igaor and multisplitting igaor methods for linear complementarity problems in this paper we propose an interval version of the generalized accelerated overrelaxation methods which we refer to as igaor for solving the linear complementarity problems lcp m q and develop a class of multisplitting igaor methods which can be easily implemented in parallel in addition in regards to the h matrix with positive diagonal elements we prove the convergence of these algorithms and illustrate their efficiency through our numerical results

limit cycles bifurcated from a class of quadratic reversible center of genus one abstract we investigate the bifurcation of limit cycles in a class of planar quadratic reversible non hamiltonian systems this systems has a center of genus one the exact upper bound of the number of limit cycles is given

bifurcation of small limit cycles in z5 equivariant planar vector fields of order 5 abstract in this paper we consider bifurcation of small limit cycles from hopf type singular points in z 5 equivariant planar vector fields of order 5 we apply normal form theory and the technique of solving coupled multivariate polynomial equations to prove that the maximal number of small limit cycles that such vector fields can have is 25 in addition we show that no large limit cycles exist thus h 5 25 where h n denotes the hilbert number of the n th degree polynomial vector fields this improves the best result of h 5 24 existing in the current literature

estimating the population size for capture recapture data with unequal catchability a point estimator and its associated confidence interval for the size of a closed population are proposed under models that incorporate heterogeneity of capture probability real data sets provided in edwards and eberhardt 1967 journal of wildlife management 31 87 96 and carothers 1973 journal of animal ecology 42 125 146 are used to illustrate this method and to compare it with other estimates the performance of the proposed procedure is also investigated by means of monte carlo experiments the method is especially useful when most of the captured individuals are caught once or twice in the sample for which case the jackknife estimator usually does not work well numerical results also show that the proposed confidence interval performs satisfactorily in maintaining the nominal levels

models of parallel chaotic iteration methods abstract we consider two models of parallel multisplitting chaotic iterations for solving large nonsingular systems of equations ax b in the first model each processor can carry out an arbitrary number of local iterations before the next global approximation to the solution is formed in the second model any processor can update the global approximation which resides in the central processor at any time this model is a generalization of a sequential iterative scheme due to ostrowski called the free steering group jacobi iterative scheme and a chaotic relaxation point iterative scheme due to chazan and miranker we show that when a is a monotone matrix and all the splittings are weak regular both models lead to convergent schemes

mixture models for estimating the size of a closed population when capture rates vary among individuals nous developpons une parametrisation du melange de lois beta et binomiale qui fournit un cadre inferentiel approprie pour estimer l effectif d une population fermee lorsque les probabilites de capture ou de detection varient entre individus nous ajustons trois classes de modeles de melange beta binomiale logistique normale et modele a classes latentes d une part a des donnees de recapture de lievres d amerique pour en estimer l abondance et d autre part a des comptages d especes d oiseaux pour estimer la richesse specifique dans les deux jeux de donnees les taux de detection varient davantage entre individus lievres ou especes qu entre occasions ou lieux de capture les estimateurs de l effectif de la population et de la richesse specifique sont sensibles aux hypotheses faites sur la distribution sous jacente des probabilites individuelles de detection nous montrons par simulations que les outils habituels d evaluation de la qualite du modele comme la deviance ne sont pas fiables pour choisir entre des modeles de melanges celui qui fournit une inference correcte de l effectif de la population lorsqu elles existent des connaissances a priori sur les causes d heterogeneite des taux de detection doivent etre utilisees pour aider a choisir quelle classe de modeles de melanges utiliser pour l inference

spectral radii of certain iteration matrices and cycle means of digraphs abstract motivated by questions arising in the study of asynchronous iterative methods for solving linear systems we consider the spectral radius of products of certain one cycle matrices the spectral radius of a matrix in our class is a monotonic increasing function of the length of the cycle of the matrix but this is known to be false for products of such matrices the thrust of our investigation is to determine sufficient conditions under which the spectral radius of the product increases decreases when the lengths of the cycles of the factors increase decrease we also find sufficient conditions for the spectral radius of the product to be independent of the order of the factors our chief tool is an auxiliary directed weighted graph whose cycle means determine the eigenvalues of the matrix product and our main results are stated in terms of the maximal cycle mean of this graph

convergence of sequential and asynchronous nonlinear paracontractions we establish the convergence of sequential and asynchronous iteration schemes for nonlinear paracontracting operators acting in finite dimensional spaces applications to the solution of linear systems of equations with convex constraints are outlined a first generalization of one of our convergence results to an infinite pool of asymptotically paracontracting operators is also presented

a general class of recapture models based on the conditional capture probabilities we propose an mhotb model for population size estimation in capture recapture studies the tb part is based on equality constraints for the conditional capture probabilities leading to an extremely rich model class observed and unobserved heterogeneity are dealt with by means of a logistic parameterization in order to explore the model class we introduce a penalized version of the likelihood the conditional likelihood and penalized conditional likelihood are maximized by means of efficient em algorithms simulations and two real data examples illustrate the approach

