a numerical solution for non classical parabolic problem based on chebyshev spectral collocation method a numerical method based on chebyshev polynomials and local interpolating functions is proposed for solving the one dimensional parabolic partial differential equation subject to non classical conditions to assess its validity and accuracy the method is applied to solve several test problem

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

krylov subspace exponential time domain solution of maxwell s equations in photonic crystal modeling the exponential time integration i e time integration which involves the matrix exponential is an attractive tool for time domain modeling involving maxwell s equations however its application in practice often requires a substantial knowledge of numerical linear algebra algorithms such as krylov subspace methods in this note we discuss exponential krylov subspace time integration methods and provide a simple guide on how to use these methods in practice while specifically aiming at nanophotonics applications we intentionally keep the presentation as general as possible and consider full vector maxwell s equations with damping i e with nonzero conductivity terms efficient techniques such as the krylov shift and invert method and residual based stopping criteria are discussed in detail numerical experiments are presented to demonstrate the efficiency of the discussed methods and their mesh independent convergence some of the algorithms described here are available as octave matlab codes from www math utwente nl botchevma expm

a numerical solution of burgers equation by pseudospectral method and darvishi s preconditioning in this paper we solve the burgers equation by pseudospectral method this equation is one dimensional quasilinear partial differential equation to reduce round off error of pseudospectral method we use darvishi s preconditioning the numerical results obtained by this method for different values of viscosity have been compared with the exact solution it was seen that they were in good agreement with each other because norm infinity of error is very small

seismic depth migration with the dirac equation we demonstrate the applicability of the dirac equation in seismic wavefield extrapolation by presenting a new explicit one way prestack depth migration scheme the method is in principle accurate up to 90 from the vertical and it tolerates lateral velocity variations this is achieved by performing the extrapolation step of migration with the dirac equation implemented in the space frequency domain the dirac equation is an exact linearization of the square root wave equation and is equivalent to keeping infinitely many terms in a taylor series or continued fraction expansion of the square root operator an important property of the new method is that the local velocity and the spatial derivatives decouple in separate terms within the extrapolation operator therefore we do not need to precompute and store large tables of convolutional extrapolator coefficients depending on velocity the main drawback of the explicit scheme is that evanescent energy must be removed at each depth step to obtain numeric

multitarget angle tracking an algorithm for data association the authors consider the problem of tracking several targets in terms of the directions of arrival doa of signals using uniform linear sensor array outputs the observations in any short interval of time around a given time point spl tau enable them to estimate the doa of the targets but not identify the target to which each estimate corresponds they propose an algorithm to set up such a correspondence between estimates and targets at each time point in a sequential manner starting from an initial position of the targets once this is done the trajectories of the different targets can be obtained by plotting the estimates against time

spectral methods in time for a class of parabolic partial differential equations in this paper we introduce a fully spectral solution for the partial differential equation u t uu x vu x x mu x x x lu x x x x 0 for periodic boundary conditions in space the use of fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a chebyshev series boundary conditions other than periodic may still be treated with reasonable though lesser efficiency for all cases very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time

an efficient algorithm for tracking the angles of arrival of moving targets a novel technique for tracking the angles of arrival of moving targets is presented the targets are modeled as signal sources that continuously emit narrowband signals which impinge on an array of sensors estimates of target angles are obtained by minimizing the norm of an error matrix function involving the covariance of the sensor outputs the algorithm yields estimates that are automatically correctly associated with previous estimates consequently the data association problem does not arise and this results in a much more efficient scheme in comparison to existing methods involving search over n factorial possible measurement target associations where n is the number of targets performance of the algorithm is illustrated by a simulation example

a multistep legendre gauss spectral collocation method for nonlinear volterra integral equations we introduce a multistep legendre gauss spectral collocation method for the nonlinear volterra integral equations of the second kind this method is easy to implement and possesses high order accuracy in addition it is very suitable for long time calculations we also derive the optimal convergence of the hp version of the multistep collocation method under the l 2 norm numerical experiments confirm the theoretical expectations

a brief biography and appreciation of calyampudi radhakrishna rao with a bibliography of his books and papers we present a brief biography and appreciation of calyampudi radhakrishna rao to whom this fifth special issue on linear algebra and statistics of linear algebra and its applications is dedicated in celebration of his 75th birthday a bibliography of his books and papers is also included

