a study of the performance of neville elimination using two kinds of partitioning techniques abstract in this paper a method to compute the solution of a system of linear equations by means of neville elimination is described using two kinds of partitioning techniques block and block striped this type of approach is especially suited to the case of totally positive linear systems which is present in different fields of application although neville elimination carried out more floating point operations than gaussian elimination in some cases in this study we confirm that these advantages disappear when we use multiprocessor systems on the other hand the overall parallel run time of neville elimination is better than gauss time as neville elimination uses a lower cost communication model

communication complexity of the gaussian elimination algorithm on multiprocessors abstract this paper proposes a few lower bounds for communication complexity of the gaussian elimination algorithm on multiprocessors three types of architectures are considered a bus architecture a nearest neighbor ring network and a nearest neighbor grid network it is shown that for the bus and the ring architectures the minimum communication time is o n2 independent of the number of processors while for the grid it is reduced to o k built 1 2 n2 o k built1 2 n for a lock step gaussian elimination algorithm and to o k built 1 2 n2 o k built1 2 for any pipelined gaussian elimination algorithm where k is the total number of processors the practical implications of these bounds are discussed

a parallel boundary element formulation for determining effective properties of heterogeneous media this paper presents a parallel implementation of the boundary element method for mimd computer architectures to determine the effective properties of two heterogeneous physical systems the first physical system is comprised of spheres sedimenting in a viscous fluid at low reynolds numbers the effective property is characterized by the hindered settling function which is a measure of the average sedimentation velocity the second physical system is a short fibre reinforced composite the effective property for this system is the composite modulus the determination of effective properties of heterogeneous media requires performing statistical analyses of several realizations of physical systems based on defining characteristics of the media the boundary element method is particularly well suited for studying such systems because of the simplification in the discretization associated with the method however as the number of heterogeneities to be modeled is increased so are the computational demands parallel computation offers the opportunity to model systems of greater complexity we discuss a parallel boundary element formulation based on the torus wrap mapping in this approach blocks of the coefficient matrix associated with the discretized boundary element equations are assigned to processors as opposed to more traditional parallel boundary element implementations where rows or columns are assigned to processors the torus wrap mapping can be shown to minimize communication volume between processors during the lu factorization therefore the present formulation scales well with increases in the number of processors

numerical linear algebra algorithms and software abstract the increasing availability of advanced architecture computers has a significant effect on all spheres of scientific computation including algorithm research and software development in numerical linear algebra linear algebra in particular the solution of linear systems of equations lies at the heart of most calculations in scientific computing this paper discusses some of the recent developments in linear algebra designed to exploit these advanced architecture computers we discuss two broad classes of algorithms those for dense and those for sparse matrices

total positivity and its applications preface i spline functions total positivity of the spline kernel and its applications b bojanov total positivity properties of lb splines t lyche l l schumaker total positivity and splines k morken totally positive systems and interpolation by subspaces of generalized splines m sommer h strauss ii matrix theory preservation of total nonnegativity under the hadamard product and related topics j garloff d g wagner vertex implications for totally nonnegative under the hadamard product and related topics j garloff on factorizations of totally positive matrices j garloff on factorizations of totally positive matrices m gasca j m pena iii geometric modeling total positivity and optimal bases j m carnicer j m pena total positivity and the shape of curves t n t goodman tchebycheff curves m l mazure h pottmann iv probability and mathematical biology analytical and probabilistic methods for totally positive matrices g s goodman some inequalities of total positivity in pure and applied mathematics s karlin z ziegler new directions and problems of multivariate total positivity motivated by genetic recombination probabilities s karlin v approximation theory tchebycheff spaces and total positivity j m carnicer j m pena cebysev and weak cebysev systems r a zalik vi complex analysis zero sets of entire fourier transforms of multiply positive density functions o m katkova vii statistics total nonnegativity of moment matrices and its application to e optimal designs in polynomial regression b heiligers analysis of regression dependence in 2 xn bivariate distributions and some applications in contingency tables s kasala m b rao viii real analysis total positivity and nonlinear analysis r q jia solutions of certain functional equations s karlin alternance and snakes in the nonlinear finite moment problem k tatalian ix combinatorics the applications of total positivity to combinatorics and conversely f brenti x integral equations spectral properties of totally positive kernels and matrices a pinkus index