monotonic sequences and rates of convergence of asynchronized iterative methods abstract in a recent paper b vemmer and the authors investigated the effect of varying the number of processors on the rate of convergence of the asynchronized parallel block jacobi method associated with monotone matrices it was found that under certain simplifying assumptions increasing the number of processors in relation to the number of blocks or what comes to the same in more general settings the number of iteration operators slows down the convergence one interpretation for these results given in that paper was that increasing the number of processors means that when the current global approximation is updated by a local approximation from one of the processors that local approximation was computed from a much earlier global approximation received from the host node hence the slowdown in the rate of convergence the principal purpose of this paper is to remove some of the simplifying assumptions that were made in the above mentioned paper and to prove that many of the results there hold under much more general conditions our present assumptions do not yield a fixed iteration matrix which models the process as was the case previously this means that different tools have to be developed to establish results comparing the rate of convergence of two assynchronized processes

computation of the simplest normal forms with perturbation parameters based on lie transform and rescaling normal form theory is one of the most power tools for the study of nonlinear differential equations in particular for stability and bifurcation analysis recently many researchers have paid attention to further reduction of conventional normal forms cnf to so called the simplest normal form snf however the computation of normal forms has been restricted to systems which do not contain perturbation parameters unfolding the computation of the snf is more involved than that of cnfs and the computation of the snf with unfolding is even more complicated than the snf without unfolding although some author mentioned further reduction of the snf no results have been reported on the exact computation of the snf of systems with perturbation parameters this paper presents an efficient method for computing the snf of differential equations with perturbation parameters unlike cnf theory which uses an independent nonlinear transformation at each order this approach uses a consistent nonlinear transformation through all order computations the particular advantage of the method is able to provide an efficient recursive formula which can be used to obtain the nth order equations containing the nth order terms only this greatly saves computational time and computer memory the recursive formulations have been implemented on computer systems using maple as an illustrative example the snf for single zero singularity is considered using the new approach

on the convergence of asynchronous paracontractions with application to tomographic reconstruction from incomplete data abstract convergence of iterative processes in c k of the form x i r i j i x 1 r i 1 1 p j i x i where j i 1 2 n i 1 2 is analyzed it is shown that if the matrices p 1 p n are paracontracting in the same smooth strictly convex norm and if the sequence j i i 1 has certain regularity properties then the above iterates converge this result implies the convergence of a parallel asynchronous implementation of the algebraic reconstruction technique art algorithm often used in tomographic reconstruction from incomplete data

a unified framework for the construction of various matrix multisplitting iterative methods for large sparse system of linear equations abstract a unified framework for the construction of various synchronous and asynchronous parallel matrix multisplitting iterative methods suitable to the simd and mimd multiprocessor systems respectively is presented and its convergence theory is established under rather weak conditions these afford general method models and systematical convergence criterions for studying the parallel iterations in the sense of matrix multisplitting in addition how the known parallel matrix multisplitting iterative methods can be classified into this new framework and what novel ones can be generated by it are shown in detail

design of a recursive shape controlling mesh generator a recursive shape controlling triangulation method is described the method is designed to produce a labelling which implies reduced fill in the solution of finite element equations assembled from such a triangulation and allows simple implementation of a nested disection algorithm for irregular domains this approach saves a substantial amount of time usually spent on discovering a suitable relabelling of the triangulation in addition the matrix of the resulting system is then endowed with a recursive doubly bordered block diagonal form this allows us to develop a recursive parallel bisection method for the solution of the system of equations

a penalized nonparametric maximum likelihood approach to species richness estimation we propose a class of penalized nonparametric maximum likelihood estimators npmles for the species richness problem we use a penalty term on the likelihood because likelihood estimators that lack it have an extreme instability problem the estimators are constructed using a conditional likelihood that is simpler than the full likelihood we show that the full likelihood npmle solution given by norris and pollock can be found with great accuracy by using an appropriate penalty term on the conditional likelihood so it is an element of our class of estimators a simple and fast algorithm for the penalized npmle is developed it can be used to greatly speed up computation of the unconditional npmle it can also be used to find profile mixture likelihoods based on our goal of attaining high stability while retaining sensitivity we propose an adaptive quadratic penalty function a systematic simulation study using a wide range of scenarios establishes the success of this method relative to its competi

on multisplitting methods for band matrices we present new theoretical results on two classes of multisplitting methods for solving linear systems iteratively these classes are based on overlapping blocks of the underlying coefficient matrix a which is assumed to be a band matrix we show that under suitable conditions the spectral radius rho h of the iteration matrix h does not depend on the weights of the method even if these weights are allowed to be negative for a certain class of splittings we prove an optimality result for rho h with respect to the weights provided that a is an m matrix this result is based on the fact that the multisplitting method can be represented by a single splitting a m n which in our situation surprisingly turns out to be a regular splitting furthermore we show by numerical examples that weighting factors alpha not in 0 1 may considerably improve the convergence

existence and stability of a unique equilibrium in continuous valued discrete time asynchronous hopfield neural networks it is shown that the assumption of d stability of the interconnection matrix together with the standard assumptions on the activation functions guarantee the existence of a unique equilibrium under a synchronous mode of operation as well as a class of asynchronous modes for the synchronous mode these assumptions are also shown to imply local asymptotic stability of the equilibrium for the asynchronous mode of operation two results are derived first it is shown that symmetry and stability of the interconnection matrix guarantee local asymptotic stability of the equilibrium under a class of asynchronous modes this is referred to as local absolute asymptotic stability second it is shown that under the standard assumptions if the nonnegative matrix whose elements are the absolute values of the corresponding elements of the interconnection matrix is stable then the equilibrium is globally absolutely asymptotically stable under a class of asynchronous modes the results obtained are discussed from the points of view of their applications robustness and their relationship to earlier results

