on gamma function inequalities on montre que certaines fonctions comportant les quotients de fonctions gamma sont completement monotones on en deduit des inegalites on etablit aussi la divisibilite infinie de plusieurs distributions de probabilite dont les transformees de laplace comportent des quotients de fonctions gamma

asymptotic expansions for large closed queueing networks with multiple job classes a closed bcmp queuing network consisting of r job classes chains k 1 single server fixed rate nodes and m sub j class j jobs j 1 2 r is considered asymptotic expansions are constructed for the partition function under assumptions 1 k 1 2 m sub j 1 for each j and 3 k m sub j o 1 analytic expressions for performance measures such as the mean queue length are also given the approach employs the ray method and the method of matched asymptotic expansions numerical comparisons illustrate the accuracy of the approximations

fast relative lempel ziv self index for similar sequences abstract recent advances in biotechnology and web technology are continuously generating huge collections of similar strings people now face the problem of storing them compactly while supporting fast pattern searching one compression scheme called relative lempel ziv compression uses textual substitutions from a reference text to represent each string in s as a concatenation of substrings from a reference string r this basic scheme gives a good compression ratio when every string in s is similar to r but does not provide any pattern searching functionality here we describe a new data structure based on relative lempel ziv compression that is space efficient and also supports fast pattern searching

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

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

several remarks on acceleration of convergence using generalized linear methods of summability some acceleration theorems for generalized linear summability methods a ank where ank are linear bounded operators from banach space b space x into b space y are derived these results are proved by the method of summability with given rapidity for this purpose some problems of summability with given rapidity are discussed

some continuous programming problems in numerical analysis many problems in the design and implementation of computational schemes may be studied using the theory and methods of mathematical programming one seeks to minimize bounds for the errors in the calculated results obtained from a given set of input data exploiting analytical relations we describe optimal quadrature rules and give an application to the evaluation of the sums of power series belonging to an important class we present results which are based on the theory of linear and semi infinite programming we also study the associated complexity issues and obtain simple qualitative results for the computational work required

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

numerical computation of the moments of a probability distribution from its transform we present a simple fast and robust algorithm for numerically computing the first n moments arbitrary n of a nonnegative probability distribution from its laplace stieltjes transform continuous mixed case or z transform discrete case the algorithm is based on numerically inverting an adaptively modified moment generating function it only requires computation of the transform at several complex values of its argument we also show that the high order moments may be used in detecting the presence of exponential or geometric tails in distributions and in case they are present the two parameters characterizing such a tail may be accurately computed several numerical examples of interest in the queueing literature illustrate the use of the algorithm they include commonly used distributions as well as the waiting time queue length and busy period in queues with poisson or more general markovian arrival processes priority queues are also considered

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

a new nonstationarity detector a new test to determine the stationarity length of a locally wide sense stationary gaussian random process is proposed based on the modeling of the process as a time varying autoregressive process the time varying model parameters are tested using a rao test the use of a rao test avoids the necessity of obtaining the maximum likelihood estimator of the model parameters under the alternative hypothesis which is intractable computer simulation results are given to demonstrate its effectiveness and to verify the asymptotic theoretical performance of the test applications are to spectral analysis noise estimation and time series modeling

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

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

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

a new parametric adaptive nonstationarity detector and application techniques for hypothesis testing can be used to solve a broad class of nonstationarity detection problems which is a key issue in a variety of applications to achieve lower complexity and to deal with real time detection in practical applications we develop a new adaptive nonstationarity detector by exploiting a parametric model a weighted maximum a posteriori map estimator is developed to estimate the parameters associated with the parametric model we then derive a regularized wald test from the weighted map estimate which is adaptively implemented by a regularized recursive least squares rls algorithm several important issues are discussed including model order selection forgetting factor and regularization parameter selection for rls and numerically stable implementation using qr decomposition which are intrinsic parts of the proposed parametric adaptive detector simulation results are presented to illustrate the efficiency of the proposed nonstationarity detector with adaptive estimation and automatic model selection especially for slowly varying type of nonstationarity such as time varying spectrums and speeches

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

on the invariance coincidence and statistical equivalence of the glrt rao test and wald test three common techniques to discriminate between alternatives in a binary hypothesis testing problem are the generalized likelihood ratio test glrt the rao test and the wald test in this paper we investigate some characteristics of the corresponding decision statistics and provide their expressions for some problems of particular interest in statistical signal processing first of all we focus on the invariance of the rao and wald tests with respect to transformations leaving the testing problem unaltered then we introduce necessary and sufficient conditions in order for their decision statistics to coincide with twice the logarithm of the glrt statistic finally we present some detection problems usually encountered in practical signal processing applications where the decision variables of the three quoted tests are equivalent namely related by strictly monotonic transformations

the cfar adaptive subspace detector is a scale invariant glrt the constant false alarm rate cfar matched subspace detector cfar msd is the uniformly most powerful invariant test and the generalized likelihood ratio test glrt for detecting a target signal in noise whose covariance structure is known but whose level is unknown previously the cfar adaptive subspace detector cfar asd or adaptive coherence estimator ace was proposed for detecting a target signal in noise whose covariance structure and level are both unknown and whose covariance structure is estimated with a sample covariance matrix based on training data we show here that the cfar asd is glrt when the test measurement is not constrained to have the same noise level as the training data as a consequence this glrt is invariant to a more general scaling condition on the test and training data than the well known glrt of kelly 1986

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

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

gradient based variable forgetting factor rls algorithm in time varying environments in this paper a new control mechanism for the variable forgetting factor vff of the recursive least square rls adaptive algorithm is presented the control algorithm is basically a gradient based method of which the gradient is derived from an improved mean square error analysis of rls the new mean square error analysis exploits the correlation of the inverse of the correlation matrix with itself that yields improved theoretical results especially in the transient and steady state mean square error it is shown that the theoretical analysis is close to simulation results for different forgetting factors and different model orders the analysis yields a dynamic equation of mean square error that can be used to derive a dynamic equation of the gradient of mean square error to control the forgetting factor the dynamic equation can produce a positive gradient when the error is large and a negative gradient when the error is in the steady state compared with other variable forgetting factor algorithms the new control algorithm gives fast tracking and small mean square model error for different signal to noise ratios snrs

testing stationarity with surrogates a time frequency approach an operational framework is developed for testing stationarity relatively to an observation scale in both stochastic and deterministic contexts the proposed method is based on a comparison between global and local time frequency features the originality is to make use of a family of stationary surrogates for defining the null hypothesis of stationarity and to base on them two different statistical tests the first one makes use of suitably chosen distances between local and global spectra whereas the second one is implemented as a one class classifier the time frequency features extracted from the surrogates being interpreted as a learning set for stationarity the principle of the method and of its two variations is presented and some results are shown on typical models of signals that can be thought of as stationary or nonstationary depending on the observation scale used

an fft based algorithm for 2d power series expansions abstract an effective numerical algorithm based on inverting a specialized laplace transform is derived for computing the two dimensional power series expansion coefficients of a two variable function due to the special structure of the constructed 2d laplace transform the accuracy of the inverted function values can be assured effectively by the generalized riemann zeta function evaluation and the multiple sets of 2d fft computation therefore the algorithm is particularly amenable to modern computers having multiprocessors and or vector processors

asymptotic map criteria for model selection the two most popular model selection rules in signal processing literature have been akaike s 1974 criterion aic and rissanen s 1978 principle of minimum description length mdl these rules are similar in form in that they both consist of data and penalty terms their data terms are identical but the penalties are different mdl being more stringent toward overparameterization aic penalizes for each additional model parameter with an equal incremental amount of penalty regardless of the parameter s role in the model in most of the literature on model selection mdl appears in a form that also suggests equal penalty for every unknown parameter this mdl criterion we refer to as naive mdl in this paper we show that identical penalization for every parameter is not appropriate and that the penalty has to depend on the model structure and type of model parameters the approach to showing this is bayesian and it relies on large sample theory we derive maximum a posteriori map rules for several different families of competing models and obtain forms that are similar to aic and naive mdl for some families however we find that the derived penalties are different in those cases our extensive simulations show that the map rule outperforms aic and naive mdl

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

on a generalization of the richardson extrapolation process a convergence result for a generalized richardson extrapolation process is improved upon considerably and additional results of interest are proved an application of practical importance is also given finally some known results concerning the convergence of levin s t transformation are reconsidered in light of the results of the present work

fully functional suffix trees and optimal text searching in bwt runs bounded space indexing highly repetitive texts such as genomic databases software repositories and versioned text collections has become an important problem since the turn of the millennium a relevant compressibility measure for repetitive texts is r the number of runs in their burrows wheeler transforms bwts one of the earliest indexes for repetitive collections the run length fm index used o r space and was able to efficiently count the number of occurrences of a pattern of length m in a text of length n in o m log log n time with current techniques however it was unable to locate the positions of those occurrences efficiently within a space bounded in terms of r in this article we close this long standing problem showing how to extend the run length fm index so that it can locate the occ occurrences efficiently in o occ log log n time within o r space by raising the space to o r log log n our index counts the occurrences in optimal time o m and locates them in optimal time as well o m occ by further raising the space by an o w log factor where is the alphabet size and w e log n is the ram machine size in bits we support count and locate in o m log w and o m log w occ time which is optimal in the packed setting and had not been obtained before in compressed space we also describe a structure using o r log n r space that replaces the text and extracts any text substring of length e in the almost optimal time o log n r e log w within that space we similarly provide access to arbitrary suffix array inverse suffix array and longest common prefix array cells in time o log n r and extend these capabilities to full suffix tree functionality typically in o log n r time per operation our experiments show that our o r space index outperforms the space competitive alternatives by 1 2 orders of magnitude in time competitive implementations of the original fm index are outperformed by 1 2 orders of magnitude in space and or 2 3 in time

document listing on repetitive collections with guaranteed performance abstract we consider document listing on string collections that is finding in which strings a given pattern appears in particular we focus on repetitive collections a collection of size n over alphabet 1 is composed of d copies of a string of size n and s edits are applied on ranges of copies we introduce the first document listing index with size o n s precisely o n lg s lg 2 n lg d bits and with useful worst case time guarantees given a pattern of length m the index reports the ndoc 0 strings where it appears in time o m lg 1 n ndoc for any constant 0 and tells in time o m lg n if ndoc 0 our technique is to augment a range data structure that is commonly used on grammar based indexes so that instead of retrieving all the pattern occurrences it computes useful summaries on them we show that the idea has independent interest we introduce the first grammar based index that on a text t 1 n with a grammar of size r uses o r lg n bits and counts the number of occurrences of a pattern p 1 m in time o m 2 m lg 2 r for any constant 0 we also give the first index using o z lg n z lg n bits where t is parsed by lempel ziv into z phrases counting occurrences in time o m lg 2 n

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

asymptotics of multivariate sequences part iii quadratic points abstract we consider a number of combinatorial problems in which rational generating functions may be obtained whose denominators have factors with certain singularities specifically there exist points near which one of the factors is asymptotic to a nondegenerate quadratic we compute the asymptotics of the coefficients of such a generating function the computation requires some topological deformations as well as fourier laplace transforms of generalized functions we apply the results of the theory to specific combinatorial problems such as aztec diamond tilings cube groves and multi set permutations

twenty combinatorial examples of asymptotics derived from multivariate generating functions let a bf r bf r in mathbb n d be a d dimensional array of numbers for which the generating function f bf z sum bf r a bf r bf z bf r is meromorphic in a neighborhood of the origin for example f may be a rational multivariate generating function we discuss recent results that allow the effective computation of asymptotic expansions for the coefficients of f our purpose is to illustrate the use of these techniques on a variety of problems of combinatorial interest the survey begins by summarizing previous work on the asymptotics of univariate and multivariate generating functions next we describe the morse theoretic underpinnings of some new asymptotic techniques we then quote and summarize these results in such a way that only elementary analyses are needed to check hypotheses and carry out computations the remainder of the survey focuses on combinatorial applications such as enumeration of words with forbidden substrings edges and cycles in graphs polyominoes and descents in permutations after the individual examples we discuss three broad classes of examples namely functions derived via the transfer matrix method those derived via the kernel method and those derived via the method of lagrange inversion these methods have the property that generating functions derived from them are amenable to our asymptotic analyses and we describe further machinery that facilitates computations for these classes of examples

parametric modeling for damped sinusoids from multiple channels the problem of parametric modeling for noisy damped sinusoidal signals from multiple channels is addressed utilizing the shift invariance property of the signal subspace the number of distinct sinusoidal poles in the multiple channels is first determined with the estimated number the distinct frequencies and damping factors are then computed with the multi channel weighted linear prediction method the estimated sinusoidal poles are then matched to each channel according to the extreme value theory of distribution of random fields simulations are performed to show the performance advantages of the proposed multi channel sinusoidal modeling methodology compared with existing methods

comments on on normalizing constants in queueing networks by p g harrison comments on harrison p g 1985 on normalizing constants in queueing networks opns res 33 464 468

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

combined data structure for previous and next smaller values let a be a static array storing n elements from a totally ordered set we present a data structure of optimal size at most nlog 2 3 22 o n bits that allows us to answer the following queries on a in constant time without accessing a 1 previous smaller value queries where given an index i we wish to find the first index to the left of i where a is strictly smaller than at i and 2 next smaller value queries which search to the right of i as an additional bonus our data structure also allows one to answer a third kind of query given indices i

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

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 simultaneous process for convergence acceleration and error control abstract let xn be a real sequence converging to the limit x and such that x n x n 1 x n n n v i 0 a i n i a0 0 0 for n large enough here we propose a repeated process using two transformations namely aitken s 2 process and brezinski s 2 algorithm which provide a sequence of intervals asymptotically containing x in particular we introduce for 1 a version of the modified iterated 2 process based on the convergence orders so generalizing a method proposed by sablonniere we establish that the order vp used in the pth iteration is vp 1 kp 1 1 kp 1 3 being an integer we give an estimation method for vp confirming the choice of kp 1

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

technical note on normalizing constants in queueing networks we present a method for deriving the normalizing constant for the state space probabilities in a closed markovian queueing network with constant service rates our method produces a much simpler expression than any obtained previously this expression takes the form of a sum of only m terms if the visitation rate to service rate ratios are distinct and is easily generalized to the degenerate case the expression also yields a closed form solution for time delay distributions in cyclic networks of any length and with any number of customers

high snr consistent linear model order selection and subset selection high snr consistency of model order selection criteria in linear regression models has attracted a lot of attention in the signal processing community recently it is now known that exponentially embedded family versions of minimum description length etc are high snr consistent however a general framework for high snr consistency in linear regression is still missing this paper fills this gap by deriving necessary and sufficient conditions nscs for model order selection criteria in both known and unknown noise variance situations to be high snr consistent many popular model order selection criteria are proved to be high snr consistent using these nscs we also provide a convergence rate analysis to discriminate between various high snr consistent model order selection criteria a direct application of model order selection techniques to the very important subset selection problem is computationally infeasible this paper establish the high snr consistency of an existing t statistics based index ordering scheme that allows the conversion of a subset selection problem into a model order selection problem combining this index ordering with high snr consistent model order selection criteria leads to a novel subset selection procedure ssp that is numerically shown to outperform existing high snr consistent ssps

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

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

time varying autoregressive tvar models for multiple radar observations we consider the adaptive radar problem where the properties of the nonstationary clutter signals can be estimated using multiple observations of radar returns from a number of sufficiently homogeneous range azimuth resolution cells we derive a method for approximating an arbitrary hermitian covariance matrix by a time varying autoregressive model of order m tvar m that is based on the dym gohberg band matrix extension technique which gives the unique tvar m model for any nondegenerate covariance matrix we demonstrate that the dym gohberg transformation of the sample covariance matrix gives the maximum likelihood ml estimate of the tvar m covariance matrix we introduce an example of tvar m clutter modeling for high frequency over the horizon radar that demonstrates its practical importance

multidimensional residues generating functions and their application to queueing networks this paper has two goals the first is to introduce applied mathematicians to a new technique involving several complex variable residue theory this is a multidimensional extension of a well known result for functions of one complex variable p griffiths and j harris principles of algebraic geometry john wiley and sons new york 1978 that yields useful asymptotic information when applied to generating functions the authors begin by reviewing the residue theory of one complex variable noting that there are useful sets of relationships between the residues of certain rational functions they use the one dimensional theory to rederive and extend a well known result of koenigsberg p g harrison oper res 33 1985 pp 464 468 these relationships to a degree can be found for residues of the analogous rational functions of several complex variables the second goal is to apply these tools to the study of product form queueing networks it is well known that for generating functions of a single v

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

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

determinantal representations for the j transformation the iterative j transformation homeier h h h 1993 some applications of nonlinear convergence accelerators int j quantum chem 45 545 562 is of similar generality as the well known e algorithm brezinski c 1980 a general extrapolation algorithm numer math 35 175 180 h vie t 1979 generalized neville type extrapolation schemes bit 19 204 213 the properties of the j transformation were studied recently in two companion papers homeier h h h 1994a a hierarchically consistent iterative sequence transformation numer algo 8 47 81 homeier h h h 1994b analytical and numerical studies of the convergence behavior of the j transformation j comput appl math to appear in the present contribution explicit determinantal representations for this sequence transformation are derived the relation to the brezinski walz theory brezinski c walz g 1991 sequences of transformations and triangular recursion schemes with applications in numerical analysis j comput appl math 34 361 383 is discussed overholt s process overholt k j 1965 extended aitken acceleration bit 5 122 132 is shown to be a special case of the j transformation consequently explicit determinantal representations of overholt s process are derived which do not depend on lower order transforms also families of sequences are given for which overholt s process is exact as a numerical example the euler series is summed using the j transformation the results indicate that the j transformation is a very powerful numerical tool