the effect of two stage sampling on ordinary least squares methods abstract we look at the effect of intracluster correlation on standard procedures in linear regression the ordinary least squares estimator of the coefficient vector performs well in most cases but the usual estimator of cov and procedures based on this such as confidence intervals and hypothesis tests can be seriously misleading the size of the effect however tends to be smaller than the corresponding effect on the variance of an estimated mean in two stage sampling provided that the cluster sample sizes are approximately equal

on the convergence of pade type approximants to analytic functions abstract for a given summability method the okada theorem describes a domain into which an arbitrary power series can be analytically continued if such a domain is known for the geometric series in this paper okada s theorem is extended to more general methods of analytic continuation this results is applied to a special rational approximation the so called pade type approximation

potential integrals associated with quadratic distributions in a triangular domain exact expressions are presented for the potentials at an arbitrary point in space due to two quadratic distributions in a triangular disc these expressions are obtained by means of extensions of the analytical techniques previously developed for evaluating the potential integrals for constant and linear distributions it is shown that the potential due to any quadratic distribution in a triangle may be obtained by using the two expressions derived here together with an expression for the potential corresponding to a linear distribution this latter expression was presented in an earlier paper 1 numerical values obtained through the use of the two expressions are compared with those which result from the numerical evaluation of the potential integrals by triangle quadratures

a new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method the purpose of this paper is to report on a new and efficient method for the evaluation of singular integrals in stress analysis of elastic and elasto plastic solids respectively by the direct boundary element method bem triangle polar co ordinates are used to reduce the order of singularity of the boundary integrals by one degree and to carry out the integration over mappings of the boundary elements onto plane squares the method was subsequently extended to the cubature of singular integrals over three dimensional internal cells as occur in applications of the bem to three dimensional elasto plasticity for this purpose so called tetrahedron polar co ordinates were introduced singular boundary integrals stretching over either linear triangular or quadratic quadilateral isoparametric boundry elements and singular volume integrals extending over either linear tetrahedral or quadratic hexahedral isoparametric internal cells are treated in case of higher order isoparametric boundary elements and internal cells division into a number of subelements and subcells respectively is necessary the analytical investigation is followed by a numerical study restricted to the use of quadratic quadrilateral isoparametric boundary elements this is justified by the fact that such elements as opposed to linear elements yield singular boundary integrals which cannot be integrated analytically the results of the numerical investigation demonstrate the potential of the developed concept

linear convergence for vector sequences and some applications abstract in this paper we first give the relation between some definitions of linearly convergent vector sequences proposed by nievergelt osada and sadok and we choose the first one in order to generalize a theorem which gives the relation between the asymptotic behaviour of the ratios of the errors and that of the differences for linear convergent scalar sequences some properties of the matrix used in the definition of linear convergence are studied and a convergence acceleration result which generalizes some results given by nievergelt and sadok is given

the summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic sextic and octic anharmonic oscillators using nonlinear sequence transformations the strongly divergent rayleigh schrodinger perturbation expansion for the ground state energy of the quartic sextic and octic anharmonic oscillator and a corresponding renormalized perturbation expansion f vinette and j ci ek j math phys 32 3392 1991 are summed by pade approximants by levin s sequence transformation d levin int j comput math b 3 371 1973 and by a closely related sequence transformation which was suggested recently e j weniger comput phys rep 10 189 1989 it is shown that the renormalized perturbation expansion can be summed much more easily than the original perturbation expansion from which it was derived and that levin s sequence transformation diverges and is not able to sum the perturbation expansions the pade summation of the renormalized perturbation expansions gives relatively good results in the quartic and sextic case in the case of the octic anharmonic oscillator even the renormalized perturbation expansion is not pade summable the best results are clearly obtained by the new sequence transformation which for instance is able to sum the renormalized perturbation expansions for the infinite coupling limits of the quartic sextic and octic anharmonic oscillator and which produces at least in the quartic and sextic case extremely accurate results