asynchronous parallel methods for enclosing solutions of nonlinear equations we consider interval arithmetic based parallel methods for enclosing solutions of nonlinear systems of equations where processors are allowed to proceed asynchronously we present a general study on the convergence of asynchronous iterations in interval spaces and apply them to a variety of methods for the nonlinear equations case the convergence results turn out to be very similar to those known for synchronous methods several practical examples on shared memory architectures are included the asynchronous methods sometimes perform substantially better than their synchronous counterparts

convergence of parallel multisplitting iterative methods for m matrices abstract despite the major recent activity in parallel processing few effective new algorithms designed exclusively for multiprocessors have been put forth one such is the multisplitting iterative algorithm suggested by o leary and white although they have given some sufficient conditions for convergence a general convergence theory has not been developed even for the classical situation where the coefficient matrix a is an m matrix or is symmetric positive definite in this paper we study the m matrix case in detail the multisplitting process for a rn n is recast as an ordinary iterative process for a certain block matrix a r kn kn where k is the number of processors and standard convergence results are used to develop a convergence theory for multisplitting iterative methods where a is an m matrix comparison results between multisplitting methods are established in terms of monotonic norms and for the case where a is irreducible in terms of the asymptotic convergence rate a key observation here is that in certain cases the rate of global convergence of these parallel iterative methods is inherent in the splitting of a and is independent of the manner in which the work is distributed among the processors thus in general one can distribute the work for load balancing purposes without affecting the convergence rate

on delay independent diagonal stability of max min congestion control network feedback in a congestion control system is subject to delay which can significantly affect stability and performance of the entire system while most existing stability conditions explicitly depend on delay di of individual flow i a recent study shows that the combination of a symmetric jacobian a and condition p a 1 guarantees local stability of the system regardless of di however the requirement of symmetry is very conservative and no further results have been obtained beyond this point in this technical note we proceed in this direction and gain a better understanding of conditions under which congestion control systems can achieve delay independent stability towards this end we first prove that if jacobian matrix a satisfies a 1 for any monotonic induced matrix norm the system is locally stable under arbitrary diagonal delay di we then derive a more generic result and prove that delay independent stability is guaranteed as long as a is schur diagonally stable which is also observed to be a necessary condition in simulations utilizing these results we identify several classes of well known matrices that are stable under diagonal delays if rho a 1 and prove stability of mkc with arbitrary parameters alphai and betai

the effect of the number of processors on the convergence of the parallel block jacobi method abstract we investigate the effect on the rate of convergence of a model of the asychronized parallel iteration method of allowing the number of processors to differ from the number of splittings under certain regularization assumptions we prove that decreasing the number of processors increases the convergence rate our interpretation of this result for the model is as follows increasing the number of processors means that each processor updates the global approximation in the host node with a local iteration which is computed from older global data hence the convergence rate is reduced to prove our results we develop theorems for comparison of the spectral radii for certain nonnegative matrices which are of interest in their own right we provide numerical examples to illustrate our results

asynchronous multisplitting aor methods for a class of systems of weakly nonlinear equations a class of asynchronous parallel multisplitting accelerated overrelaxation aor methods for solving the system of weakly nonlinear equations email protected u g u in which a e l n f u f 1 u 1 f 2 u 2 f n u n t and g u g 1 g 2 u g n u t is proposed and its global convergence theory is set up under suitable conditions

asynchronous multisplitting two stage iterations for systems of weakly nonlinear equations for the large sparse systems of weakly nonlinear equations arising in the discretizations of many classical differential and integral equations this paper presents a class of asynchronous parallel multisplitting two stage iteration methods for getting their solutions by the high speed multiprocessor systems under suitable assumptions we study the global convergence properties of these asynchronous multisplitting two stage iteration methods moreover for this class of new methods we establish their local convergence theories and precisely estimate their asymptotic convergence factors under some reasonable assumptions when the involved nonlinear mapping is only assumed to be directionally differentiable numerical computations show that our new methods are feasible and efficient for parallely solving the system of weakly nonlinear equations

on structure oriented hybrid two stage iteration methods for the large and sparse blocked system of linear equations in this paper we first present a class of structure oriented hybrid two stage iteration methods for solving the large and sparse blocked system of linear equations as well as the saddle point problem as a special case and the new methods converge to the solution under suitable restrictions for instance when the coefficient matrix is positive stable matrix generally numerical experiments for a model generalized saddle point problem are given and the results show that our new methods are feasible and efficient and converge faster than the classical uzawa method

a convergence theorem for chaotic asynchronous relaxation abstract we present a convergence result for chaotic asynchronous relaxation that is a modification of the result of chazan and miranker the modification is a restriction to the case of global memory or fast communication the extra restriction is that each update is based on a prior state of the system rather than on prior substates

