 2 moreover we prove that this upper bound is a projective metric in the set of n n definite pairs

shape sensing of 3d frame structures using an inverse finite element method abstract a robust and efficient computational method for reconstructing the elastodynamic structural response of truss beam and frame structures using measured surface strain data is presented known as shape sensing this inverse problem has important implications for real time actuation and control of smart structures and for monitoring of structural integrity the present formulation based on the inverse finite element method ifem uses a least squares variational principle involving section strains also known as strain measures of timoshenko theory for stretching torsion bending and transverse shear the present ifem methodology is based on strain displacement relations only without invoking force equilibrium consequently both static and time varying displacement fields can be reconstructed without the knowledge of material properties applied loading or damping characteristics two finite elements capable of modeling frame structures are derived using interdependent interpolations in which interior degrees of freedom are condensed out at the element level in addition relationships between the order of kinematic element interpolations and the number of required strain gauges are established several example problems involving cantilevered beams and three dimensional frame structures undergoing static and dynamic response are discussed to simulate experimentally measured strains and to establish reference displacements high fidelity msc nastran finite element analyses are performed furthermore numerically simulated measurement errors based on gaussian distribution are also considered in order to verify the stability and robustness of the methodology the ifem solution accuracy is examined with respect to various levels of discretization and the number of strain gauges

an inexact newton type method for inverse singular value problems in this paper an inexact newton type approach is proposed for solving inverse singular value problems we show that the method converges superlinearly this method can reduce significantly the oversolving problem of the newton type method and improve the efficiency numerical experiments is also presented to illustrate our results

a class of nonlinear evolution equations subjected to nonlocal initial conditions abstract we prove the existence of c 0 solutions for a class of nonlinear evolution equations subjected to nonlocal initial conditions of the form u t a u t f t f t f t u t u 0 g u where a d a x x is an m accretive operator acting on the infinite dimensional banach space x f 0 2 d a x is an almost strongly weakly u s c multi function which satisfies an appropriate sign condition while g c 0 2 d a d a is a continuous function

global existence for semilinear evolution equations with nonlocal conditions abstract in this paper we study the global existence of solutions for semilinear evolution equations with nonlocal conditions via a fixed point analysis approach using the leray schauder alternative we derive conditions under which a solution exists globally

numerical solution to a two dimensional inverse heat conduction problem description de la methode de programmation dynamique pour la resolution de problemes inverses de conduction thermique application a un probleme impliquant la determination de 2 evolutions dans le temps inconnues de flux thermique sur les 2 faces d une plaque execution de differentes experiences numeriques pour etudier les effets du bruit et des parametres de ponderation

inverse boundary traction reconstruction with the bem abstract a boundary integral formulation is presented for the solution of the inverse elastostatics problem iesp of reconstructing missing boundary tractions in two dimensional structural members traction reconstruction may involve the determination of the location of the traction distribution in addition to its extent and amplitude the missing boundary tractions are rebuilt from measured quantities such as displacements strains or stresses these quantities may be obtained from sensors located at some internal or boundary points of the object the proposed formulation starts with an initial guess for the magnitude extent and location of the missing boundary tractions and proceeds towards the final traction distribution in a sequence of iterative steps the inverse problem is written as an optimization problem with the objective function being the sum of the squares of the differences between the measured quantities at each sensor location and the corresponding computed quantities for the assumed boundary traction distribution the constraints that the missing traction distribution lies within a certain portion of the boundary of the object are imposed this is done using the step retraction and inverse penalty function approach in which the objective function is augmented by the constraint equations using a penalty parameter the unknown traction distribution and its location are defined in terms of load and geometric parameters and the sensitivities with respect to these parameters are obtained in the boundary element framework using the implicit differentiation approach a series of numerical examples involving the reconstruction of linear parabolic and trigonometric boundary tractions respectively are solved using the present approach the effect of gaussian errors in the sensors is also studied good reconstruction of the missing boundary tractions is obtained for the examples studied the advantages of the present boundary element formulation over the corresponding finite element formulations are also outlined

on a new class of abstract integral equations and applications abstract in this paper we introduce a new class of abstract integral equations which enables us to study in a unified manner several different types of differential equations