improvement of accuracy in numerical methods for inverting laplace transforms based on the post widder formula abstract the paper proposes a new computational version for numerical inversion of laplace transforms at a point and on an interval based on the post widder formula in this version the original sequence of post widder approximants is calculated using operations on series and the approximate value of the sought function is constructed as a limit of this sequence using polynomial and rational extrapolation to the limit some procedures are proposed for improvement of accuracy in the problem of inversion at equidistant points of an interval without computing additional approximants an extension of the method to the two dimensional case is discussed the one dimensional version is illustrated with some probabilistic examples involving both explicit and implicit functions the accuracy achieved in these examples with using the standard double precision arithmetic evaluated in terms of relative errors is about 10 10 10 14 even in case of out of scale parameters computational aspects are discussed in comparison with previously known realizations of the post widder method

random group effects and the precision of regression estimates abstract when explanatory variable data in a regression model are drawn from a population with grouped structure the regression errors are often correlated within groups error component and random coefficient regression models are considered as models of the intraclass correlation this paper analyzes several empirical examples to investigate the applicability of random effects models and the consequences of inappropriately using ordinary least squares ols estimation in the presence of random group effects the principal findings are that the assumption of independent errors is usually incorrect and the unadjusted ols standard errors often have a substantial downward bias suggesting a considerable danger of spurious regression

extended procedures for extrapolation to the limit in this paper new procedures for the extrapolation to the limit of slowly convergent sequences and functions are proposed they are based on the notions of error estimates and annihilation operators we obtain generalizations of the discrete and confluent e transformation which are the most general sequence and function transformations known so far it is shown that many transformations studied in the literature are included in our formalism particular cases of these procedures are discussed then several extensions of the e algorithm are given finally the procedure q is applied to our procedures to produce new procedures for extrapolation to the limit

stieltjes transforms and the stokes phenomenon recently berry olver and jones have found uniform asymptotic expansions for the exponentially small remainder terms that result when asymptotic expansions are optimally truncated these uniform expansions describe the rapid change in the behaviour of the remainders as a stokes line is crossed we show how such uniform expansions may be found when a function can be expressed as a stieltjes transform such an approach has the following advantages the uniform expansion is calculated directly non uniform expansions away from the stokes line are readily found and explicit error bounds may be established we illustrate the method by application to the modified bessel function k v z

green s functions for the biharmonic equation bonded elastic media a comprehensive formulation of green s functions for biharmonic equations with respect to perfectly bonded bimaterial linear isotropic elastic media is presented this is accomplished by extending mindlin s nuclei of strain method which employs the method of images the analysis involves properly scaling the nuclei grouping the nuclei into different classes and introducing a matrix structure for each class the strength vectors of the nuclei required at the object and image points to represent the solution are obtained by matrix vector multiplications involving two invariant matrices the reflection matrix and the transmission matrix algebraic expressions for the elements of the reflection and transmission matrices which depend on the elastic properties of the materials are presented

the kauffman model on small world topology abstract we apply kauffman s automata on small world networks to study the crossover between the short range and the infinite range case we perform accurate calculations on square lattices to obtain both critical exponents and fractal dimensions particularly we find an increase of the damage propagation and a decrease in the fractal dimensions when adding long range connections

a continuous euler transformation and its application to the fourier transform of a slowly decaying fuction the euler transformation is a linear sequence transformation to accelerate the convergence of an alternating series the sequence of weights of the transformation is extended to a continuous weight function which can accelerate fourier type integrals including hankel transforms with a slowly convergent integrand we show that the continuous weight function can also be used to compute the fourier transform of a slowly decaying function using fft

a new proof of the cross rule for the e algorithm based on schur complements abstract matrices of the form h ge 1 f are called schur complements they are closely related to elimination procedures and to determinantal identities in this paper the quotient property for schur complements is used to establish the schur complement method a useful tool for proving certain formulas as an example a new proof of the cross rule for the algorithm is presented

estimation under a general partitioned linear model abstract in this paper we consider a general partitioned linear model and a corresponding reduced model we derive a necessary and sufficient condition for the blue for the expectation of the observable random vector under the reduced model to remain blue in the partitioned model the former is shown to be always an admissible estimator under a mild condition we also regard alternative linear estimators and their coincidence with the blue under the partitioned model

new summation technique for rapidly divergent perturbation series hydrogen atom in magnetic field the perturbation series for the ground state energy of the hydrogen atom in the external magnetic field is summed via the sequence transformations the formula for the large order behavior of the partial sums of the series is derived from this formula a new general sequence transformation is suggested this transformation contains free parameters that can be further optimized it is shown that if the renormalization approach is used the optimal choice of these parameters leads to the previously suggested weniger transformation