the number of limit cycles of a class of polynomial differential systems abstract in this paper we consider the bifurcation of limit cycles of a class of polynomial differential systems of the form x y 1 x 4 e p n x y y x 1 x 4 e q n x y where p n q n are arbitrary polynomials of degree n we prove that there is a system of the above form having at least 3 n 1 2 2 limit cycles in hopf bifurcation then applying the argument principle we obtain that up to first order in e the number of limit cycles that bifurcate from period annulus surrounding the origin of this system is at most 5 n 1 4 n 1 2 for n 5

sequential and parallel synchronous alternating iterative methods the so called parallel multisplitting nonstationary iterative model a was introduced by bru elsner and neumann linear algebra and its applications 103 175 192 1988 for solving a nonsingular linear system ax b using a weak nonnegative multisplitting of the first type in this paper new results are introduced when a is a monotone matrix using a weak nonnegative multisplitting of the second type and when a is a symmetric positive definite matrix using a p regular multisplitting also nonstationary alternating iterative methods are studied finally combining model a and alternating iterative methods two new models of parallel multisplitting nonstationary iterations are introduced when matrix a is monotone and the multisplittings are weak nonnegative of the first or of the second type both models lead to convergent schemes also when matrix a is symmetric positive definite and the multisplittings are p regular the schemes are also convergent

on the convergence of iterative methods for solving singular linear systems in this paper we first show that for the stationary iterative methods for solving consistent singular linear systems the convergence and the quotient convergence are equivalent then we use this assertion to analyze the convergence of the multisplitting algorithms for the solution of linear systems when the coefficient matrices of the linear systems are singular hermitian positive semidefinite and the linear systems are consistent

a general asynchronous block iterative model with related convergence conditions abstract this paper formulates a general time varying asynchronous block iterative model a convergence condition for asynchronous block iterations based on this model is given compared to existing conditions for similar and shown to be strictly weaker

on identifiability in capture recapture models we study the issue of identifiability of mixture models in the context of capture recapture abundance estimation for closed populations such models are used to take account of individual heterogeneity in capture probabilities but their validity was recently questioned by link 2003 biometrics 59 1123 1130 on the basis of their nonidentifiability we give a general criterion for identifiability of the mixing distribution and apply it to establish identifiability within families of mixing distributions that are commonly used in this context including finite and beta mixtures our analysis covers binomial and geometrically distributed outcomes in an example we highlight the difference between the identifiability issue considered here and that in classical binomial mixture models

on the convergence of the discretized parallel chaotic waveform relaxation method in this paper we establish several algorithm of discretized parallel chaotic waveform relaxation methods for solving linear ordinary differential systems based on some given models under some different assumptions on the coefficient matrix a and its multisplittings we obtain corresponding sufficient conditions for convergence of the algorithms also a discussion on convergence speed comparison of synchronous and asynchronous algorithms is given

convergence and comparison theorems for a generalized alternating iterative method using as a principal tool the convergence results of standard iterative process for the solution of linear systems alternating iterative methods are studied we extend the convergence theorem for the stationary alternating iterative method of benzi and szyld numererische mathematik 76 1997 309 for weak nonnegative splittings of the first type of a monotone matrix to weak nonnegative splitting of the second type on the other hand we introduce a more general method the nonstationary alternating iterative method establishing convergence results for weak nonnegative splittings of a monotone matrix and for p regular splittings of a symmetric positive definite matrix

generalized nonlinear diagonal dominance and applications to asynchronous iterative methods abstract we introduce a concept of generalized diagonal dominance for nonlinear functions as in the linear case this brings together several apparently different classes of nonlinear functions such as strictly diagonally dominant functions and certain m functions with our concept we easily obtain a quite far reaching result on the global convergence of asynchronous iterative methods for finding zeros of nonlinear functions special cases include some known and several new convergence results for special iterative methods such as the nonlinear jor sor and ssor method

a generalization of chao s estimator for covariate information this note generalizes chao s estimator of population size for closed capture recapture studies if covariates are available chao s estimator was developed under unobserved heterogeneity in which case it represents a lower bound of the population size if observed heterogeneity is available in form of covariates we show how this information can be used to reduce the bias of chao s estimator the key element in this development is the understanding and placement of chao s estimator in a truncated poisson likelihood it is shown that a truncated poisson likelihood with log link with all counts truncated besides ones and twos is equivalent to a binomial likelihood with logit link this enables the development of a generalized chao estimator as the estimated expected value of the frequency of zero counts under a truncated all counts truncated except ones and twos poisson regression model if the regression model accounts for the heterogeneity entirely the generalized chao estimator is asymptotically unbiased a simulation study illustrates the potential in gain of bias reduction comparisons of the generalized chao estimator with the homogeneous zero truncated poisson regression approach are supplied as well the method is applied to a surveillance study on the completeness of farm submissions in great britain

stability of asynchronous systems with poisson transitions we consider the stability of an asynchronous system modeled as a collection of coupled processes with independent poisson state transitions using lyapunov functions sufficient conditions for both mean square and almost sure convergence independent of state transition rates are developed for the linear case and weaker transition rate dependent conditions are derived for the linear and nonlinear case an illustrative example is discussed and simulated

