the multifrontal method for sparse matrix solution theory and practice this paper presents an overview of the multifrontal method for the solution of large sparse symmetric positive definite linear systems the method is formulated in terms of frontal matrices update matrices and an assembly tree formal definitions of these notions are given based on the sparse matrix structure various advances to the basic method are surveyed they include the role of matrix reorderings the use of supernodes and other implementatjon techniques the use of the method in different computational environments is also described

generalized quadratic minimization and blind multichannel deconvolution this paper deals with the problem of quadratic minimization subject to linear equality constraints unlike the standard formulation we assume the most general case of a possibly singular quadratic form we explain that the existing formal solution to this problem has several drawbacks our new approach is free from most of these drawbacks in particular it has a simple interpretation and is relatively easy to implement the practical importance of this result lies in its numerous applications filter design spectral analysis direction finding and blind deconvolution of multiple fir channels here we focus on the blind deconvolution application for which we present a novel solution with enhanced performance

maximum likelihood direction of arrival estimation in unknown noise fields using sparse sensor arrays we address the problem of maximum likelihood ml direction of arrival doa estimation in unknown spatially correlated noise fields using sparse sensor arrays composed of multiple widely separated subarrays in such arrays intersubarray spacings are substantially larger than the signal wavelength and therefore sensor noises can be assumed to be uncorrelated between different subarrays this leads to a block diagonal structure of the noise covariance matrix which enables a substantial reduction of the number of nuisance noise parameters and ensures the identifiability of the underlying doa estimation problem a new deterministic ml doa estimator is derived for this class of sparse sensor arrays the proposed approach concentrates the ml estimation problem with respect to all nuisance parameters in contrast to the analytic concentration used in conventional ml techniques the implementation of the proposed estimator is based on an iterative procedure which includes a stepwise concentration of the log likelihood ll function the proposed algorithm is shown to have a straightforward extension to the case of uncalibrated arrays with unknown sensor gains and phases it is free of any further structural constraints or parametric model restrictions that are usually imposed on the noise covariance matrix and received signals in most existing ml based approaches to doa estimation in spatially correlated noise

the generalized richardson extrapolation process grep 1 and computation of derivatives of limits of sequences with applications to the d 1 transformation abstract let sm be an infinite sequence whose limit or antilimit s can be approximated very efficiently by applying a suitable extrapolation method e0 to sm assume that the sm and hence also s are differentiable functions of some parameter d d s being the limit or antilimit of d d sm and that we need to approximate d d s a direct way of achieving this would be by applying again a suitable extrapolation method e1 to the sequence d d sm and this approach has often been used efficiently in various problems of practical importance unfortunately as has been observed at least in some important cases when d d sm and sm have essentially different asymptotic behaviors as m the approximations to d d s produced by this approach despite the fact that they are good do not converge as quickly as those obtained for s and this is puzzling in a recent paper a sidi extrapolation methods and derivatives of limits of sequences math comp 69 2000 305 323 we gave a rigorous mathematical explanation of this phenomenon for the cases in which e0 is the richardson extrapolation process and e1 is a generalization of it and we showed that the phenomenon has nothing to do with numerics following that we proposed a very effective procedure to overcome this problem that amounts to first applying the extrapolation method e0 to sm and then differentiating the resulting approximations to s as a practical means of implementing this procedure we also proposed the direct differentiation of the recursion relations of the extrapolation method e0 used in approximating s we additionally provided a thorough convergence and stability analysis in conjunction with the richardson extrapolation process from which we deduced that the new procedure for d d s has practically the same convergence properties as e0 for s finally we presented an application to the computation of integrals with algebraic logarithmic endpoint singularities via the romberg integration in this paper we continue this research by treating sidi s generalized richardson extrapolation process grep 1 in detail we then apply the new procedure to various infinite series of logarithmic type whether convergent or divergent in conjunction with the d 1 transformation of levin and sidi both the theory and the numerical results of this paper too indicate that this approach is the preferred one for computing derivatives of limits of infinite sequences and series

parallel factor analysis in sensor array processing this paper links multiple invariance sensor array processing mi sap to parallel factor parafac analysis which is a tool rooted in psychometrics and chemometrics parafac is a common name for low rank decomposition of three and higher way arrays this link facilitates the derivation of powerful identifiability results for mi sap shows that the uniqueness of single and multiple invariance esprit stems from uniqueness of low rank decomposition of three way arrays and allows tapping on the available expertise for fitting the parafac model the results are applicable to both data domain and subspace mi sap formulations the paper also includes a constructive uniqueness proof for a special parafac model

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

extrapolation methods and derivatives of limits of sequences let s m be an infinite sequence whose limit or antilimit s can be approximated very efficiently by applying a suitable extrapolation method e 0 to s m assume that the s m and hence also s are differentiable functions of some parameter d d s being the limit or antilimit of d d s m and that we need to approximate d d s a direct way of achieving this would be by applying again a suitable extrapolation method e 1 to the sequence d d s m and this approach has often been used efficiently in various problems of practical importance unfortunately as has been observed at least in some important cases when d d s m and s m have essentially different asymptotic behaviors as m the approximations to d d s produced by this approach despite the fact that they are good do not converge as quickly as those obtained for s and this is puzzling in this paper we first give a rigorous mathematical explanation of this phenomenon for the cases in which e 0 is the richardson extrapolation process and e 1 is a generalization of it thus showing that the phenomenon has very little to do with numerics following that we propose a procedure that amounts to first applying the extrapolation method e 0 to s m and then differentiating the resulting approximations to s and we provide a thorough convergence and stability analysis in conjunction with the richardson extrapolation process it follows from this analysis that the new procedure for d d s has practically the same convergence properties as e 0 for s we show that a very efficient way of implementing the new procedure is by actually differentiating the recursion relations satisfied by the extrapolation method used and we derive the necessary algorithm for the richardson extrapolation process we demonstrate the effectiveness of the new approach with numerical examples that also support the theory we discuss the application of this approach to numerical integration in the presence of endpoint singularities we also discuss briefly its application in conjunction with other extrapolation methods

rank reduction direction of arrival estimators with an improved robustness against subarray orientation errors the problem of signal direction of arrival doa estimation in partly calibrated arrays composed of multiple subarrays with unknown intersubarray parameters and imperfectly known subarray orientations is studied the recently developed spectral and root versions of the rank reduction estimator rare are applicable to scenarios where no intersubarray calibration is available but unfortunately these algorithms are very sensitive to subarray orientation errors therefore the conventional rare algorithms can be applied to partly calibrated arrays with subarray orientation errors only if these errors are negligibly small in this correspondence a new robust modification of the rare algorithm with a reduced sensitivity to subarray misorientations is proposed and expressions for the corresponding stochastic crame spl acute r rao bound crb are derived the performance of our robust rare algorithm is demonstrated to be close to this bound in the case of moderate subarray orientation errors

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

efficient subspace based algorithm for adaptive bearing estimation and tracking in some practical applications of array processing the directions of the incident signals should be estimated adaptively and or the time varying directions should be tracked promptly in this paper an adaptive bearing estimation and tracking abest algorithm is investigated for estimating and tracking the uncorrelated and correlated narrow band signals impinging on a uniform linear array ula based on the subspace based method without eigendecomposition sumwe where a linear operator is obtained from the array data to form a basis for the null space by exploiting the array geometry and its shift invariance property specifically the null space is estimated using the least mean square lms or normalized lms nlms algorithm and the directions are updated using the approximate newton method the transient analyses of the lms and nlms algorithms are studied where the weight i e the linear operator is in the form of a matrix and there is a correlation between the additive noise and input data that involve the instantaneous correlations of the received array data in the updating equation and the step size stability conditions are derived explicitly in addition the analytical expressions for the mean square error mse and mean square deviation msd learning curves of the lms algorithm are clarified the effectiveness of the abest algorithm is verified and the theoretical analyses are corroborated through numerical examples simulation results show that the abest algorithm is computationally simple and has good adaptation and tracking abilities