a boundary element formulation for the inverse elastostatics problem iesp of flaw detection a boundary integral formulation is presented for the detection of flaws in planar structural members from the displacement measurements given at some boundary locations and the applied loading such inverse problems usually start with an initial guess for the flaw location and size and proceed towards the final configuration in a sequence of iterative steps a finite element formulation will require a remeshing of the object corresponding to the revised flaw configuration in each iteration making the procedure computationally expensive and cumbersome no such remeshing is required for the boundary element approach the inverse problem is written as an optimization problem with the objective function being the sum of the squares of the differences between the measured displacements and the computed displacements for the assumed flaw configuration the geometric condition that the flaw lies within the domain of the object is imposed using the internal penalty function approach in which the objective function is augmented by the constraint using a penalty parameter a first order regularization procedure is also implemented to modify the objective function in order to minimize the numerical fluctuations that may be caused in the numerical procedure due to errors in the experimental measurements for displacements the flaw configuration is defined in terms of geometric parameters and the sensitivities with respect to these parameters are obtained in the boundary element framework using the implicit differentiation approach a series of numerical examples involving the detection of circular and elliptical flaws of various sizes and orientations are solved using the present approach good predictions of the flaw shape and location are obtained

numerical methods for inverse singular value problems3 two numerical methods one continuous and the other discrete are proposed for solving inverse singular value problems the first method consists of solving an ordinary differential equation obtained from an explicit calculation of the projected gradient of a certain objective function the second method generalizes an iterative process proposed originally by friedland nocedal and overton siam j numer anal 24 1987 pp 634 667 for solving inverse eigenvalue problems with the geometry understood from the first method it is shown that the second method also the method proposed by friedland nocedal and overton for inverse eigenvalue problems is a variation of the newton method while the continuous method is expected to converge globally at a slower rate in finding a stationary point of the objective function the discrete method is proved to converge locally at a quadratic rate if there is a solution some numerical examples are presented

identification of geometric shapes and material properties of inclusions in two dimensional finite bodies by boundary parameterization a system identification scheme based on the boundary element method bem is proposed to determine geometric shape and elastic material properties of an inclusion in a finite body the proposed algorithm is based on the minimization of least squared errors between measured displacement and calculated displacement by a boundary element model a regularization function that consists of the geometric term and material property term is added to the error function to overcome ill posedness of inverse problems to deal with the shape variation of an inclusion during the optimization process the boundary parameterization technique is applied to the bem the recursive quadratic programming rqp technique with line search is used for optimization

inequalities for the schatten p norm iv we present some inequalities for the schattenp norm of operators on a hilbert space it is shown among other things that ifa is an operator such that rea a 0 then for any operatorx ax xa p 2a x p also for any two operatorsa andb a b 2 2 a b 2 2 2 a b 2 2

on perturbations of matrix pencils with real spectra a revisit this paper continues earlier studies by bhatia and li on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectra a unifying framework for creating crucial perturbation equations is developed with the help of a recent result on generalized commutators involving unitary matrices new and much sharper bounds are obtained

an integral equations method combined minimum norm solution for 3d elastostatics cauchy problem abstract in this paper we establish new density results for the equilibrium equations based on the denseness result of the elastic potential functions the cauchy problem for the equilibrium equations is investigated for this ill posed problem we construct a regularizing solution using the single layer potential function the well posedness of the regularizing solution as well as the convergence property is rigorously analyzed the advantage of the proposed scheme is that the regularizing solution is of the explicit analytic solution and therefore is easy to be implemented the method combines minimum norm solution with morozov discrepancy principle to solve an inverse problem convergence and stability estimates are then given with some examples for numerical verification on the efficiency of the proposed method the numerical convergence accuracy and stability of the method with respect to the discretisation about the integral equations on pseudo boundary and the distance between the pseudo boundary and the real boundary of the solution domain and decreasing the amount of noise added into the input data respectively are also analysed with some examples

a boundary element solution of an inverse elasticity problem and applications to determining residual stress and contact stress abstract a boundary element solution is developed for an inverse elasticity problem in this inverse problem boundary conditions are incompletely specified strains can be determined experimentally in practice at a number of internal points and used as input to completely resolve these boundary conditions in this paper these strains including random errors are numerically simulated this inverse problem finds applications in the evaluation of residual stress and contact stress in contrast to previous studies the construction of the sensitivity matrix is embedded in the boundary element formulation thereby avoiding the solution of a series of forward problems further the effects of prescribed non zero boundary conditions and body forces are included in the relation between measured strains and the primary traction unknowns unfortunately the inverse problem is still ill posed physical constraints are introduced to stabilize the solution as a result the algorithm presented here has reasonable tolerance to error in the measurement of strains numerical examples are given to validate the inverse algorithm in these examples the input strains are numerically simulated and stable and accurate solutions are obtained with up to 5 random error in the input