vector sequence transformations methodology and applications to linear systems in this paper a methodology for the construction of various vector sequence transformations is formulated leading to a unified presentation of the subject and to new results the connections to the general interpolation problem and to projections are discussed various particular cases are examined in more details applications to the solution of systems of linear equations will end the paper and in particular their relation with lanczos method will be studied some numerical examples will be given

properties of ordinary least squares estimators in regression models with nonspherical disturbances abstract a general discussion is presented of the properties of the ols estimator in regression models where the disturbances do not have a scalar identity covariance matrix several new and interesting characterizations are provided together with a synthesis of existing results a distinguishing feature of the paper is the unified treatment of the issues of efficiency and inference the theoretical material is illustrated by examples covering a wide range of models of interest to applied econometricians

a high order 3d boundary integral equation solver for elliptic pdes in smooth domains we present a high order boundary integral equation solver for 3d elliptic boundary value problems on domains with smooth boundaries we use nystrom s method for discretization and combine it with special quadrature rules for the singular kernels that appear in the boundary integrals the overall asymptotic complexity of our method is o n3 2 where n is the number of discretization points on the boundary of the domain and corresponds to linear complexity in the number of uniformly sampled evaluation points a kernel independent fast summation algorithm is used to accelerate the evaluation of the discretized integral operators we describe a high order accurate method for evaluating the solution at arbitrary points inside the domain including points close to the domain boundary we demonstrate how our solver combined with a regular grid spectral solver can be applied to problems with distributed sources we present numerical results for the stokes navier and poisson problems

estimation of time dependent parameters in linear models using cross sections panels or both in this paper we consider the estimation of time dependent parameters in linear models from panel data cross sections or both we determine the fraction of individuals that should be reinterviewed each period in order to minimize the variance of the most efficient estimator of linear combinations of the parameters moreover we derive simple sufficient conditions for the optimal fraction to be zero or one respectively

summability of hermite expansions ii we study the summability of n dimensional hermite expansions where n 1 we prove that the critical index for the riesz summability is n 1 2 we also prove analogues of the fejer lebesgue theorem and riemann s localisation principle when the index of the riesz means is 3n 2 6

on a partitioned linear model and some associated reduced models abstract in this paper we consider a partitioned linear model y x 1 1 x 2 2 2 where is positive definite but x x1 x2 can be rank deficient we also consider some associated reduced models involving only 2 and not 1 and study how far the inferences on the estimable linear functions of 2 in the full model coincide with those in the reduced models the results of aigner and balestra 1988 and nurhonen and puntanen 1992 follow as special cases we also point out a flaw in the paper by nurhonen and puntanen 1992 and correct it suitably finally we apply the results proved to obtain explicitly the statistic for turkey s test of nonadditivity in two way classified data with a block intraclass correlation structure

convergence acceleration methods the past decade abstract the aim of this paper is to present a review of the most significant results obtained the past ten years on convergence acceleration methods it is divided into four sections dealing respectively with the theory of sequence transformations the algorithms for such transformations the practical problems related to their implementation and their applications to various subjects of numerical analysis

asymptotic equivalence of ordinary least squares and generalized least squares in regressions with integrated regressors abstract it is shown that in the multiple regression model y 1 x 1 u t where u t is a stationary autoregressive process and x 1 is an integrated m vector process the asymptotic distributions of the ordinary least squares ols and generalized least squares gls estimators of are identical this generalizes a result obtained by kramer 1986 for two variate regression and extends fixed regressor theory developed by grenander and rosenblatt 1957 our approach uses a multivariate invariance principle and yields explicit representations of the asymptotic distributions in terms of functionals of vector brownian motion we also provide some useful asymptotic results for hypothesis tests of the model thus if x 1 is generated by a vector autoregressive integrated moving average arima r l s model and u t is generated by an independent autoregressive ar p process then and have the same limiting distribution where and are the ols and gls estimators respectively this distribution is nonnor