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

time domain calculation of acoustical wave propagation in discontinuous media using acoustical wave propagator with mapped pseudospectral method the acoustical wave propagator awp scheme involves an effective time domain calculation of sound propagation using the combination of chebyshev polynomial expansion and the fourier pseudospectral method the accuracy of this scheme degrades when the media has discontinuities due to the well known gibbs phenomenon in this paper several issues concerning awp are addressed including an analysis of the effect of gibbs phenomenon on the accuracy a mapped pseudospectral method is proposed wherein the grid points are redistributed with the emphasis across the media discontinuities by a pre determined smooth mapping curve then the spatial derivatives are calculated through a modified fourier pseudospectral method using this method the influence of the gibbs phenomenon is effectively alleviated while the computational efficiency of awp is still maintained the superiority of this improved awp scheme is illustrated by three one dimensional 1 d numerical examples

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

accurate and efficient seismic modeling in random media the optimum method for seismic modeling in random media must 1 be highly accurate to be sensitive to subtle effects of wave propagation 2 allow coarse sampling to model media that are large compared to the scale lengths and wave propagation distances which are long compared to the wavelengths this is necessary to obtain statistically meaningful overall attributes of wavefields high order staggered grid finite difference algorithms and the pseudospectral method combine high accuracy in time and space with coarse sampling investigations for random media reveal that both methods lead to nearly identical wavefields the small differences can be attributed mainly to differences in the numerical dispersion this result is important because it shows that errors of the numerical differentiation which are caused by poor polynomial interpolation near discontinuities do not accumulate but cancel in a random medium where discontinuities are numerous the differentiator can be longer than the medium scale leng

legendre spectral collocation in space and time for pdes spectral methods solve partial differential equations numerically with errors bounded by an exponentially decaying function of the number of modes when the solution is analytic for time dependent problems almost all focus has been on low order finite difference schemes for the time derivative and spectral schemes for spatial derivatives spectral methods which converge spectrally in both space and time have appeared recently this paper shows that a legendre spectral collocation method of tang and xu for the heat equation converges exponentially quickly when the solution is analytic we also derive a condition number estimate of the method another space time spectral scheme which is easier to implement is proposed numerical experiments verify the theoretical results

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

one step wave extrapolation matrix method for reverse time migration abstractwe have developed a new method for solving the acoustic full wave equation which we call the one step wave extrapolation ose matrix method in our method the wave equation is redefined by introducing a complex analytic wavefield and reformulating the traditional acoustic full wave equation as a first order partial differential equation in time afterward the analytical wavefield is separated to its real and imaginary parts and the resulting first order coupled set of equations is solved by the tal ezer s technique which consists of using the chebyshev polynomial expansion to approximate the matrix exponential operator the matrix is antisymmetrical with a square root pseudodifferential operator which is computed using the fourier method in this way the implementation of the proposed method is straightforward and if the appropriate number of chebyshev polynomial expansion terms is chosen the proposed numerical algorithm is unconditionally stable and propagates seismic waves free of num

spectral methods in time for parabolic problems a pseudospectral explicit scheme for solving linear periodic parabolic problems is described it has infinite accuracy both in time and in space the high accuracy is achieved while the time resolution parameter m m o 1 delta t for time marching algorithm and the space resolution parameter n n o 1 delta x must satisfy m o n 1 varepsilon varepsilon 0 compared to the common stability condition m o n 2 which must be satisfied in any explicit finite order time algorithm

spectral methods in time for hyperbolic equations a pseudospectral numerical scheme for solving linear periodic hyperbolic problems is described it has infinite accuracy both in time and in space the high accuracy in time is achieved without increasing the computational work and memory space which is needed for a regular one step explicit scheme the algorithm is shown to be optimal in the sense that among all the explicit algorithms of a certain class it requires the least amount of work to achieve a certain given resolution the class of algorithms referred to consists of all explicit schemes which may be represented as a polynomial in the spatial operator