a nonlinear parallel algorithm with application to the stefan problem the algebraic problem b gamma e a beta e eta which may evolve from elliptic or parabolic partial differential equations is studied conditions are given so that a parallel algorithm of a nonlinear gauss seidel type converges to the unique solution an application is given to the solidification of a channel in which the continuum problem is discretized by the finite element method these computations show a significant decrease in computing times as compared to serial algorithms

parallel multisplitting iteration methods based on m splitting for the pagerank problem a class of iterative schemes based on the regular splitting is proposed for pagerank computation by some specific splitting these methods will reduce to some well known iterative schemes like jacobi method and successive overrelaxation method to suit computational requirements of the modern high speed multiprocessor environments we further study synchronous parallel counterparts for the new splitting iteration methods by using the m splitting of the coefficient matrix we establish the convergence theory of these synchronous multisplitting iteration methods finally some numerical experiments are presented to illustrate the feasibility stability and effectiveness of the proposed algorithms

on the convergence of parallel multisplitting asynchronous gaor method for h matrix in this paper we establish several algorithms of parallel chaotic generalized aor iterative methods for solving large nonsingular systems based on some given models under some different assumptions of coefficient matrix a and its multisplittings we obtain corresponding sufficient conditions of convergence for some relaxed parameters

on the convergence of parallel asynchronous block iterative computations abstract this paper considers the convergence problem of parallel asynchronous block iterative computation schemes a new mathematical state space model for a class of nonlinear time varying parallel iterative schemes is proposed using this model which generalizes several models of the chazan miranker type together with large scale systems and liapunov techniques it is shown that the well known quasidominance condition on a certain aggregated matrix guarantees exponential convergence of this class of methods

on the convergence of asynchronous iteration methods for nonlinear paracontractions and consistent linear systems abstract elsner et al l elsner i koltracht m neumann numer math 62 1992 305 319 introduced the concept of paracontracting operators for fixed point problems and their solution with asynchronous iteration methods their results are extended with respect to the properties of the pool of operators from which a common fixed point is searched also a more general kind of asynchronous iterations than theirs is presented as an application of this theory asynchronous iteration methods for consistent linear systems ax b are considered where a is a singular m matrix lubashevski and mitra b lubashevski d mitra j acm 33 1 1986 130 150 investigated asynchronous iteration methods for the perron vector problem i e determining a positive solution of tx p t x where t is an irreducible nonnegative matrix and its spectral radius is know their result can be fortified and extended to the reducible affine case by using a quite different approach the developed theory of paracontractions and confluence

nonidentifiability of population size from capture recapture data with heterogeneous detection probabilities heterogeneity in detection probabilities has long been recognized as problematic in mark recapture studies and numerous models developed to accommodate its effects individual heterogeneity is especially problematic in that reasonable alternative models may predict essentially identical observations from populations of substantially different sizes thus even with very large samples the analyst will not be able to distinguish among reasonable models of heterogeneity even though these yield quite distinct inferences about population size the problem is illustrated with models for closed and open populations

chaotic iterative methods for the linear complementarity problems a class of parallel multisplitting chaotic relaxation methods is established for the large sparse linear complementarity problems and the global and monotone convergence is proved for the h matrix and the l matrix classes respectively moreover comparison theorem is given which describes the influences of the parameters and the multiple splittings upon the monotone convergence rates of the new methods

distributed asynchronous computation of fixed points we present an algorithmic model for distributed computation of fixed points whereby several processors participate simultaneously in the calculations while exchanging information via communication links we place essentially no assumptions on the ordering of computation and communication between processors thereby allowing for completely uncoordinated execution we provide a general convergence theorem for algorithms of this type and demonstrate its applicability to several classes of problems including the calculation of fixed points of contraction and monotone mappings arising in linear and nonlinear systems of equations optimization problems shortest path problems and dynamic programming

convergence of the parallel chaotic waveform relaxation method for stiff systems in this paper we establish several algorithms for parallel chaotic waveform relaxation methods for solving linear ordinary differential systems based on some given models under some different assumptions on the coefficient matrix a and its multisplittings we obtain corresponding sufficient conditions of convergence of the algorithms also a discussion on convergence speed comparison of synchronous and asynchronous algorithms is given

a chaotic asynchronous algorithm for computing the fixed point of a nonnegative matrix of unit spectral radius given a nonnegative irreducible matrix p of spectral radius unity there exists a positive vector such that p if p also happens to be stochastic then gives the stationary distribution of the markov chain that has state transition probabilities given by the elements of p this paper gives an algorithm for computing that is particularly well suited for parallel processing the main attraction of our algorithm is that the timing and sequencing restrictions on individual processors are almost entirely eliminated and consequently the necessary coordination between processors is negligible and the enforced idle time is also negligible under certain mild and easily satisfied restrictions on p and on the implementation of the algorithm x the vectors of computed values are proved to converge to within a positive finite constant of proportionality of it is also proved that a natural measure of the projective distance of x from vanishes geometrically fast and at a rate for which a lower bound is given we have conducted extensive experiments on random matrices p and the results show that the improvement over the parallel implementation of the synchronous version of the algorithm is substantial sometimes exceeding the synchronization penalty to which the latter is always subject

overlapping block diagonal dominance and existence of liapunov functions the main objective of this paper is to formulate a generalization of block diagonal dominance which can be used to establish nonsingularity of matrices via overlapping diagonal blocks a number of stability results are derived in the new setting by exploiting the well known m matrix properties as well as extensions of the normalization scaling and alternative norm utilization a link between generalized block diagonal dominance and vector liapunov functions is established which can be applied in the stability analysis of interconnected dynamic systems

a class of parallel hybrid two stage iteration methods for block bordered linear systems a class of parallel hybrid two stage iteration method and its accelerated overrelaxation variant are established for solving the large sparse block bordered system of linear equations and their convergence are proved when the coefficient matrix of this linear system is an m matrix and an h matrix respectively

estimating the number of classes via sample coverage abstract assume that a random sample is drawn from a population with unknown number of classes and possibly unequal class probabilities a nonparametric estimation technique is proposed to estimate the number of classes using the idea of sample coverage which is defined as the sum of the cell probabilities of the observed classes since expected sample coverage can be well estimated we were motivated to find its role in the estimation of the number of classes this work generalizes the result of esty to a nonparametric approach and extends darroch and ratcliff to incorporate the heterogeneity of the class probabilities the coefficient of variation of the class sizes is shown to play an important role in the recommended estimation procedures the performance of the proposed estimators is investigated by means of monte carlo simulations

convergence of non stationary parallel multisplitting methods for hermitian positive definite matrices non stationary multisplitting algorithms for the solution of linear systems are studied convergence of these algorithms is analyzed when the coefficient matrix of the linear system is hermitian positive definite asynchronous versions of these algorithms are considered and their convergence investigated

a class of asynchronous multisplitting two stage iterations for large sparse block systems of weakly nonlinear equations abstract for the block system of weakly nonlinear equations ax g x where a r n n is a large sparse block matrix and g r n r n is a block nonlinear mapping having certain smoothness properties we present a class of asynchronous parallel multisplitting block two stage iteration methods in this paper these methods are actually the block variants and generalizations of the asynchronous multisplitting two stage iteration methods studied by bai and huang journal of computational and applied mathematics 93 1 1998 13 33 and they can achieve high parallel efficiency of the multiprocessor system especially when there is load imbalance under quite general conditions that a r n n is a block h matrix of different types and g r n r n is a block p bounded mapping we establish convergence theories of these asynchronous multisplitting block two stage iteration methods numerical computations show that these new methods are very efficient for solving the block system of weakly nonlinear equations in the asynchronous parallel computing environment

limit cycles near a homoclinic loop by perturbing a class of integrable systems abstract in this paper the problem of limit cycle bifurcation is investigated by perturbing a class of integrable systems with a homoclinic loop under the assumption that the homoclinic loop passes through a degenerate singular point at the origin the asymptotic expansion of the melnikov function along the level curves of the first integral inside the homoclinic loop is studied near the loop meanwhile the formulas for the first coefficients in the expansion are given which can be used to study the number of limit cycles near the homoclinic loop finally an example is provided to demonstrate the obtained results

new comparison results for parallel multisplitting iterative methods abstract the parallel multisplitting nonstationary iterative model a and models 1 2 were introduced by bru et al bru elsner neumann models of parallel chaotic iteration methods linear algebra appl 103 1988 175 192 and climent et al climent perea tortosa zamora convergence theorems for parallel alternating iterative methods appl math comput 148 2004 497 517 respectively using nonnegative splitting theory we present some new comparison theorems between two general parallel multisplittings of model a and models 1 2 when the coefficient matrix is a monotone matrix particularly we establish some sufficient conditions for strict inequalities in comparisons of spectral radii of different iteration matrices

on the convergence of parallel chaotic nonlinear multisplitting newton type methods abstract a class of parallel chaotic nonlinear multisplitting newton type methods for solving the nonlinear system of equations f x 0 f d r n r n is established and its local convergence theory is presented

nonstationary two stage multisplitting methods with overlapping blocks abstract parallel synchronous two stage multisplitting methods with overlap for the solution of linear systems of equations are studied it is shown that under certain hypotheses the method with overlap is faster in some measure than that without overalp our results extend the comparison results of multisplittings with overlapping blocks with those of nonoverlapping blocks from a frommer b pohl a comparison result for multisplittings and wave form relaxation methods numer linear algebra appl 2 1995 335 346 and m t jones d b szyld two stage multisplitting methods with overlapping blocks numer linear algebra appl 3 1996 113 124 to the two stage nonstationary case

stability of asynchronous two dimensional fornasini marchesini dynamical systems abstract conditions for stability of two dimensional 2d fornasini marchesini fm models with variable shifts are derived using nonnegative matrix theory the conditions are shift independent the stability is proved under a general boundary condition bc