model based analyses of bioequivalence crossover trials using the stochastic approximation expectation maximisation algorithm in this work we develop a bioequivalence analysis using nonlinear mixed effects models nlmem that mimics the standard noncompartmental analysis nca we estimate nlmem parameters including between subject and within subject variability and treatment period and sequence effects we explain how to perform a wald test on a secondary parameter and we propose an extension of the likelihood ratio test for bioequivalence we compare these nlmem based bioequivalence tests with standard nca based tests we evaluate by simulation the nca and nlmem estimates and the type i error of the bioequivalence tests for nlmem we use the stochastic approximation expectation maximisation saem algorithm implemented in monolix we simulate crossover trials under h 0 using different numbers of subjects and of samples per subject we simulate with different settings for between subject and within subject variability and for the residual error variance the simulation study illustrates the accuracy of nlmem based geometric means estimated with the saem algorithm whereas the nca estimates are biased for sparse design nca based bioequivalence tests show good type i error except for high variability for a rich design type i errors of nlmem based bioequivalence tests wald test and likelihood ratio test do not differ from the nominal level of 5 type i errors are inflated for sparse design we apply the bioequivalence wald test based on nca and nlmem estimates to a three way crossover trial showing that omnitrope sandoz gmbh kundl austria powder and solution are bioequivalent to genotropin pfizer pharma gmbh karlsruhe germany nlmem based bioequivalence tests are an alternative to standard nca based tests however caution is needed for small sample size and highly variable drug

analysis and convergence of a covolume method for the generalized stokes problem we introduce a covolume or mac like method for approximating the generalized stokes problem two grids are needed in the discretization a triangular one for the contimlity equation and a quadrilateral one for the momentum equation the velocity is approximated using nonconforming piecewise linears and the pressure piecewise constants error in the l 2 norm for the pressure and error in a mesh dependent h 1 norm as well as in the l 2 norm for the velocity are shown to be of first order provided that the exact velocity is in h 2 and the true pressure in h i we also introduce the concept of a network model into the discretized linear system so that an efficient pressure recovering technique can be used to simplify a great deal the computational work involved in the augmented lagrangian method given is a very general decomposition condition under which this technique is applicable to other fluid problems that can be formulated as a saddle point problem

superconvergence and asymptotic expansion for semidiscrete bilinear finite volume element approximation of the parabolic problem abstract we first derive the asymptotic expansion of the bilinear finite volume element for the linear parabolic problem by employing the energy embedded method on uniform grids and then obtain a high accuracy combination pointwise formula of the derivatives for the finite volume element approximation based on the above asymptotic expansion furthermore we prove that the approximate derivatives have the convergence rate of order two numerical experiments confirm the theoretical results

an analysis of scatter decomposition a formal analysis of a powerful mapping technique known as scatter decomposition is provided scatter decomposition divides an irregular computational domain into a large number of equally sized pieces and distributes them modularly among processors a probabilistic model of workload in one dimension is used to formally explain why and when scatter decomposition works the first result is that if a correlation in workload is a convex function of distance then scattering a more finely decomposed domain yields a lower average processor workload variance the second result shows that if the workload process is a stationary gaussian and the correlation function decreases linearly in distance until becoming zero and then remain zero scattering a more finely decomposed domain yields a lower expected maximum processor workload it is shown that if the correlation function decreases linearly across the entire domain then among all mappings that assign an equal number of domain pieces to each processor scatter decomposition minimizes the average processor workload variance the dependence of these results on the assumption of decreasing correlation is illustrated with situations where a coarser granularity actually achieves better load balance

bias of two one sided tests procedures in assessment of bioequivalence the current applications of schuirmann s two one sided tests procedure for the original scale ignore the variability of the least squares mean of the reference formulation when it substitutes for the unknown reference average of pharmacokinetic responses we propose a modified two one sided test procedure that takes into account the variability of the least squares mean of the reference formulation the non parametric version of the modified procedure is also available we conducted a simulation study to examine the true level of significance and empirical power of four current parametric and non parametric two one sided tests procedures under a 2 x 2 crossover design with different combinations of sample size intrasubject variability and correlation between the two responses from a subject both theoretical results and empirical evidence show that the true level of significance of the current two one sided tests procedures converges to 0 5 when the correlation of the two responses approaches 1 however not only is the modified two one sided tests procedure a test of size alpha but empirical evidence indicates it is also an unbiased test the modified non parametric procedure also controls the size of the tests and is competitive even under normality assumption