new space time spectral and structured spectral element methods for high order problems abstract we propose new space time spectral and structured spectral element methods for high order problems by matrix decomposition we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients based on new basis functions in space and a dual petrov galerkin formulation in time we propose a new space time spectral method for a time dependent problem and proved their spectral accuracy both in space and time numerical results demonstrate their high efficiency and coincide well with theoretical analysis further to ultimately promote the numerical performance and efficiency we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high order problems besides to increase the flexibility a c 1 conforming rectangular spectral method in analogy to argyris or bell triangular elements are proposed for fourth order equations which serves as a preparative work towards conforming quadrilateral spectral elements for high order equations

solving the maxwell equations by the chebyshev method a one step finite difference time domain algorithm we present a one step algorithm that solves the maxwell equations for systems with spatially varying permittivity and permeability by the chebyshev method we demonstrate that this algorithm may be orders of magnitude more efficient than current finite difference time domain fdtd algorithms

boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium we consider an isotropic lame system for an elastic medium consisting of finitely many imperfections of small diameter embedded in a homogeneous reference medium the lame coefficients of the imperfections are different from those of the background medium first we establish an asymptotic formula for the displacement vector in terms of the reference lame coefficients the location of the imperfections and their geometry second we use this asymptotic expansion to establish continuous dependence estimates for certain characteristics of the imperfections in terms of the boundary data and to derive integral boundary formulae that yield to a very effective identification procedure

an algorithm for pole zero modeling and spectral analysis an explicit connection between fitting exponential models and pole zero models to observed data is made the fitting problem is formulated as a constrained nonlinear minimization problem this problem is then solved using a simplified iterative algorithm the algorithm is applied to simulated data and the performance of the algorithm is compared to previous results

global properties of pseudospectral methods abstract we apply polynomial interpolation methods both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations the derivative matrix for a general sequence of collocation points is explicitly constructed we explore the effect of several factors on the performance of these methods we show that global methods cannot be interpreted in terms of local methods for example the accuracy of the approximation differs when large gradients of the function occur near the center of the region or in the vicinity of the boundary this difference does not depend on the density of the collocation points near the boundaries hence intuition based on finite difference methods can lead to false results

symplectic scheme and the poynting vector in reverse time migration abstractwe developed a new numerical solution for the wave equation that combines symplectic integrators and the rapid expansion method rem this solution can be used for seismic modeling and reverse time migration rtm in seismic modeling and rtm spatial derivatives are usually calculated by finite differences fds or by the fourier method and the time evolution is normally obtained by a second order fd approach if the spatial derivatives are computed by higher order fd schemes then the time step needs to be small enough to avoid numerical dispersion therefore increasing the computational time however by using rem with the fourier method for the spatial derivatives we can apply the proposed method to propagate the wavefield for larger time steps moreover if the appropriate number of expansion terms is chosen this method is unconditionally stable and propagates seismic waves free of numerical dispersion the use of a symplectic numerical scheme provides the solution of the wave equation an

time step n tupling for wave equations abstractwe have constructed novel temporal discretizations for wave equations we first select an explicit time integrator that is of second order leading to classic time marching schemes in which the next value of the wavefield at the discrete time t t is computed from current values known at time t and the previous time t t then we determine how the time step can be doubled tripled or generally n tupled producing a new time stepping method in which the next value of the wavefield at the discrete time t n t is computed from current values known at time t and the previous time t n t in between time values of the wavefield are eliminated using the fourier method to calculate space derivatives the new time integrators allow larger stable time steps than traditional time integrators however like the lax wendroff procedure they require more computational effort per time step because the new schemes are developed from the classic second order time stepping scheme they will have the same proper

a spectral method of characteristics for hyperbolic problems a new numerical technique is introduced for first order hyperbolic equations based on combining the spectral method with explicit timestepping along the characteristics which permits the use of large timesteps at no cost in accuracy the method is unconditionally stable and spectrally accurate the theoretical results are illustrated by numerical experiments

an interpolatory approximation of the matrix exponential based on faber polynomials in this paper we introduce a method for the approximation of the matrix exponential obtained by interpolation in zeros of faber polynomials in particular we relate this computation to the solution of linear ivps numerical examples arising from practical problems are examined