estimating the number of species a review how many kinds are there suppose that a population is partitioned into c classes in many situations interest focuses not on estimation of the relative sizes of the classes but on estimation of c itself for example biologists and ecologists may be interested in estimating the number of species in a population of plants or animals numismatists may be concemed with estimating the number of dies used to produce an ancient coin issue and linguists may be interested in estimating the size of an author s vocabulary in this article we review the problem of statistical estimation of c many approaches have been proposed some purely data analytic and others based in sampling theory in the latter case numerous variations have been considered the population may be finite or infinite if finite samples may be taken with replacement multinomial sampling or without replacement hypergeometric sampling or by bernoulli sampling if infinite sampling may be multinomial or bernoulli or the sample may be th

on the convergence of the parallel multisplitting aor algorithm abstract we present a class of relaxed parallel multisplitting algorithms called the parallel multisplitting aor algorithm for solving large nonsingular systems of equations ax b this new algorithm is a generalization and improvement of the relaxed parallel multisplitting method linear algebra appl 119 141 152 1989 based on the new algorithm model we establish another algorithm called the relaxed parallel multisplitting aor algorithm the convergence of these algorithms is discussed under the condition that a is a monotone matrix we obtain corresponding convergence results these convergence conditions are convenient to verify

on stein rosenberg type theorems for nonnegative and perron frobenius splittings abstract the stein rosenberg theorem is extended and generalized to the class of nonnegative splittings a m 1 n 1 m 2 n 2 as well as to the most generalized class of perron frobenius splittings two types of the stein rosenberg theorem are stated and proved for both classes these theorems allow us to obtain comparison results for the rate of convergence of the associated iterative methods specific assumptions are given under which the inequalities of the spectral radii become equalities or strict inequalities the theoretical results are confirmed by numerical examples

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

on the convergence of parallel nonstationary multisplitting iteration methods the convergence properties of a variant of the parallel chaotic multisplitting iteration method called the nonstationary multisplitting iteration method for solving large sparse systems of linear equations are further discussed when the coefficient matrix is an h matrix or a positive definite matrix respectively moreover when the coefficient matrix is a monotone matrix the monotone convergence theory and the monotone comparison theorem about this method are established this directly leads to several novel sufficient conditions for guaranteeing the convergence of this parallel nonstationary multisplitting iteration method

generalizations of the nonstationary multisplitting iterative method for symmetric positive definite linear systems in this paper we generalize the nonstationary parallel multisplitting iterative method for solving the symmetric positive definite linear systems with several choices of variable weighting matrices the convergence properties of these generalized methods can be improved finally the numerical comparison of several nonstationary parallel multisplitting methods are shown

on the number of limit cycles near a homoclinic loop with a nilpotent singular point abstract in this article we study the expansion of the first melnikov function appearing by perturbing an integrable and reversible system with a homoclinic loop passing through a nilpotent singular point and obtain formulas for computing the first coefficients of the expansion based on these coefficients we obtain a lower bound for the maximal number of limit cycles near the homoclinic loop moreover as an application of our main results we consider a type of integrable and reversible polynomial systems obtaining at least 3 4 or 5 limit cycles respectively

parallel chaotic extrapolated jacobi like methods parallel chaotic schemes based on the extrapolated jacobi method and a second degree stationary method are studied sufficient conditions for the convergence of the above methods for the synchronous and asynchronous models are given these sufficient conditions are related to properties of the block jacobi matrix the schemes are illustrated by computational results on a shared memory multiprocessor vector computer

some notes on multisplltting methods and m step preconditioners for linear systems abstract to solve the real nonsingular linear system ax b on parallel and vector machines multisplitting methods and m step preconditioners are considered in this work in particular 1 we extend adams and ong s idea and theory of the m step additive preconditioners and ruggiero and galligani s method of the arithmetic mean and we generalize the corresponding convergence results 2 we determine suitable relaxed m step preconditioners and solve the problem of minimizing the related condition number with respect to the relaxation extrapolation parameter involved 3 finally we complete the theoretical solution of the problem of determining the optimum sor additive iterative method for 2 cyclic positive definite matrices

on asynchronous iterations asynchronous iterations arise naturally on parallel computers if one wants to minimize idle times this paper reviews certain models of asynchronous iterations using a common theoretical framework the corresponding convergence theory and various domains of applications are presented these include nonsingular linear systems nonlinear systems and initial value problems

generalized multisplitting asynchronous iteration abstract we give a generalized asynchronous iteration based on the multisplitting of linear or nonlinear operators to solve systems of equations the condition for convergence can be imposed only on the components which actually enter the computation the results contain synchronous multisplitting iterations as a special case

on a class of physically important integrable equations abstract a methodology introduced by fuchssteiner and the author is used to derive a class of physically important integrable evolution equations among these equations are integrable generalizations of the korteweg devries kdv of the modified kdv of the nonlinear schrodinger nls and of the sine gordon equations the modeling of water waves as well as general asymptotic considerations are used to illustrate the occurrence of the generalized modified kdv and nls equations respectively

convergence theorems for parallel alternating iterative methods the parallel multisplitting nonstationary iterative model a was introduced by bru elsner and neumann linear algebra appl 103 1988 175 192 for solving nonsingular linear system ax b using a weak nonnegative multisplitting of the first type in this paper new results using a weak nonnegative multisplitting of the second type are introduced when a is a monotone matrix and using p regular multisplitting when a is a symmetric positive definite matrix combining model a and alternating iterative methods two new models of parallel multisplitting nonstationary iterations are introduced it is shown that when matrix a is monotone and the multisplittings are weak nonnegative of the first or second type both models lead to convergent schemes when matrix a is symmetric positive definite and the multisplittings are p regular the schemes are also convergent