a perturbation bound for definite pencils we attempt to generalize a well known result on spectral variations of a hermitian matrix due to mirsky to the definite generalized eigenvalue problem we also point out that some results on perturbations of definite pencils due to stewart can be slightly improved

a backward error for the inverse singular value problem a backward error for inverse singular value problems with respect to an approximate solution is defined and an explicit expression for the backward error is derived by extending the approach described in j g sun backward errors for the inverse eigenvalue problem numer math 82 1999 339 349 the expression may be useful for testing the stability of practical algorithms

existence for impulsive neutral integrodifferential inclusions with nonlocal initial conditions via fractional operators abstract this paper is mainly concerned with existence of mild solutions for a first order impulsive neutral integrodifferential inclusions with nonlocal initial conditions in norm we assume that the linear part generates an analytic semigroup and transform it into an integral inclusion by using a fixed point theorem for multi valued maps due to dhage a main existence theorem is established finally we present an example to illustrate this main theorem

generalized eigenvalues of a definite hermitian matrix pair abstract in this note we study some basic properties of generalized eigenvalues of a definite hermitian matrix pair in particular we prove an interlacing theorem and a minimax theorem we also obtain upper bounds for the variation of the generalized eigenvalues under perturbation these results extend and improve those of r c li j g sun and g w stewart on the topic

existence for a class of partial differential equations with nonlocal conditions abstract this paper is concerned with the existence of mild and classical solutions of nonlocal cauchy problems we assume that the linear part generates an analytic compact bounded semigroup and that the nonlinear part is a holder continuous function with respect to the fractional power norm of the linear part considering the nonlocal conditions in the norm we generalize the recent conclusions on this topic the results obtained will be applied to a class of functional partial differential equations with nonlocal conditions in 1 2 norm

fading regularization mfs algorithm for inverse boundary value problems in two dimensional linear elasticity abstract we investigate the numerical reconstruction of the missing displacements dirichlet data and tractions neumann data on an inaccessible part of the boundary in the case of two dimensional linear isotropic elastic materials from the knowledge of over prescribed noisy measurements taken on the remaining accessible boundary part this inverse problem is solved using the fading regularization method originally proposed by cimetiere et al 2000 2001 for the laplace equation in conjunction with a meshless method namely the method of fundamental solutions mfs the stabilisation of the numerical method proposed herein is achieved by stopping the iterative procedure according to morozov s discrepancy principle morozov 1966

load distribution modelling for pin jointed trusses by an inverse approach the paper considers the load distribution modelling for pin jointed trusses when an approximate value of the normal stress on a suitable number of elements is known this inverse problem is formulated in the least square sense directly relating the stress on the elements with the external loads and successively solved using an iterative scheme which uses a standard decomposition method for the stiffness matrix and the conjugate direction strategy in order to obtain a regularized solution of this problem and so cut out the errors contained in the known term of the equation system the generalized cross validation criterion is used in a form suitable for iterative methods some numerical results allow an analysis of the algorithm s performance

investigation of regularization parameters and error estimating in inverse elasticity problems the method of tarantola1 based on bayesian statistical theory for solving general inverse problems is applied to inverse elasticity problems and is compared to the spatial regularization technique presented in schnur and zabaras 2 it is shown that when normal gaussian distributions are assumed and the error in the data is uncorrelated the bayesian statistical theory takes a form similar to the deterministic regularization method presented earlier in schnur and zabaras 2 as such the statistical theory can be used to provide a statistical interpretation of regularization and to estimate error in the solution of the inverse problem examples are presented to demonstrate the effect of the regularization parameters and the error in the initial data on the solution

on computing the forces from the noisy displacement data of an elastic body this study is concerned with the accurate computation of the unknown forces applied on the boundary of an elastic body using its measured displacement data with noise vision based minimally intrusive force sensing using elastically deformable grasping tools is the motivation for undertaking this problem since this problem involves incomplete and inconsistent displacement force of ail elastic body it leads to an ill posed problem known as cauchy s problem in elasticity vision based displacement measurement necessitates large displacements of the elastic body for reasonable accuracy therefore we use geometrically non linear modelling of the elastic body which was not considered by others who attempted to solve cauchy s elasticity problem before we present two methods to solve the problem the first method uses the pseudo inverse of an over constrained system of equations this method is shown to be not effective when the noise in the measured displacement data is high we attribute this to the appearance of spurious forces at regions where there should not be any forces the second method focuses on minimizing the spurious forces by varying the measured displacements within the known accuracy of the measurement technique both continuum and frame elements are used in the finite element modelling of the elastic bodies considered in the numerical examples the performance of the two methods is compared using seven numerical examples all of which show that the second method estimates the forces with an error that is not more than the noise in the measured displacements an experiment was also conducted to demonstrate the effectiveness of the second method in accurately estimating the applied forces