a space time spectral method for the time fractional diffusion equation in this paper we consider the numerical solution of the time fractional diffusion equation essentially the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term in the former case the first order time derivative is replaced by a fractional derivative making the problem global in time we propose a spectral method in both temporal and spatial discretizations for this equation the convergence of the method is proven by providing a priori error estimate numerical tests are carried out to confirm the theoretical results thanks to the spectral accuracy in both space and time of the proposed method the storage requirement due to the global time dependence can be considerably relaxed and therefore calculation of the long time solution becomes possible

space time spectral method for a weakly singular parabolic partial integro differential equation on irregular domains abstract the spectral method is proposed for the partial integro differential equations with a weakly singular kernel on irregular domains the space discretization is based on the nodal spectral element method using the lagrange polynomials basis associated with the gauss lobatto legendre quadrature nodes also the model is discretized in time with the legendre spectral galerkin method the discretization leads to conversion of the problem to a sylvester matrix equation which can be solved efficiently by the qz algorithm gardiner et al 1992 the convergence of the method is proven by providing a priori l 2 error estimate numerical results illustrate the efficiency and spectral accuracy of the proposed method

unconditionally stable integration of maxwell s equations numerical integration of maxwell s equations is often based on explicit methods accepting a stability step size restriction in literature evidence is given that there is also a need for unconditionally stable methods as exemplified by the successful alternating direction implicit finite difference time domain scheme in this paper we discuss unconditionally stable integration for a general semi discrete maxwell system allowing non cartesian space grids as encountered in finite element discretizations such grids exclude the alternating direction implicit approach particular attention is given to the second order trapezoidal rule implemented with preconditioned conjugate gradient iteration and to second order exponential integration using krylov subspace iteration for evaluating the arising phi functions a three space dimensional test problem is used for numerical assessment and comparison with an economical second order implicit explicit integrator we further pay attention to the chebyshev series expansion for computing the exponential operator for skew symmetric matrices

an efficient pastd algorithm implementation for multiple direction of arrival tracking we propose a simple direction of arrival doa tracking scheme involving the projection approximation subspace tracking with deflation pastd algorithm and a kalman filter the doas are obtained via a newton type method initialized with the doas predicted by the kalman filter the data association is then avoided the tracking capability of the proposed algorithm is demonstrated by computer simulations in scenarios involving targets with crossing trajectories

the topological asymptotic expansion for the dirichlet problem the topological sensitivity analysis provides an asymptotic expansion of a shape function when creating a small hole inside a domain this expansion yields a descent direction which can be used for shape optimization if one wishes to keep a classical domain throughout the optimization process in this paper such an expansion is obtained for the poisson equation for a large class of cost functions and arbitrarily shaped holes in the three dimensional case this expansion depends on the shape of the hole but not on its orientation if the cost function involves only the solution u to the underlying partial differential equation whereas it may also depend on its orientation if the cost function involves the gradient nabla u in contrast the asymptotic expansion is independent of the shape in the two dimensional case a numerical example illustrates the use of the asymptotic expansion which yields a minimizing sequence of classical domains in a case where no classical solution exists

an easily implementable fourth order method for the time integration of wave problems abstract we are concerned with the time integration of systems of ordinary differential equations arising from the space discretization of partial differential wave equations with smooth solutions a method is suggested that while being as easily implementable as the standard implicit mid point rule is fourth order accurate the new method is symplectic so that it is very well suited for long time integrations of problems with a hamiltonian structure numerical experiments are reported that refer to a fourth order galerkin space discretization of the korteweg de vries equation and to a pseudospectral space discretization of the same equation

treatment of angular derivatives in the schro dinger equation by the finite fourier series method abstract we describe a finite fourier series method for treating the angular derivatives in the angular momentum term of the time dependent schrodinger equation in spherical coordinates the method involves a power series expansion of the evolution operator and treatment of singularities at 0 by l hospital s rule it is demonstrated that the method is accurate across the entire spectrum of the angular momentum operator for an appropriate sampling grid