elimination technique from extrapolation to totally positive matrices and cagd in this survey we will show some connections between several mathematical problems such as extrapolation linear systems totally positive matrices and computer aided geometric design with elimination techniques as the common tool to deal with all of them

symmetric modified finite volume element methods for self adjoint elliptic and parabolic problems the finite volume element method is a discretization technique for partial differential equations but in general case the coefficient matrix of its linear system is not symmetric even for the self adjoint continuous problem in this paper we develop a kind of symmetric modified finite volume element methods both for general self adjoint elliptic and for parabolic problems on general discretization their coefficient matrix are symmetric we give the optimal order energy norm error estimates we also prove that the difference between the solutions of the finite volume element method and symmetric modified finite volume element method is a high order term

optimal scheduling algorithms for parallel gaussian elimination this paper uses a graph theoretic approach to derive asymptotically optimal algorithms for parallel gaussian elimination on simd mimd couputers with a shared memory system given a problem of sinze n and using p n processors where 2 43 0 305 the asymptotically optimal algorithms are of efficiency e 1 1 3 0 972 this evidences the high degree of parallelism that can be achieved

assignment and scheduling in parallel matrix factorization abstract we consider the problem of factoring a dense n n matrix on a network consisting of p mimd processors with no shared memory when the network is smaller than the number of elements in the matrix p n 2 the specific example analyzed is a computational network that arises in computing the lu qr or cholesky factorizations we prove that if the nodes of the network are evenly distributed among processors and if computations are scheduled by a round robin or a least recently executed scheduling algorithm then optimal order of speedup is achieved however such speedup is not necessarily achieved for other scheduling algorithms or if the computation for the nodes is inappropriately split across processors and we give examples of these phenomena lower bounds on execution time for the algorithm are established for two important node assignment strategies

sample size determination for assessing equivalence based on proportion ratio under a randomized trial with non compliance and missing outcomes when a generic drug is developed it is important to assess the equivalence of therapeutic efficacy between the new and the standard drugs although the number of publications on testing equivalence and its relevant sample size determination is numerous the discussion on sample size determination for a desired power of detecting equivalence under a randomized clinical trial rct with non compliance and missing outcomes is limited in this paper we derive under the compound exclusion restriction model the maximum likelihood estimator mle for the ratio of probabilities of response among compliers between two treatments in a rct with both non compliance and missing outcomes using the mle with the logarithmic transformation we develop an asymptotic test procedure for assessing equivalence and find that this test procedure can perform well with respect to type i error based on monte carlo simulation we further develop a sample size calculation formula for a desired power of detecting equivalence at a nominal level to evaluate the accuracy of the sample size calculation formula we apply monte carlo simulation again to calculate the simulated power of the proposed test procedure corresponding to the resulting sample size for a desired power of 80 per cent at 0 05 level in a variety of situations we also include a discussion on determining the optimal ratio of sample size allocation subject to a desired power to minimize a linear cost function and provide a sensitivity analysis of the sample size formula developed here under an alterative model with missing at random copyright 2007 john wiley sons ltd

total positivity and neville elimination abstract neville elimination is described in terms of schur complements of matrices and used to improve some well known characterizations of totally positive and strictly totally positive matrices

an immersed finite volume element method for 2d pdes with discontinuous coefficients and non homogeneous jump conditions an immersed finite volume element method is developed to solve 2d elliptic interface problems with a variable coefficient that has a finite jump across an interface the solution and the flux may also have a finite jump across the interface using the source removal technique an equivalent elliptic interface problem with homogeneous jump conditions is obtained the nodal basis functions are constructed to satisfy the homogeneous jump conditions near the interface and the usual finite element nodal basis functions are applied away from the interface the resulting linear problem is simple and easy to solve a proof of the error estimate in the energy norm is given numerical experiments demonstrate the convergence rates of the proposed method with the usual o h 2 in the l 2 the l norms and o h in the h 1 norm