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

parallel cholesky factorization on a shared memory multiprocessor abstract a parallel algorithm is developed for cholesky factorization on a shared memory multiprocessor the algorithm is based on self scheduling of a pool of tasks the subtasks in several variants of the basic elimination algorithm are analyzed for potential concurrency in terms of precedence relations work profiles and processor utilization this analysis is supported by simulation results the most promising variant which we call column cholesky is identified and implemented for the denelcor hep multiprocessor experimental results are given for this machine

a complete convergence and stability theory for a generalized richardson extrapolation process let a y sim a sum k 1 infty q k log y y sigma k as y rightarrow 0 where y is a discrete or continuous variable and q k xi are polynomials in xi it is assumed that sigma k and the degree of q k xi or an upper bound for it are known for each k and that a y is known for all possible y in 0 b the aim is to find a whether it is the limit or antilimit of a y for y rightarrow 0 a very effective way of doing this is by the generalized richardson extrapolation in this paper this procedure is described and a very efficient recursive algorithm for its implementation is given when the set of extrapolation points is y l y 0 omega l l 0 1 ldots for some omega in 0 1 in addition a complete theory of convergence and stability for the columns and the diagonals of the corresponding extrapolation table is provided finally two applications are considered in detail one of which is to generalized romberg integration of functions with algebraic and logarithmic endpoint singularities

efficient implementation of second order stochastic approximation algorithms in high dimensional problems stochastic approximation sa algorithms have been widely applied in minimization problems when the loss functions and or the gradient information are only accessible through noisy evaluations stochastic gradient sg descent a first order algorithm and a workhorse of much machine learning is perhaps the most famous form of sa among all sa algorithms the second order simultaneous perturbation stochastic approximation 2spsa and the second order stochastic gradient 2sg are particularly efficient in handling high dimensional problems covering both gradient free and gradient based scenarios however due to the necessary matrix operations the per iteration floating point operations flops cost of the standard 2spsa 2sg is o p 3 where p is the dimension of the underlying parameter note that the o p 3 flops cost is distinct from the classical spsa based per iteration o 1 cost in terms of the number of noisy function evaluations in this work we propose a technique to efficiently implement the 2spsa 2sg algorithms via the symmetric indefinite matrix factorization and show that the flops cost is reduced from o p 3 to o p 2 the formal almost sure convergence and rate of convergence for the newly proposed approach are directly inherited from the standard 2spsa 2sg the improvement in efficiency and numerical stability is demonstrated in two numerical studies

analysis of state space system identification methods based on instrumental variables and subspace fitting subspace based state space system identification 4sid methods have recently been proposed as an alternative to more traditional techniques for multivariable system identification the advantages are that the user has simple and few design variables and that the methods have robust numerical properties and relatively low computational complexities though subspace techniques have been demonstrated to perform well in a number of cases the performance of these methods is neither fully understood nor analyzed our principal objective is to undertake a statistical investigation of subspace based system identification techniques the studied methods consist of two steps the subspace spanned by the extended observability matrix is first estimated the asymptotic properties of this subspace estimate are derived herein in the second step the structure of the extended observability matrix is used to find a system model estimate two possible methods are considered the simplest one only uses a certain shift invariance property while in the other method a parametric representation of the null space of the observability matrix is exploited explicit expressions for the asymptotic estimation error variances of the corresponding pole estimates are given

efficient eigenspace based array signal processing using multiple shift invariant subarrays this paper deals with the construction of eigensubspaces for adaptive array signal processing an efficient technique for extracting the eigensubspaces spanned by the data vector received by an n element adaptive array is presented we first decompose the original array into several subarrays with multiple shift invariances and find the eigensubspaces corresponding to each of the subarrays by solving a least squares ls or total least squares tls problem the signal and noise subspaces corresponding to the original array can be found from the eigensubspaces spanned by the subarray data vectors hence there is no need to perform the eigenvalue decomposition of the n spl times n correlation matrix of the received data vector the proposed technique significantly reduces the required computational complexity as compared to the conventional eigenspace based esb methods in conjunction with the spatial smoothing scheme or a proposed cross correlation method this technique can also deal with the case of coherent signals the effectiveness of the proposed technique is demonstrated by several computer simulations

two dimensional direction estimation for a mixture of noncoherent and coherent signals this paper deals with the two dimensional 2 d direction of arrival doa estimation of a mixture of noncoherent including uncorrelated and partially correlated and coherent i e fully correlated narrowband signals impinging on a planar sensor array composed of two parallel uniform linear arrays ulas an oblique projection based approach for 2 d direction estimation opade is proposed by using some cross correlations between the received array data in the proposed opade the oblique projection is utilized to isolate the coherent signals from the noncoherent ones and the effect of additive noise is alleviated while the computationally intensive eigendecomposition is avoided and the estimated elevation and azimuth angles are paired automatically further an iterative alternating scheme is presented to improve the estimation accuracy of the oblique projector and hence that of the doas of coherent signals the cramer rao lower bound crb for the mixture of noncoherent and coherent signals is also derived explicitly where the prior knowledge of the signal correlation is incorporated into the 2 d doa estimation of noncoherent signals finally the effectiveness of the opade and the theoretical analysis are substantiated through numerical examples

experiments with an ordinary differential equation solver in the parallel solution of method of lines problems on a shared memory parallel computer abstract we consider method of lines solutions of partial differential equations on shared memory parallel computers solutions using the ordinary differential equation solver sdriv3 which is similar to the well known lsode solver are considered it is shown that portions of the solver may be implemented in parallel in particular formation of the jacobian matrix and the linear algebra required to solve the corrector equations are natural candidates for parallel implementation since these portions dominate the cost of solving large systems of equations a variant of gaussian elimination is described which allows efficient parallel solution of systems of linear equations an implementation of sdriv3 which performs the jacobian related calculations in parallel and which uses this variant of gaussian elimination is described the modified solver is used to solve a model hyperbolic fluid flow problem timing results obtained using a sequent balance parallel computer are given which demonstrate that substantial speedups are possible extensions of the techniques to sparse problems are discussed and illustrated for a problem involving a humidification column which contacts air and water

exploiting arrays with multiple invariances using music and mode this paper describes several new techniques for direction of arrival doa estimation using arrays composed of multiple translated and uncalibrated subarrays the new algorithms can be thought of as generalizations of the music root music and mode techniques originally developed for fully calibrated arrays the advantage of these new approaches is that the doas can be estimated using either a simple one dimensional 1 d search or by rooting a polynomial as opposed to the multidimensional search required by multiple invariance mi esprit when it can be applied the proposed mi mode algorithm shares the statistical optimality of mi esprit while mi music and root mi music are only optimal for uncorrelated sources they perform better than a single invariance implementation of esprit and are thus better suited for finding the initial conditions required by the mi esprit search

music maximum likelihood and cramer rao bound further results and comparisons the problem of determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements are studied a number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization music and the maximum likelihood ml estimators for the above problems this work extends those results in several directions first it establishes that in the class of weighted music estimators the unweighted music achieves the best performance i e the minimum variance of estimation errors in large samples next it derives the covariance matrix of the ml estimator and presents detailed analytic studies of the statistical efficiency of music and ml estimators these studies include performance comparisons of music and mle with each other as well as with the ultimate performance corresponding to the cramer rao bound finally some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays

an algorithm for a generalization of the richardson extrapolation process in this paper we present a recursive method designated the w m algorithm for implementing a generalization of the richardson extrapolation process that has been ntroduced in 8 compared to the direct solution of the linear systems of equations defining the extrapolation procedure this method requires a small number of arithmetic operations and very little storage the technique is also applied to solve recursively the coefficient problem associated with the rational approximations obtained by applying the d transformation of 6 13 to power series in the course of development a new recursive algorithm for implementing a very general extrapolation procedure is introduced which is similar to that given in 2 4 for solving the same problem a fortran program for the w m algorithm is also appended

closed form 2 d angle estimation with rectangular arrays in element space or beamspace via unitary esprit the uca esprit is a closed form algorithm developed for use in conjunction with a uniform circular array uca that provides automatically paired source azimuth and elevation angle estimates the 2 d unitary esprit is presented as an algorithm providing the same capabilities for a uniform rectangular array ura in the final stage of the algorithm the real and imaginary parts of the ith eigenvalue of a matrix are one to one related to the respective direction cosines of the ith source relative to the two major array axes the 2 d unitary esprit offers a number of advantages over other proposed esprit based closed form 2 d angle estimation techniques first except for the final eigenvalue decomposition of a dimension equal to the number of sources it is efficiently formulated in terms of real valued computation throughout second it is amenable to efficient beamspace implementations that are presented third it is applicable to array configurations that do not exhibit identical subarrays e g two orthogonal linear arrays finally the 2 d unitary esprit easily handles sources having one member of the spatial frequency coordinate pair in common simulation results are presented verifying the efficacy of the method

multicentre two electron coulomb and exchange integrals over slater functions evaluated using a generalized algorithm based on nonlinear transformations when calculating molecular electronic energies the contributions involving the coulomb operator for bielectronic terms are required rapidly and to high chemically significant accuracy the atomic orbital basis functions chosen in the present work are slater type functions stfs these functions can be expressed as finite linear combinations of b functions which are suitable to apply the fourier transform method the difficulties of the numerical evaluation of the analytic expressions of the integrals of interest arise mainly from the presence of two or three dimensional integral representations in this work we present a generalized algorithm for a precise and fast numerical evaluation of molecular integrals over stfs numerical results obtained with c2h2 c2h4 and ch4 molecules show the efficiency of the approach presented in this work comparisons with the existing codes are also listed

eigenstructure techniques for 2 d angle estimation with uniform circular arrays the problem of 2d angle estimation azimuth and elevation of multiple plane waves incident on a uniform circular array uca of antennas is considered two eigenstructure based estimation algorithms that operate in beamspace and employ phase mode excitation based beamformers have been developed the first uca rb music is a beamspace version of music that offers numerous advantages over element space operation including reduced computation as subspace estimates are obtained via real valued eigendecompositions enhanced performance in correlated source scenarios due to the attendant forward backward averaging effect and the applicability of root music the second uca esprit represents a significant advance in the area of 2d angle estimation it is a novel closed form algorithm that provides automatically paired source azimuth and elevation estimates with uca esprit the eigenvalues of a matrix have the form spl mu sub i sin spl theta sub i e sup j spl phi i where spl theta sub i and spl phi sub i are the elevation and azimuth angles respectively expensive search procedures being thus avoided uca esprit is superior to existing 2d angle estimation algorithms with respect to computational complexity finally asymptotic expressions for the variances of the element space music and uca rb music estimators for the 2d scenario have been derived results of simulations that compare uca rb music and uca esprit and also validate the theoretical performance expressions are presented

performance analysis of root music the authors analyze the performance of root music a variation of the music algorithm for estimating the direction of arrival doa of plane waves in white noise in the case of a linear equispaced sensor array the performance of the method is analyzed by examining the perturbation in the roots of the polynomial formed in the intermediate step of root music in particular asymptotic results for the mean squared error in the estimates of the direction of arrival are derived simplified expressions are presented for the one and two source case and compared to those obtained for least squares esprit computer simulations are also presented and they are in close agreement with the theory an important outcome of this analysis is the fact that the error in the signal zeros has a largely radial component this provides an explanation as to why the root music is superior to the spectral music algorithm

simultaneous schur decomposition of several nonsymmetric matrices to achieve automatic pairing in multidimensional harmonic retrieval problems this paper presents a new jacobi type method to calculate a simultaneous schur decomposition ssd of several real valued nonsymmetric matrices by minimizing an appropriate cost function thereby the ssd reveals the average eigenstructure of these nonsymmetric matrices this enables an r dimensional extension of unitary esprit to estimate several undamped r dimensional modes or frequencies along with their correct pairing in multidimensional harmonic retrieval problems unitary esprit is an esprit type high resolution frequency estimation technique that is formulated in terms of real valued computations throughout for each of the r dimensions the corresponding frequency estimates are obtained from the real eigenvalues of a real valued matrix the ssd jointly estimates the eigenvalues of all r matrices and thereby achieves automatic pairing of the estimated r dimensional modes via a closed form procedure that neither requires any search nor any other heuristic pairing strategy moreover we describe how r dimensional harmonic retrieval problems with r spl ges 3 occur in array signal processing and model based object recognition applications

oblique projection based enumeration of mixed noncoherent and coherent narrowband signals in many application scenarios the signals impinging on the array of sensors comprise the noncoherent uncorrelated and or partially correlated signals and the coherent signals with several groups due to multipath propagation in this paper we consider the problem of estimating the number of noncoherent narrowband signals and that of coherent narrowband signals with multiple groups impinging on a planar sensor array composed of two parallel uniform linear arrays ulas and an oblique projection based enumerator for the mixed signals opems is proposed by utilizing the qr decomposition based ratio criterion qrrc for rank determination of a matrix in the opems the number of noncoherent signals and that of coherent signals in each group are estimated separately where only the elevation angles of noncoherent signals are estimated to isolate the coherent signals from the noncoherent ones and the computationally intensive and time consuming eigendecomposition procedure is avoided the consistency of the proposed opems is analyzed and its effectiveness is verified through numerical examples

multiple invariance esprit a subspace fitting formulation of the esprit problem is presented that provides a framework for extending the algorithm to exploit arrays with multiple invariances in particular a multiple invariance mi esprit algorithm is developed and the asymptotic distribution of the estimates is obtained simulations are conducted to verify the analysis and to compare the performance of mi esprit with that of several other approaches the excellent quality of the mi esprit estimates is explained by recent results which state that under certain conditions subspace fitting methods of this type are asymptotically efficient

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

weights whose biorthogonal polynomials admit a rodrigues formula abstract let 0 and x x let w be a non negative integrable function on an interval i let p n be a polynomial of degree n determined by the biorthogonality conditions i p n j w 0 j 0 1 n 1 we determine for which weights w p n admits an analogue of the classical rodrigues formula for orthogonal polynomials and present the formula whenever it exists we also provide generating functions and fairly explicit representations for p n

maximum likelihood methods for direction of arrival estimation five methods of direction of arrival doa estimation which can be derived from the maximum likelihood ml principle are considered the ml method mlm results from the application of the ml principle to the statistics of the observed raw data the standard multiple signal classification music procedure called music 1 is obtained as a brute force approximation of the mlm an improved music procedure named music 2 is obtained by applying the ml principle to the statistics of certain linear combinations of the sample noise space eigenvectors a procedure which compromises between the good performance of the mlm and the computational simplicity of music is a method of direction estimation mode 1 which is derived as a large sample realization of the mlm a fifth method called mode 2 is obtained by using the ml principle on the statistics of certain linear combinations of the sample eigenvectors mode 2 is computationally less demanding than the mlm it is of the same complexity as mode 1 and statistically more efficient a numerical comparison of these five doa estimation methods is presented it confirms the analytic results on their theoretical performance levels

implementing linear algebra algorithms for dense matrices on a vector pipeline machine this paper examines common implementations of linear algebra algorithms such as matrix vector multiplication matrix matrix multiplication and the solution of linear equations the different versions are examined for efficiency on a computer architecture which uses vector processing and has pipelined instruction execution by using the advanced architectural features of such machines one can usually achieve maximum performance and tremendous improvements in terms of execution speed can be seen over conventional computers

an algorithm for the finite difference approximation of derivatives with arbitrary degree and order of accuracy in this paper we introduce an algorithm and a computer code for numerical differentiation of discrete functions the algorithm presented is suitable for calculating derivatives of any degree with any arbitrary order of accuracy over all the known function sampling points the algorithm introduced avoids the labour of preliminary differencing and is in fact more convenient than using the tabulated finite difference formulas in particular when the derivatives are required with high approximation accuracy moreover the given matlab computer code can be implemented to solve boundary value ordinary and partial differential equations with high numerical accuracy the numerical technique is based on the undetermined coefficient method in conjunction with taylor s expansion to avoid the difficulty of solving a system of linear equations an explicit closed form equation for the weighting coefficients is derived in terms of the elementary symmetric functions this is done by using an explicit closed formula for the vandermonde matrix inverse moreover the code is designed to give a unified approximation order throughout the given domain a numerical differentiation example is used to investigate the validity and feasibility of the algorithm and the code it is found that the method and the code work properly for any degree of derivative and any order of accuracy

discriminative relational topic models relational topic models rtms provide a probabilistic generative process to describe both the link structure and document contents for document networks and they have shown promise on predicting network structures and discovering latent topic representations however existing rtms have limitations in both the restricted model expressiveness and incapability of dealing with imbalanced network data to expand the scope and improve the inference accuracy of rtms this paper presents three extensions 1 unlike the common link likelihood with a diagonal weight matrix that allows the same topic interactions only we generalize it to use a full weight matrix that captures all pairwise topic interactions and is applicable to asymmetric networks 2 instead of doing standard bayesian inference we perform regularized bayesian inference regbayes with a regularization parameter to deal with the imbalanced link structure issue in real networks and improve the discriminative ability of learned latent representations and 3 instead of doing variational approximation with strict mean field assumptions we present collapsed gibbs sampling algorithms for the generalized relational topic models by exploring data augmentation without making restricting assumptions under the generic regbayes framework we carefully investigate two popular discriminative loss functions namely the logistic log loss and the max margin hinge loss experimental results on several real network datasets demonstrate the significance of these extensions on improving prediction performance

bi iteration multiple invariance subspace tracking and adaptive esprit a class of adaptive bi iteration svd bi svd algorithms for tracking structured subspaces of the form e e e spl psi sub 1 e spl psi sub 2 e spl psi sub n 1 is introduced where e is an n spl times r n spl ges r orthonormal core basis matrix and spl psi sub 1 spl psi sub 2 spl psi sub n 1 is a set of r spl times r subrotors structured subspaces of this kind arise in all forms of multiple invariance mi techniques such as mi esprit an adaptive mi esprit algorithm using bi svd mi subspace tracking is developed computer experiments validate the theoretical results

two dimensional modal analysis based on maximum likelihood the authors present a method for estimating the parameters of 2 d damped harmonic modal signals in additive gaussian noise this method applies in the cases of single or multiexperiment data and incoherent or coherent signals both synthesis and analysis models for the data are developed central to these models are the signal and orthogonal subspaces under the assumption of distinct modes in one of the two dimensions there exists an invertible function between the parameters of these two subspaces this function can be used to express the optimization problem given by maximum likelihood in terms of the orthogonal subspace the resulting problem can be solved by any of several methods including total least squares and iterative quadratic maximum likelihood iqml