on the internal interfaces in finite difference schemes abstractimplementing sharp internal interfaces in finite difference schemes with high spatial accuracy is challenging the propagation of fields in a locally homogeneous part of a model can be performed with spectral accuracy the implementations of interfaces are generally considered accurate to at best second order this situation can be improved by a proper band limitation of the simulation grid interfaces can be located anywhere on the grid however the fine detail information regarding the interface location must be imprinted correctly in the coarse simulation grid this can be done by starting out with a representation of a sharp material jump in the wavenumber domain and limiting the highest wavenumber to the maximum wavenumber allowed for the simulation grid the resulting wavenumber representation is then transformed to the space domain an alternative procedure is to create a fine grid model that is low pass filtered to remove wavenumbers above the maximum wavenumber allowed for the coarse s

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

a staggered time integrator for the linear acoustic wave equation using the jacobi anger expansion abstract in this study we introduce a staggered time integrator with the fourier pseudospectral method to solve the first order linear wave equation which is accelerated by using the jacobi anger expansion the proposed method can reduce the computational cost by approximately half compared to the scheme whose temporal order of accuracy is extended by the lax wendroff method under the equivalent modeling conditions such as time step length grid interval and maximum wave propagation speed this is because the jacobi anger expansion can effectively approximate the sinusoidal function which in our case is the sine function in the wavenumber domain based on the wavenumber domain analysis of the proposed method a strategy to optimally design the simulation parameters to maintain a preset level of accuracy is also introduced according to the strategy as the time step length increases not only the computational cost of the simulation is reduced but also the accuracy of the numerical solution is improved numerical simulations are also performed by using both homogeneous and heterogeneous models to validate the introduced strategy which supports the practicality of the proposed method

topological sensitivity and shape optimization for the stokes equations the topological sensitivity analysis provides an asymptotic expansion of a shape function with respect to the insertion of a small hole or obstacle inside a domain this expansion can then be used for shape optimization in this paper such an expansion is obtained for the stokes equations with general shape functions and arbitrarily shaped holes a numerical example illustrates the use of the topological sensitivity in a shape optimization problem

using the rapid expansion method for accurate time stepping in modeling and reverse time migration reverse time migration is based on seismic forward modeling algorithms where spatial derivatives usually are calculated by finite differences or by the fourier method time integration in general is done by finite difference time stepping of low orders if the spatial derivatives are calculated by high order methods and time stepping is based on low order methods there is an imbalance that might require that the time step size needs to be very small to avoid numerical dispersion as a result computing times increase using the rapid expansion method rem avoids numerical dispersion if the number of expansion terms is chosen properly comparisons with analytical solutions show that the rem is preferable especially at larger propagation times for reverse time migration the rem needs to be applied in a time stepping manner this is necessary because the original implementation based on very large time spans requires that the source term is separable in space and time this is not appropriate for reverse time migration where the sources have different time histories in reverse time migration it might be desirable to use the poynting vector information to estimate opening angles to improve the quality of the image in the solution of the wave equation this requires that one calculates not only the pressure wavefield but also its time derivative the rapid expansion method can be extended easily to provide this time derivative with negligible extra cost

on the topological derivative in shape optimization in this paper the topological derivative for an arbitrary shape functional is defined examples are provided for elliptic equations and the elasticity system in the plane the topological derivative can be used for solving shape optimization problems in structural mechanics

on the performance of signal subspace processing part i narrow band systems this paper presents an analytical evaluation of detection determination of the number of sources and estimation performances of narrow band signal subspace processing for multiple source direction finding the probabilities of underestimating and overestimating the number of sources are derived under asymptotic conditions and around the threshold regions in terms of the choice of a penalty function and signal noise and array parameters for the cases of at most two closely spaced sources in the spatially white noise a scalar measure is introduced for the evaluation of the quality of the estimated signal subspace based on the statistics of this measure performance thresholds are demonstrated for the signal to noise ratio angle separation and correlation between two equipowered sources