capture recapture estimation with samples of size one using frequency data summary one way in which a capture recapture experiment can be designed is to count each capture occasion as a separate sample and tally the number of individuals caught once twice and so on this paper discusses the estimators currently used for this type of experiment and suggests some new ones each of the estimators is categorized by its derivation following this their properties are discussed particularly their bias and variance with the aim of choosing one or two of the estimators which are the best to use especially in handling a heterogeneous population it is found that the bias adjusted estimator of chao 1989 is the best to use when the number of captures is relatively small and that the estimator of darroch ratcliff 1980 should be used otherwise

asynchronous two stage iterative methods parallel block two stage iterative methods for the solution of linear systems of algebraic equations are studied convergence is shown for monotone matrices and for h matrices two different asynchronous versions of these methods are considered and their convergence investigated

some convergence results for asynchronous algorithms nous presentons dans cet article des resultats de convergence des algorithmes asynchrones bases essentiellement sur la notion classique de contraction nous generalisons en particulier tous les resultats de convergence de ces algorithmes qui font l hypothese de contraction en norme vectorielle qui recemment a ete tres souvant utilisee par ailleurs l hypothese de contraction en norme vectorielle peut se trouver difficile voire impossible a verifier pour certains problemes qui peuvent etre cependant abordes dans le cadre de la contraction classique que nous adoptons in this paper we present convergence results for the asynchronous algorithms based essentially on the notion of classical contraction we generalize in particular all convergence results for those algorithms which are based on the vectorial norm hypothesis in wide spread use recently certain problems for which the vectorial norm hypothesis can be difficult or even impossible to verify can nontheless be tackled within the scope of the classical contraction that we adopte

further results on convergence of asynchronous linear iterations abstract this paper focuses on the convergence problem of asynchronous linear iterations a stronger version of the necessity part of the classical chazan miranker theorem is proved and new results for special classes of iteration matrices are also presented

equivalence of truncated count mixture distributions and mixtures of truncated count distributions summary this article is about modeling count data with zero truncation a parametric count density family is considered the truncated mixture of densities from this family is different from the mixture of truncated densities from the same family whereas the former model is more natural to formulate and to interpret the latter model is theoretically easier to treat it is shown that for any mixing distribution leading to a truncated mixture a usually different mixing distribution can be found so that the associated mixture of truncated densities equals the truncated mixture and vice versa this implies that the likelihood surfaces for both situations agree and in this sense both models are equivalent zero truncated count data models are used frequently in the capture recapture setting to estimate population size and it can be shown that the two horvitz thompson estimators associated with the two models agree in particular it is possible to achieve strong results for mixtures of truncated poisson densities including reliable global construction of the unique npmle nonparametric maximum likelihood estimator of the mixing distribution implying a unique estimator for the population size the benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities which is less appealing for the practitioner but theoretically easier mixtures of truncated count densities form a convex linear model for which a developed theory exists including global maximum likelihood theory as well as algorithmic approaches once the problem has been solved in this class it might readily be transformed back to the original problem by means of an explicitly given mapping applications of these ideas are given particularly in the case of the truncated poisson family

asynchronous block iterative methods for almost linear equations abstract this paper gives convergence conditions for asynchronous block iterative methods for the solution of the almost linear equation ax f x where a is a linear operator f a block diagonal lipschitz continuous operator and x a vector in terms of a splitting of a and the lipschitz constant of f the methods used are a combination of the contraction mapping approach using a vectorial norm and a large scale systems approach using vector difference inequalities the load flow equations for a power system are almost linear in the above sense and considerable speedup can be obtained on a four transputer machine

nonstationary parallel relaxed multisplitting methods abstract relaxed nonstationary multisplitting methods are studied for the parallel solution of nonsingular linear systems convergence results of the synchronous and asynchronous versions for systems with h matrices are presented computational results of these methods on a shared memory multiprocessor vector computer are reported these results show that nonstationary methods synchronous and asynchronous are better than the standard ones especially when the matrix of the linear system has a relatively small bandwidth moreover asynchronous versions always behave better than the synchronous ones

the performance of mixture models in heterogeneous closed population capture recapture summarydorazio and royle 2003 biometrics59 351 364 investigated the behavior of three mixture models for closed population capture recapture analysis in the presence of individual heterogeneity of capture probability their simulations were from the beta binomial distribution with analyses from the beta binomial the logit normal and the finite mixture latent class models in this response simulations from many different distributions give a broader picture of the relative value of the beta binomial and the finite mixture models and provide some preliminary insights into the situations in which these models are useful

bifurcations of travelling wave solutions for the k n n 2n equations abstract by using the bifurcation theory of dynamical systems to the k n n 2 n equations given by wazwaz the existence of solitary wave solutions solitary cusp wave solutions kink and anti kink wave solutions and uncountably infinite many smooth and non smooth periodic wave solutions is obtained under different parametric conditions various sufficient conditions to guarantee the existence of the above solutions are given some exact explicit parametric representations of the above waves are determined