the sensitivity of ols when the variance matrix is partially unknown we consider the standard linear regression model y xb u with all standard assumptions except that the variance matrix is assumed to be p2x h where x depends on m unknown parameters h 1 2 h m our interest lies exclusively in the mean parameters b or xb we introduce a new sensitivity statistic b1 which is designed to decide whether yl or bk is sensitive to covariance misspeci cation we show that the durbin watson test is inappropriate in this context because it measures the sensitivity of pl 2 to covariance misspeci cation our results demonstrate that the estimator bk and the predictor yl are not very sensitive to covariance misspeci cation the statistic is easy to use and performs well even in cases where it is not strictly applicable 1999 elsevier science s a all rights reserved

analysis and evaluation of singular integrals by the invariant imbedding approach the invariant imbedding formulae for evaluating singular integrals on flat domains are used to analyse the singular integrals which arise in the boundary element method although all orders of singularity are considered the primary objective of the paper is the evaluation of cauchy principal value integrals cpv conditions for boundedness of the cpv are derived and evaluation techniques are presented for situations in which the singular point lies on or is in close proximity to an element boundary specific cases analysed include straight and curved element boundaries and corners other numerical aspects of the formulae are also discussed by way of example the analysis techniques are applied to the volume integrals which arise in continuum inelastic problems

an extended multistep shanks transformation and convergence acceleration algorithm with their convergence and stability analysis the molecule solution of an extended discrete lotka volterra equation is constructed from which a new sequence transformation is proposed a convergence acceleration algorithm for implementing this sequence transformation is found it is shown that our new sequence transformation accelerates some kinds of linearly convergent sequences and factorially convergent sequences with good numerical stability some numerical examples are also presented

accurate numerical integration of singular boundary element kernels over boundaries with curvature use of the green function for the solution of boundary value problems frequently results in singular integral equations algorithms are presented for the accurate and efficient treatment of singular kernels frequently encountered in the boundary element method bem they are based upon the use of appropriately weighted gaussian quadrature formulae together with numerical geometrical transformations of the region of integration the use of high order subdomain expansion functions for interpolation over nonplanar elements allows boundary curvature to be accommodated in particular the handling of green functions with logarithmic and r 1 behaviour are detailed volume integrals with r 2 singularity are outlined operations are performed on a simplex thus resulting in generality and ease of automation this scheme has been incorporated into boundary element method software and successfully applied to a variety of problems

advanced boundary element analysis of two and three dimensional problems of elasto plasticity an advanced formulation of the boundary element method has been developed for inelastic analysis based on an initial stress approach the iterative solution algorithm makes use of an accelerated initial stress approach in which the past history of initial stresses are used to obtain an initial estimate for the current increment in the present analysis the geometry and functions are represented by higher order quadratic shape functions to model complex geometries and rapid functional variations accurately the methods of numerical integration of the kernels particularly the singular type are substantially improved by devising suitable automatic sub segmentation routines that incorporate the recent developments in mapping procedures the formulations have been implemented for two dimensional plane stress plane strain and three dimensional elasto plasticity problems

the hasse principle for similarity of hermitian forms the hasse principle for similarity is established for restricted classes of skew hermitian forms over quaternion division algebras with canonical involution and for hermitian forms over division algebras with involution of the second kind a counterexample is produced to show that the principle cannot hold for skew hermitian forms over quaternion division algebras in general this settles the two final cases of hasse principles for similarity of forms that were missing in the literature

construction of lighthill s unitary functions the imbricate series of unity the poisson sum theorem implies that every spatially periodic function f x can be written as a so called imbricate series that is as the superposition of an infinite number of evenly space copies of a pattern function a x the pattern is the fourier transform of a function a n that specifies the usual fourier coefficients because there are many a n which coincide with a given set of fourier coefficients aj when n is an integer the pattern function a x is not unique in this work we show how to construct pattern functions of the form a x f x w x where f x is the periodic function itself the imbrication of a x and where w x is what lighthill called a unitary function we derive an explicit formula to construct all possible unitary functions and tabulate eight examples we also prove that all unitary functions are pattern functions of unity that is for the imbricate series that sums to f x 1 x

some properties of the sobolev laguerre polynomials abstract in this paper we study the case 0 of the sobolev laguerre polynomials we determine a generating function for the polynomials and an expansion formula