likelihood ratio and score tests to test the non inferiority or equivalence of the odds ratio in a crossover study with binary outcomes we consider the non inferiority or equivalence test of the odds ratio or in a crossover study with binary outcomes to evaluate the treatment effects of two drugs to solve this problem lui and chang 2011 proposed both an asymptotic method and a conditional method based on a random effects logit model kenward and jones 1987 proposed a likelihood ratio test lrtm based on a log linear model these existing methods are all subject to model misspecification in this paper we propose a likelihood ratio test lrt and a score test that are independent of model specification monte carlo simulation studies show that in scenarios considered in this paper both the lrt and the score test have higher power than the asymptotic and conditional methods for the non inferiority test the lrt score and asymptotic methods have similar power and they all have higher power than the conditional method for the equivalence test when data can be well described by a log linear model the lrtm has the highest power among all the five methods lrtm lrt score asymptotic and conditional for both non inferiority and equivalence tests however in scenarios for which a log linear model does not describe the data well the lrtm has the lowest power for the non inferiority test and has inflated type i error rates for the equivalence test we provide an example from a clinical trial that illustrates our methods copyright 2016 john wiley sons ltd

convergence of finite volume schemes for poisson s equation on nonuniform meshes an error analysis of a family of cell center finite volume schemes for poisson s equation on cartesian product nonuniform meshes in two dimensions is presented optimal order error estimates are derived in the discrete h 1 norm under minimum smoothness requirements on the exact solution and without any additional assumption on the regularity of the mesh on quasi uniform meshes analogous estimates are obtained in the maximum norm

centroidal voronoi tessellation based finite element superconvergence in this article a finding on finite element superconvergence is reported the laplacian operator with dirichlet boundary condition is considered the linear finite element solutions have an o h2 0 5 superconvergence in l2 norm at nodes on an almost equilateral triangular mesh generated based on centroidal voronoi tessellation for an arbitrary 2d bounded domain extensive numerical examples are presented to demonstrate the superconvergence property copyright 2008 john wiley sons ltd

parallel algorithms for dense linear algebra computations scientific and engineering research is becoming increasingly dependent upon the development and implementation of efficient parallel algorithms on modern high performance computers numerical linear algebra is an indispensable tool in such research and this paper attempts to collect and describe a selection of some of its more important parallel algorithms the purpose is to review the current status and to provide an overall perspective of parallel algorithms for solving dense banded or block structured problems arising in the major areas of direct solution of linear systems least squares computations eigenvalue and singular value computations and rapid elliptic solvers a major emphasis is given here to certain computational primitives whose efficient execution on parallel and vector computers is essential in order to obtain high performance algorithms

test non inferiority and equivalence based on the odds ratio under a simple crossover trial for testing the non inferiority or equivalence of a generic drug to a standard drug the odds ratio or of patient response rates has been recommended to measure the relative treatment efficacy on the basis of a random effects logistic regression model we develop asymptotic test procedures for testing non inferiority and equivalence with respect to the or of patient response rates under a simple crossover design we further derive exact test procedures which are especially useful for the situations in which the number of patients in a crossover trial is small we address sample size calculation for testing non inferiority and equivalence based on the asymptotic test procedures proposed here we also discuss estimation of the or of patient response rates for both the treatment and period effects finally we include two examples one comparing two solution aerosols in treating asthma and the other one studying two inhalation devices for asthmatics to illustrate the use of the proposed test procedures and estimators

a new class of high order finite volume methods for second order elliptic equations in the numerical simulation of many practical problems in physics and engineering finite volume methods are an important and popular class of discretization methods due to the local conservation and the capability of discretizing domains with complex geometry however they are limited by low order approximation since most existing finite volume methods use piecewise constant or linear function space to approximate the solution in this paper a new class of high order finite volume methods for second order elliptic equations is developed by combining high order finite element methods and linear finite volume methods optimal convergence rate in h 1 norm for our new quadratic finite volume methods over two dimensional triangular or rectangular grids is obtained

complexity of dense linear system solution on a multiprocessor ring abstract different algorithms based on gaussian elimination for the solution of dense linear systems of equations are discussed for a multiprocessor ring the number of processors is assumed not to exceed the problem size a fairly general model for data transfer is proposed and the algorithms are analyzed with respect to their requirements of arithmetic as well as communication times

symmetric finite volume discretizations for parabolic problems based on a linear finite element space in this paper one semi discrete symmetric finite volume scheme and two full discrete symmetric finite volume schemes for a class of parabolic problems are presented and analyzed some numerical examples are reported

procedures for comparing samples with multiple endpoints summary five procedures are considered for the comparison of two or more multivariate samples these procedures include a newly proposed nonparametric rank sum test and a generalized least squares test also considered are the following tests ordinary least squares hotelling s p and a bonferroni per experiment error rate approach applications are envisaged in which each variable represents a qualitatively different measure of response to treatment the null hypothesis of no treatment difference is tested with power directed towards alternatives in which at least one treatment is uniformly better than the others in all simulations the nonparametric procedure provided relatively good power and accurate control over the size of the test and is recommended for general use alternatively the generalized least squares procedure may also be useful with normally distributed data in moderate or large samples a convenient expression for this procedure is obtained and its asymptotic relative efficiency with respect to the ordinary least squares test is evaluated clinical trials are often conducted for the purpose of evaluating the relative efficacy of two or more modes of therapy when the therapies are administered to independent groups and efficacy is measured on the basis of a single response variable appropriate parametric and nonparametric one way analysis of variance anova procedures and their properties are well known often however efficacy is measured by more than one variable although univariate methods for assessing each characteristic individually are useful in this setting there is often the additional need for a single overall objective probability statement that addresses the question of whether or not the experimental therapy is efficacious this need is particularly acute when the medical question is controversial and the sample size is small although a large literature exists on the comparison of multivariate samples the procedures tend to be infrequently used in practice as pointed out by meier 1975 p 523 the standard analysis for the comparison of two multivariate samples which is based on hotelling s t2 statistic addresses somewhat the wrong question and consequently has very poor power for the alternatives of primary interest specifically the t2 procedure addresses the question are one or more of the treatments different making no distinction between variables that change favorably and variables that change unfavorably a second approach would be to assign per experiment error rates to each of the univariate tests by using bonferroni s inequality i e by multiplying each univariate p value by the number of variables studied the desired overall probability statement is then given by the minimum of the per experiment univariate p values although this approach may be useful in some settings it may lack power for alternatives in which most or all measures of efficacy are improved this will be of particular concern when the number k of endpoints studied is large relative to sample size in fact statistical significance will not be possible in some instances this problem will be exacerbated when the measures of efficacy are highly

factorizations of confluent cauchy vandermonde matrices abstract the confluent cauchy vandermonde matrices are considered which were studied earlier by various authors in different way in this paper we analyze the factorization of the inverse of a special type of confluent cauchy vandermonde matrix as a product of block bidiagonal matrices by using block neville elimination factorizations of confluent cauchy vandermonde matrices are also considered which generalize the results of j j martinez j m pena factorizations of cauchy vandermonde matrices linear algebra appl 284 1998 229 237

neville elimination a study of the efficiency using checkerboard partitioning abstract it is well known that checkerboard partitioning can exploit more concurrency than striped partitioning because the matrix computation can be divided among more processors than in the case of striping in this work we analyze the performance of neville method when a checkerboard partitioning is used focusing on the special case of block cyclic checkerboard partitioning this method is an alternative to gaussian elimination and it has been proved to be very useful for some classes of matrices such as totally positive matrices the performance of this parallel system is measured in terms of the efficiency the fraction of time for which a processor is usefully employed which in our model is close to one when the optimum block size is used also we have executed our algorithms on a parallel pc cluster observing that both efficiencies theoretical and empirical are quite similar

a matricial description of neville elimination with applications to total positivity abstract the neville elimination process used by the authors in some previous papers in connection with totally positive matrices is studied in detail in the case of nonsingular matrices a wide class of matrices is found where neville elimination has a lower computational cost than gauss elimination finally some new characterizations are obtained for strictly totally positive and nonsingular totally positive matrices in terms of their neville elimination and that of their inverses

parallel direct methods for solving banded linear systems abstract we propose several implementations of gaussian elimination for solving banded linear systems on multiprocessors three simple architectures are considered a multiprocessor ring a grid array and a hypercube our complexity analysis fully accounts for communication delays by using simple models where both latency and actual transfer times are incorporated when the number of processors is small relative to the bandwidth of the system a row interleaved implementation of gaussian elimination algorithm is attractive otherwise a two dimensional grid is essential for achieving higher speedup the hypercube architecture gives the smallest communication latency times

superconvergence and asymptotic expansions for bilinear finite volume element approximation on non uniform grids abstract we initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise for the isoparametric bilinear finite volume element scheme by employing the energy embedded method on some non uniform grids furthermore we prove that the approximate derivatives are convergent of order two numerical examples confirm theoretical results

an optimal schedule for gaussian elimination on an mimd architecture in this paper we propose an algorithm for allocating the tasks of the well known gaussian elimination algorithm on an mimd architecture and prove that the schedule is optimal in order of magnitude up to a polylog factor