an algorithm for symmetric generalized inverse eigenvalue problems abstract using qr like decomposition with column pivoting and least squares techniques we propose a new and efficient algorithm for solving symmetric generalized inverse eigenvalue problems and give its locally quadratic convergence analysis we also present some numerical experiments which illustrate the behaviour of our algorithm

existence and uniqueness of mild solution of time fractional semilinear differential equations with a nonlocal final condition abstract in this paper we investigate a time fractional semilinear differential equation with final nonlocal condition u x t g u x j 1 m j u x t j under some assumptions we establish the existence and uniqueness of a mild solution in some suitable spaces of continuous functions the results are based on some fixed point theorems two examples are presented to illustrate our results

error estimates for the combined spatial and angular approximations of the transport equation for slab geometry we study the convergence of the discrete ordinates method in the numerical solution of the transport equation for slab geometry in particular the combined effect of spatial and angular approximations is analyzed general conditions are given which guarantee the stability of the combined approximations error estimates are derived for both the scalar flux in the l p norm 1 leqq p leqq infty and for the approximate critical eigenvalues a comparison with numerical results indicates that the eigenvalue error estimates are optimal

a relaxation method of an alternating iterative algorithm for the cauchy problem in linear isotropic elasticity we propose two algorithms involving the relaxation of either the given dirichlet data boundary displacements or the prescribed neumann data boundary tractions on the over specified boundary in the case of the alternating iterative algorithm of kozlov et al 16 applied to cauchy problems in linear elasticity a convergence proof of these relaxation methods is given along with a stopping criterion the numerical results obtained using these procedures in conjunction with the boundary element method bem show the numerical stability convergence consistency and computational efficiency of the proposed method

on perturbations of matrix pencils with real spectra perturbation bounds for the generalized eigenvalue problem of a diagonalizable matrix pencil a ab with real spectrum are developed it is shown how the chordal distances between the generalized eigenvalues and the angular distances between the generalized eigenspaces can be bounded in terms of the angular distances between the matrices the applications of these bounds to the spectral variations of definite pencils are conducted in such a way that extra attention is paid to their peculiarities so as to derive more sophisticated perturbation bounds our results for generalized eigenvalues are counterparts of some celebrated theorems for the spectral variations of hermitian matrices such as the weyl lidskii theorem and the hoffman wielandt theorem and those for generalized eigenspaces are counterparts of the celebrated davis kahan sin 0 sin 20 theorems for the eigenspace variations of hermitian matrices the paper consists of two parts part i is for generalized eigenvalue perturbations while part ii deals with generalized eigenspace perturbations

some inequalities for norm ideals several inequalities for norms of operators are extended to more operators and or to more norms these include results of halmos and bouldin on approximating a normal operator by another with restricted spectrum the powers stormer and the van hemmen ando inequalities for the distance between the square roots of two positive operators and also some recent generalisations of these latter results by kittaneh

a boundary element strategy for elastostatic inverse problems involving uncertain boundary conditions in this paper a convenient strategy is developed to find solutions for a class of uncertain boundary value problems by the boundary element method bem such problems are ill posed but ill conditioning of the associated algebraic systems of equations can be controlled to a large extent and useful boundary data can be obtained despite ill conditioning interior data of not only sufficient quantity but also of good quality at good locations contribute to good solutions our strategy permits the condition number of the algebraic systems as a function of interior data locations to be monitored such that measured data from displacement sensors and or strain sensors at locations found to be good ones for the problem at hand can be used the present strategy is based upon the concept of a green s function library through partitioning of the bem algebraic system algebraic systems are solved using least squares via singular value decomposition svd the library idea takes advantage of modern data storage and retrieval technology and permits the process of repeated trials in order to determine good data sensor locations to be done quickly and efficiently several numerical examples are given to demonstrate the strategy some examples examine the consequences of errors in measured data copyright 1999 john wiley sons ltd