recursive integral time extrapolation methods for waves a comparative review abstractwe compared several families of algorithms for recursive integral time extrapolation rite algorithms for waves in isotropic and anisotropic media these methods allow simulating accurate wave extrapolation with little numerical dispersion even when using larger time steps than are usually possible for conventional finite difference methods these various rite algorithms all share the use of mixed space wavenumber domain operators derived from fourier integral solutions of single mode wave equations we evaluated a taxonomy for rite methods based on how they approximated the influence of medium heterogeneity one family of methods uses mixed domain series expansions to provide accurate approximations to heterogeneous extrapolators even for large time steps we compared several methods for deriving coefficients for such series approximations another family of methods uses interpolation between different homogeneous extrapolations to approximate heterogeneous time extrapolation such methods can b

a pseudospectral legendre method for hyperbolic equations with an improved stability condition abstract this paper introduces a new pseudospectral method for solving hyperbolic partial differential equations this method uses different grid points from previously used pseudospectral methods in fact the grid points are related to the zeroes of the legendre polynomials the main advantage of this method is that the allowable time step is proportional to the inverse of the number of grid points i n rather than to 1 n 2 as in the case of other pseudospectral methods applied to mixed initial boundary value problems a highly accurate time discretization suitable for these spectral methods is discussed

performance analysis of an adaptive algorithm for tracking dominant subspaces this paper provides a performance analysis of a least mean square lms dominant invariant subspace algorithm based on an unconstrained minimization problem this algorithm is a stochastic gradient algorithm driving the columns of a matrix w to an orthonormal basis of a dominant invariant subspace of a correlation matrix we consider the stochastic algorithm governing the evolution of ww sup h to the projection matrix onto this dominant invariant subspace and study its asymptotic distribution a closed form expression of its asymptotic covariance is given in the case of independent observations and is further analyzed to provide some insights into the behavior of this lms type algorithm in particular it is shown that even though the algorithm does not constrain w to have orthonormal columns there is deviation from orthonormality of the first order we also give a closed form expression of the asymptotic covariance of the doas estimated by the music algorithm applied to the adaptive estimate of the projector it is found that the asymptotic distributions have a structure that is very similar to those describing batch estimation techniques because both algorithms are obtained from the minimization of the same criterion finally the accuracy of the asymptotic analysis is checked by numerical simulations and is found to be valid not only for a small step size but in a very large domain

tracking the direction of arrival of multiple moving targets the authors focus on the problem of tracking the direction of arrival doa of multiple moving targets the targets are assumed to be moving with constant accelerations subject to minor random perturbations and emitting narrow band signals that impinge on an array of passive sensors estimates of the doa vector of the targets are obtained from the sensor data based on the maximum likelihood ml principle in such a way that the association between the estimates made at different time points is maintained at each stage the current ml estimates of doa are treated as measurements and refined via a kalman filter tracking is accomplished without the need to perform unduly heavy computations an efficient strategy for dealing with closely spaced targets is also presented finally the performance of the tracking algorithm is illustrated via computer simulations

control of a mechanical aeration process via topological sensitivity analysis the topological sensitivity analysis method gives the variation of a criterion with respect to the creation of a small hole in the domain in this paper we use this method to control the mechanical aeration process in eutrophic lakes a simplified model based on incompressible navier stokes equations is used only considering the liquid phase which is the dominant one the injected air is taken into account through local boundary conditions for the velocity on the injector holes a 3d numerical simulation of the aeration effects is proposed using a mixed finite element method in order to generate the best motion in the fluid for aeration purposes the optimization of the injector location is considered the main idea is to carry out topological sensitivity analysis with respect to the insertion of an injector finally a topological optimization algorithm is proposed and some numerical results showing the efficiency of our approach are presented