an invariant imbedding method for singular integral evaluation on finite domains the invariant imbedding technique is used to develop versatile and powerful integration formulae for the evaluation of singular integrals on finite domains encountered in continuum problems in engineering and applied science this method is considerably simpler than the several ad hoc integral evaluation methods presented in the recent literature moreover the method provides new insight into the central role played by the residue in the evaluation of principal value integrals this relationship is embodied as a gauge condition the main emphasis of the paper is on developing a general approach from which specific cases follow several examples chosen from different areas of engineering computation are provided in order to show the advantage of this approach

the efficiency of rotating panel designs in an analysis of variance model in this paper we consider the relative efficiency of rotating panel designs in analysis of variance models throughout we assume that the parameter of interest is a linear combination of period means in the analysis of variance model results from spectral theory are used to obtain manageable expressions for the variance of the blue of this parameter relative efficiencies of the blue for rotating panels with different rotation periods are presented e g for the period means themselves of differences or of averages of means moreover we present bounds on the relative efficiency which are valid irrespective of the parameter of interest the analysis shows that the gains from choosing an optimal rotation design can be quite substantial even if the cost of a reinterview equals the cost of a first observation in many cases either the smallest or the highest possible rotation period is optimal the analysis is illustrated with an empirical example concerning monthly consumer expenditures on food and clothing

solution of integral equations using generalised inverse function valued pade approximants i abstract neumann series solutions for the linear integral equation x 1 1 0 1 x y y d y converge for small values of we use generalised inverse function valued pade approximants to accelerate the convergence of the neumann series and to estimate the singular value of these estimates are found to compare very favourably with those from the fredholm determinant method and the pade approximant method

convergence acceleration by extraction of linear subsequences logarithmic sequences are usually difficult to accelerate in this paper we show how to extract a subsequence converging linearly this subsequence can be easily accelerated by classical algorithms theoretical results are given as well as an algorithmic extraction procedure numerical examples illustrate the results

a study of semiiterative methods for nonsymmetric systems of linear equations given a nonsingular linear systema x b a splittinga m n leads to the one step iteration 1 x m t x m 1 c witht m 1n andc m 1 b we investigate semiiterative methods sim s with respect to 1 under the assumption that the eigenvalues oft are contained in some compact set of with 1 there exist sim s which are optimal with respect to but except for some special sets such optimal methods are not explicitly known in general using results about maximal convergence of polynomials and uniformly distributed nodes from approximation and function theory we describe here sim s which are asymptotically optimal with respect to it is shown that euler methods extensively studied by niethammer varga nv are special sim s various algorithms for sim s are also derived here a 1 1 correspondence between euler methods and sim s generated by generalized faber polynomials is further established here this correspondence gives that asymptotically optimal euler methods are quite near the optimal sim s

asymptotic summation of hermite series a new method for the numerical evaluation of slowly convergent or even divergent series involving the hermite functions is presented the author considers series with either of the forms where cm decays algebraically as m to infinity the first series is a fourier hermite series while the second arises in the representation of green functions for problems whose eigenfunctions involve the hermite functions by use of the poisson summation formula the author derives rapidly convergent asymptotic expansions for the remainders of these series after a sufficiently large number of terms the series can then be evaluated as a partial sum plus an asymptotic approximation to its remainder the asymptotic expansion for the remainder of g x y also reveals the nature of the possible singular behaviour of this series near x y

on the equivalence of estimations under a general linear model and its transformed models abstract some necessary and sufficient conditions are given for two equalities of ordinary least squares estimators and best linear unbiased estimators of an estimable vector of parametric functions under a general linear model and its transformed linear model to hold

asymptotics on laguerre or hermite polynomial expansions and their applications in gauss quadrature abstract in this paper we present asymptotic analysis on the coefficients of functions expanded in forms of laguerre or hermite polynomial series which shows the decay of the coefficients and derives new error bounds on the truncated series moreover by applying the asymptotics new estimates on the errors for gauss laguerre radau laguerre and gauss hermite quadrature are deduced these results show that gauss laguerre type and gauss hermite type quadratures are nearly of same convergence rates

some special interpolation formulae for triangular and quadrilateral elements presented herein are methods to generate special interpolation formulae of the following type i c0 continuous interpolation over triangular elements which induces a given type of singularity for the first derivatives at one of the vertices and yet preserves rigid and constant strain motions ii c1 continuous interpolation over triangular elements which induces a given type of singularity for second derivatives at one of the vertices

the epsilon algorithm and related topics the epsilon algorithm is recommended as the best all purpose acceleration method for slowly converging sequences it exploits the numerical precision of the data to extrapolate the sequence to its limit we explain its connections with pade approximation and continued fractions which underpin its theoretical base then we review the most recent extensions of these principles to treat application of the epsilon algorithm to vector valued sequences and some related topics in this paper we consider the class of methods based on using generalised inverses of vectors and the formulation specifically includes the complex case wherever possible

new vector sequence transformations many numerical methods produce sequences of vectors converging to the solution of a problem when the convergence is slow the sequence can be transformed into a new vector sequence which under some assumptions converges faster to the same limit the construction of a sequence transformation is based on its kernel that is the set of sequences which are transformed into a constant sequence in this paper new vector sequence transformations are built from kernels which extent those of the most general transformations known so far

on condition numbers of the shanks transformation abstract quasi linear functions generate sequence transformation methods whose conditioning depends upon the nature of the sequence to be accelerated these methods are often well conditioned when they are applied to alternating sequences however they are relatively ill conditioned in case of monotonic convergence the condition numbers of the shanks transformation e k s n are given in order to prove that the closely related e algorithm to a such transformation is ill conditioned when performed on the set of totally monotonic sequences in the same way we show that this algorithm is well conditioned on the set of totally oscillating sequences

convergence acceleration of fourier series by analytical and numerical application of poisson s formula a form of the poisson summation formula appropriate for the transformation of infinite fourier series is derived and shown to be applicable to slowly converging series arising in the solution of laplace s equation in a rectangular electrochemical cell the result is a rapidly convergent fourier series which is particularly useful in giving the potential close to the electrode surface results obtained from the analytical expression are found to be in close agreement with those resulting from numerical evaluation of the fourier integrals using simpson s rule and the euler transformation and direct summation by using goertzel s 1958 algorithm

singular and near singular integrals in the bem a global approach a unified approach for analyzing and evaluating singular and near singular integrals relevant to the boundary element method bem is obtained the original n dimensional integral is mapped to one that is performed exclusively on the boundary of the integration domain therefore the dimensionality of the integration is reduced by l and integrand evaluations close to the singularity are avoided the new formulae are obtained through a straightforward one dimensional analytical integration regardless of the dimensionality of the problem and can be used generally for numerical integration the formulae for evaluating near singular integrals are a generalization of those obtained by the invariant imbedding technique for singular integrals and reduce to the singular integral formulae in the limit in this sense the singular integrals are treated as limits or continuations of nonsingular ones this leads to a general interpretation that includes the singular integrals as a special case in particular t

completely monotonic functions associated with the gamma function and its q analogues several functions involving the gamma function x and the q gamma function q x are proved to be completely monotonic some of these results are used to establish the infinite divisibility of a number of probability distributions defined via their moment generating functions

calculating normalization constants of closed queueing networks by numerically inverting their generating functions a new algorithm is developed for calculating normalization constants partition functions and moments of product form steady state distributions of closed queuing networks and related models the essential idea is to numerically invert the generating function of the normalization constant and related generating functions appearing in expressions for the moments it is known that the generating function of the normalization constant often has a remarkably simple form but numerical inversion evidently has not been considered before for p dimensional transforms as occur with queuing networks having p closed chains the algorithm recursively performs p one dimensional inversions the required computation grows exponentially in the dimension but the dimension can often be reduced by exploiting conditional decomposition based on special structure for large populations the inversion algorithm is made more efficient by computing large sums using euler summation the inversion algorithm also has a very low storage requirement a key ingredient in the inversion algorithm is scaling an effective static scaling is developed for multichain closed queuing networks with only single server and optionally infinite server queues an important feature of the inversion algorithm is a self contained accuracy check which allows the results to be verified in the absence of alternative algorithms

the isometry classification of hermitian forms over division algebras abstract the isometry classification problem occupies a central role in the theory of quadratic and hermitian forms this article is a survey of results on the problem for quadratic and hermitian forms over a field and also for hermitian and skew hermitian forms over a noncommutative division algebra with involution rather than adopting a very abstract approach the problems are stated in matrix or linear algebraic terms the known solutions depend crucially on the particular field considered although there are some general results which are mentioned while many of the results date back a long time some recent results especially those on skew hermitian forms over a quaternion algebra over a number field are included

bayesian estimation and prediction using asymmetric loss functions abstract estimators and predictors that are optimal relative to varian s asymmetric linex loss function are derived for a number of well known models their risk functions and bayes risks are derived and compared with those of usual estimators and predictors it is shown that some usual estimators for example a scalar sample mean or a scalar least squares regression coefficient estimator are inadmissible relative to asymmetric linex loss by providing alternative estimators that dominate them uniformly in terms of risk

comparison of four nonlinear transforms on some classes of logarithmic fixed point sequences abstract let log be the set of logarithmic sequences i e of convergent sequences sn satisfying lim e n 1 e n 1 where en sn s and s limsn this paper is devoted to the comparison of four nonlinear sequence transforms on some subsets lf r of log for any positive integer r lf r denotes the set of fixed point sequences sn whose associated error sequences en sn s s limsn have an asymptotic expansion of the following type en 1 en i 1 ien1 ir where 1 c 0 r 1 2 r 1 2 1 2 is different from zero for sn lf r there holds e n a 1 n 1 r o n 1 1 r log n with a 1 r 1 1 r the four are respectively modifications of the algorithm and of the iterated 2 transform the iterated lubkin s transform and the algorithm of brezinski all of them accelerate the convergence of sequences in lf r we give accurate results concerning the asymptotic behaviour of transformed sequences we also study two algorithms combining the second and third transforms numerical examples are given to illustrate theoretical results

a study of optimal membrane triangles with drilling freedoms abstract this article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms the term optimal is used in the sense of exact inplane pure bending response of rectangular mesh units of arbitrary aspect ratio following a comparative summary of element formulation approaches the construction of an optimal three node triangle using the andes formulation is presented the construction is based upon techniques developed by 1991 in student term projects but taking advantage of the more general framework of templates developed since the optimal element that fits the andes template is shown to be unique if energy orthogonality constraints are enforced two other formulations are examined and compared with the optimal model retrofitting the conventional linear strain triangle element by midpoint migrating and congruential transformations is shown unable to produce an optimal element while rank deficiency is inevitable use of the quadratic strain field of the 1988 allman triangle or linear filtered versions thereof is also unable to reproduce the optimal element moreover these elements exhibit serious aspect ratio lock these predictions are verified on benchmark examples

optimal experimental design for error components models on peut utiliser l observation pre experimentale du groupe de traitement comme alternative a l etablissement d un groupe de controle on analyse la substitution entre ces deux types de controles comme une fonction de leur cout relatif et du contenu de l information

the continuation approach a general framework for the analysis and evaluation of singular and near singular integrals the continuation approach presented in this paper is a simple and unified framework for analyzing and computing a large class of singular and near singular integrals such as those that arise in the boundary element method the analysis formulates singular and near singular integrals consistently as instances of a single phenomenon with all types of algebraic singularities treated in a similar way for domains of arbitrary dimension singular integrals are viewed merely as continuations of nonsingular but perhaps near singular ones by placing the singularity of the integrand outside the integration domain and taking the limit as it approaches the domain the technique exploits the functional homogeneity shared by the green s functions of many physical problems for flat surfaces this allows the integral to be mapped to the contour of the integration domain curved surfaces are handled by projecting the integration domain to a tangent hyperplane where the singular components of the integral can be

a new concept in near singular integral evaluation the continuation approach the functional homogeneity of green functions is exploited in the derivation of continuation formulae for the accurate evaluation of near singular integrals these formulae provide a means of systematically continuing such unconventional integrals as the principal value and finite part integrals of singular functions to conventional integrals of nonsingular functions a new concept the notion of continuum integral which is applicable to singular as well as to nonsingular integrals is introduced as a generalization of principal value and finite part integrals numerical examples are provided that illustrate the computational advantages of the continuation method and give a new perspective on the subtleties of singular and near singular integrals

numerical analysis 2000 vol ii interpolation and extrapolation multivariate polynomial interpolation is a basic and fundamental subject in approximation theory and numerical analysis which has received and continues receiving not deep but constant attention in this short survey we review its development in the rst 75 years of this century including a pioneering paper by kronecker in the 19th century c 2000 elsevier science b v all rights reserved