relaxation procedures for an iterative mfs algorithm for the stable reconstruction of elastic fields from cauchy data in two dimensional isotropic linear elasticity we investigate two numerical procedures for the cauchy problem in linear elasticity involving the relaxation of either the given boundary displacements dirichlet data or the prescribed boundary tractions neumann data on the over specified boundary in the alternating iterative algorithm of kozlov et al 1991 the two mixed direct well posed problems associated with each iteration are solved using the method of fundamental solutions mfs in conjunction with the tikhonov regularization method while the optimal value of the regularization parameter is chosen via the generalized cross validation gcv criterion an efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase is also presented the mfs based iterative algorithms with relaxation are tested for cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence stability accuracy and computational efficiency of the proposed method

finding a positive definite linear combination of two hermitian matrices abstract let a and b be n by n hermitian matrices over the complex field a result of au yeung 1 and stewart 8 states that if x a ib x 0 for all nonzero n vectors x then there is a linear combination of a and b which is positive definite in this article we present an algorithm which finds such a linear combination in a finite number of steps we also discuss the implementation of the algorithm in case a and b are real symmetric sparse matrices

numerical solution of nonlinear inverse heat conduction problem with a radiation boundary condition a finite difference solution for the transient nonlinear heat conduction equation in a finite slab with a radiation boundary condition is proposed an implicit finite difference approximation is used which enables accurate estimation of the surface temperature as well as prevention of oscillation of computed values at the surfaces a two time level implicit method is used while taylor s forward projection method is employed for taking account of the nonlinearities an iterative method is described which predicts unknown surface conditions an example is illustrated which is typical of those that arise in practical applications the results demonstrate that the method is remarkable in its stability to predict surface conditions without debilitation

absolute and relative weyl theorems for generalized eigenvalue problems abstract weyl type eigenvalue perturbation theories are derived for hermitian definite pencils a b in which b is positive definite the results provide a one to one correspondence between the original and perturbed eigenvalues and give a uniform perturbation bound we give both absolute and relative perturbation results defined in the standard euclidean metric instead of the chordal metric that is often used

the perturbation bounds for eigenspaces of a definite matrix pair leta andb be hermitian matrices the matrix pair a b is called definite pair and the corresponding eigenvalue problem ax bx is definite if c a b equiv mathop min limits left x right 1 x h a ib x 0 the perturbation bounds for eigenspaces of a definite pair on every unitary invariant matrix norm were obtained by imposing additional restrictions on the location of the generalized eigenvalues thus it gives a positive answer for an open question proposed by stewart 7 the famous davis kahan sin theorems and sin 2 theorem 2 can also be deduced from the present results

the nearest definite pair for the hermitian generalized eigenvalue problem the generalized eigenvalue problem ax lambda bx has special properties when a b is a hermitian and definite pair given a general hermitian pair a b it is of interest to find the nearest definite pair having a specified crawford number delta 0 we solve the problem in terms of the inner numerical radius associated with the field of values of a ib we show that once the problem has been solved it is trivial to rotate the perturbed pair a da b db to a pair widetilde a widetilde b for which lambda min widetilde b achieves its maximum value delta which is a numerically desirable property when solving the eigenvalue problem by methods that convert to a standard eigenvalue problem by inverting b numerical examples are given to illustrate the analysis

a backward error for the symmetric generalized inverse eigenvalue problem abstract in this paper we discuss the backward error for the symmetric generalized inverse eigenvalue problem which extends the result of sun 1999 10 the optimal backward error is defined for symmetric generalized inverse eigenvalue problem with respect to an approximate solution and the upper and lower bounds are derived for the optimal backward error the expressions may be useful for testing the stability of practical algorithms

an inverse method for determining elastic material properties and a material interface the problem consists of determining the location and size of a circular inclusion in a finite matrix and the elastic material properties of the inclusion and the matrix

existence of solutions for a class of abstract differential equations with nonlocal conditions abstract we discuss the existence of mild classical and strict solutions for a class of abstract differential equations with nonlocal conditions our technical approach allows the study of partial differential equations with nonlocal conditions involving partial derivatives or nonlinear expressions of the solution some concrete applications to partial differential equations are considered

existence of mild solutions for fractional integrodifferential equations of sobolev type with nonlocal conditions abstract this paper is concerned with the fractional integrodifferential equations of sobolev type with nonlocal condition in a separable banach space with the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps we obtain the existence result of mild solutions for above equations two examples are given to illustrate the existence theorem

boundary element solution for the cauchy problem in linear elasticity using singular value decomposition abstract in this paper the singular value decomposition svd truncated at an optimal number is analysed for obtaining approximate solutions to ill conditioned linear algebraic systems of equations which arise from the boundary element method bem discretisation of an ill posed boundary value problem in linear elasticity the regularisation parameter namely the optimal truncation number is chosen according to the discrepancy principle the numerical results obtained confirm that the svd bem produces a convergent and stable numerical solution with respect to decreasing the mesh size discretisation and the amount of noise added into the input data

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

on perturbations of matrix pencils with real spectra ii a well known result on spectral variation of a hermitian matrix due to mirsky is the following let a and a be two n x n hermitian matrices and let 1 n and 1 n be their eigenvalues arranged in ascending order then diag 1 1 n n a a for any unitarily invariant norm in this paper we generalize this to the perturbation theory for diagonalizable matrix pencils with real spectra the much studied case of definite pencils is included in this

existence uniqueness and regularity of solutions to semilinear nonlocal functional differential problems abstract in this paper we consider a semilinear nonlocal functional differential problem in a banach space we first establish the existence uniqueness and continuation of a mild solution we then prove some regularity results for this mild solution under different conditions finally we consider some applications of the abstract results

existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions abstract in this work we establish several results about the existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions we assume that the linear part generates a strongly continuous semigroup on a general banach space

an effective algorithm for reconstructing boundary conditions in elastic solids this paper discusses the reconstruction of boundary conditions for linear elastic solids when there are not enough known boundary conditions but the stress tensor is known in a sufficient number of internal points starting with a refined boundary elements discretization of the elastic solid an iterative strategy based on the conjugate gradient method is presented this iterative strategy uses a monte carlo simulation of the generalized cross validation criterion to select the optimal solution the proposed algorithm possesses some advantages with respect to direct approaches indeed it furnishes almost as accurate results but at a low computational cost some numerical results allow an analysis of the algorithm s performance

a finite difference solution of non linear systems of radiative conductive heat transfer equations a finite difference solution for a system of non linear integro differential equations modelling the steady state combined radiative conductive heat transfer is proposed a new backward forward finite difference scheme is formulated for the radiative transfer equation the non linear heat conduction equation is solved using the kirchhoff transformation associated with a centred finite difference scheme the coupled system of equations is solved using a fixed point method which relates to the temperature field an application on a real insulator composed of silica fibres is illustrated the results show that the method is very efficient copyright 2002 john wiley sons ltd

a quadratically convergent algorithm based on matrix equations for inverse eigenvalue problems abstract we propose a quadratically convergent algorithm for inverse symmetric eigenvalue problems based on matrix equations the basic idea is seen in a recent study by ogita and aishima while they derive an efficient iterative refinement algorithm for symmetric eigenvalue problems using special matrix equations in other words this study is interpreted as a unified view on quadratically convergent algorithms for eigenvalue problems and inverse eigenvalue problems based on matrix equations to the best of our knowledge such a unified development of algorithms is provided for the first time since the proposed algorithm for the inverse eigenvalue problems can be regarded as the newton s method for the matrix equations the quadratic convergence is naturally proved our algorithm is interpreted as an improved version of the cayley transform method for the inverse eigenvalue problems although the cayley transform method is one of the effective iterative methods the cayley transform takes o n 3 arithmetic operations to produce an orthogonal matrix using a skew symmetric matrix in each iteration our algorithm can refine orthogonality without the cayley transform which reduces the operations in each iteration it is worth noting that our approach overcomes the limitation of the cayley transform method to the inverse standard eigenvalue problems resulting in an extension to inverse generalized eigenvalue problems

finite difference approximations and superconvergence for the discrete ordinate equations in slab geometry a unified framework is developed for calculating the order of the error for a class of finite difference approximations to the monoenergetic linear transport equation in slab geometry in particular the global discretization errors for the step characteristic diamond and linear discontinuous methods are shown to be of order two while those for the linear moments and linear characteristic methods are of order three and that for the quadratic method is of order four a superconvergence result is obtained for the three linear methods in the sense that the cell averaged flux approximations are shown to converge at one order higher than the global errors

a least squares variational method for full field reconstruction of elastic deformations in shear deformable plates and shells abstract a variational principle is formulated for the inverse problem of full field reconstruction of three dimensional plate shell deformations from experimentally measured surface strains the formulation is based upon the minimization of a least squares functional that uses the complete set of strain measures consistent with linear first order shear deformation theory the formulation which accommodates for transverse shear deformation is applicable for the analysis of thin and moderately thick plate and shell structures the main benefit of the variational principle is that it is well suited for c 0 continuous displacement finite element discretizations thus enabling the development of robust algorithms for application to complex civil and aeronautical structures the methodology is especially aimed at the next generation of aerospace vehicles for use in real time structural health monitoring systems