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

efficient 3d frequency response modeling with spectral accuracy by the rapid expansion method frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the fourier transform the former approach requires solving systems of linear equations which becomes progressively difficult to tackle for larger scale models and for higher frequency components on the contrary the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses commonly used explicit time integration methods correspond to the truncated taylor series approximations that can cause significant errors for large time steps the rapid expansion method rem uses the chebyshev expansion and offers an optimal solution to the second order in time wave equations when applying the fourier transform to the time domain wavefield solution computed by the rem we can derive a frequency response modeling formula that has the same form as the original time domain rem equation but with different summation coefficients in particular the summation coefficients for the frequency response modeling formula corresponds to the fourier transform of those for the time domain modeling equation as a result we can directly compute frequency responses from the chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods when combined with the pseudospectral method in space this new frequency response modeling method can produce spectrally accurate results with high efficiency

stability of pseudospectral and finite difference methods for variable coefficient problems it is shown that pseudospectral approximation to a special class of variable coefficient one dimensional wave equations is stable and convergent even though the wave speed changes sign within the domain computer experiments indicate similar results are valid for more general problems similarly computer results indicate that the leapfrog finite difference scheme is stable even though the wave speed changes sign within the domain however both schemes can be asymptotically unstable in time when a fixed spatial mesh is used

subspace based adaptive method for estimating direction of arrival with luenberger observer in this paper we propose a computationally simple and efficient subspace based adaptive method for estimating directions of arrival amend for multiple coherent narrowband signals impinging on a uniform linear array ula where the previously proposed qr based method is modified for the number determination a new recursive least squares rls algorithm is proposed for null space updating and a dynamic model and the luenberger state observer are employed to solve the estimate association of directions automatically the statistical performance of the rls algorithm in stationary environment is analyzed in the mean and mean squares senses and the mean square error mse and mean square derivation msd learning curves are derived explicitly furthermore an analytical study of the rls algorithm is carried out to quantitatively compare the performance between the rls and least mean square lms algorithms in the steady state the theoretical analyses and effectiveness of the proposed rls algorithm are substantiated through numerical examples

space time spectral element method for solution of second order hyperbolic equations abstract a two field mixed hybrid spectral element formulation in time and space is presented explicit stsee and implicit stsei algorithms are developed and used to solve a second order scalar hyperbolic equation the algorithms were analyzed and their characteristics in terms of truncation error and stability are presented this analysis was confirmed by numerical results the improvement in accuracy in comparison with semi discrete schemes is remarkable

optimality of high resolution array processing using the eigensystem approach in the classical approach to underwater passive listening the medium is sampled in a convenient number of look directions from which the signals are estimated in order to build an image of the noise field in contrast a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously in a gaussian context it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels this paper aims to compute such estimators when the wavefront shapes are not assumed known a priori this justifies results previously found using the asymptotical properties of the eigenvalue eigenvector decomposition of the estimated spectral density matrix of the sensor signals they have led to a variety of high resolution array processing methods more specifically a covariance matrix test for equality of the smallest eigenvalues is presented for source detection for source localization a best fit method and a test of orthogonality between the smallest eigenvectors and the source vectors are discussed

detection of point forces location using topological algorithm in stokes flows we consider a viscous incompressible fluid under the action of a finite number of particles located inside the flow domain each particle exerts a pointwise force on the fluid the main objective is the detection of point forces locations through minimization of a given performance functional the regularity lack of the state does not allow to derive optimalities conditions and build numerical algorithms to overcome this difficulty a relaxation technique is used and the detection problem is formulated as a topological optimization one a topological sensitivity analysis is derived and efficient numerical algorithms are proposed

an algorithm for multisource beamforming and multitarget tracking a new algorithm for simultaneous robust multisource beamforming and adaptive multitarget tracking is proposed self robustness to locations errors or variations is introduced by a source subspace based tracking procedure of steering vectors in the array manifold this lms type procedure is generalized from a former work we developed in the single source case two beamforming structures are actually proposed the first is adaptive and optimal for uncorrelated sources and correlated noise the second is conventional and optimal for correlated sources and uncorrelated white noise the proposed algorithm and music show an identical asymptotic variance in localization for immobile sources whereas for the mobile case the proposed algorithm is highly advantageous then it is shown that the additional use of some kinematic parameters i e speed acceleration etc inferred from the reconstructed trajectories improves the tracking performance and overcomes some of the problems of crossing targets the efficiency of multitarget tracking and the robustness of multisource beamforming are proved and then confirmed by simulation the number of sources can be initialized and tracked by a marginal proposed procedure the beamforming performance is shown to be optimal as the single source case finally the algorithm has a very low order of arithmetic complexity

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed