hierarchical bases for elliptic problems linear systems of equations with positive and symmetric matrices often occur in the numerical treatment of linear and nonlinear elliptic boundary value problems if the cg algorithm is used to solve these equations one is able to speed up the convergence by preconditioning the method of preconditioning with hierarchical basis has already been considered for the laplace equation in two space dimensions and for linear conforming elements in the present work this method is generalized to a large class of conforming and nonconforming elements 0 introduction consider elliptic problems in variational form of order 2m let x htm 2 ci and q w be a bounded domain we want to find u x such that 0 1 a u v i a vmu vmv f v vv x ja here a denotes a strictly positive possibly x dependent matrix f is a functional on x and a is assumed to satisfy c0lmlm 2 o colmlm 2 0 for all u x the solution of this problem exists according to the lax milgram theorem one way to solve this problem numerically is to approximate x by a sequence of finite dimensional spaces xn for a en if ui i xyn is a basis of xn writing u in the form

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

composition of pseudo almost automorphic and asymptotically almost automorphic functions this paper is concerned with pseudo almost automorphic functions which are more general and complicated than pseudo almost periodic functions and asymptotically almost automorphic functions new results concerning the composition of pseudo almost automorphic functions are established

dispersion estimation from linear array data in the time frequency plane we consider the problem of estimating the dispersion of a wave field from data recorded by a linear array of geophones the fact that the data we are looking at may contain several propagating waves make this even more challenging in this paper a new algorithm is proposed to solve this issue currently there are two methods for estimating wave dispersion described in the literature the first method estimates the group delay function from the time frequency representation tfr of each sensor separately it is efficient as long as the patterns of the different waves do not overlap in the time frequency plane the second method estimates the dispersion from the two dimensional 2 d fourier transform of the profile or more generally from a velocity frequency representation this assumes that the dispersion is constant along the entire sensor array it is efficient as long as the patterns of the waves do not overlap in the frequency domain our method can be thought of as a hybrid of the above two methods as it is based on the construction of a tfr where the energy of waves that propagate at a selected velocity are amplified the primary advantage of our algorithm is the use of the velocity variable to separate the patterns of the propagating waves in the time frequency plane when applied to both synthetic and real data this new algorithm gives much improved results when compared with other standard methods

the conditioning of the stiffness matrix for certain elements approximating the incompressibility condition in fluid dynamics in order to solve the stokes equations numerically crouzeix and raviart introduced elements satisfying a discrete divergence condition for the two dimensional case and uniform triangulations it is shown that using the standard basis functions the conditioning of the stiffness matrix is of ordern 2 wheren is the dimension of the corresponding finite element space hierarchical bases are introduced which give a condition number of ordern log n 3

estimation of parameters of exponentially damped sinusoids using fast maximum likelihood estimation with application to nmr spectroscopy data we present fast maximum likelihood fml estimation of parameters of multiple exponentially damped sinusoids the fml algorithm was motivated by the desire to analyze data that have many closely spaced components such as the nmr spectroscopy data of human blood plasma the computational efficiency of fml lies in reducing the multidimensional search involved in ml estimation into multiple 1 d searches this is achieved by using our knowledge of the shape of the compressed likelihood function clf in the parameter space the proposed fml algorithm is an iterative method that decomposes the original data into its constituent signal components and estimates the parameters of the individual components efficiently using our knowledge of the shape of the clf the other striking features of the proposed algorithm are that it provides procedures for initialization has a fast converging iteration stage and makes use of the information extracted in preliminary iterations to segment the data suitably to increase the effective signal to noise ratio snr the computational complexity and the performance of the proposed algorithm are compared with other existing methods such as those based on linear prediction kiss iqml alternating projections ap and expectation maximization em

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

a posteriori error estimators for the stokes equations ii non conforming discretizations we present an a posteriori error estimator for the non conforming crouzeix raviart discretization of the stokes equations which is based on the local evaluation of residuals with respect to the strong form of the differential equation the error estimator yields global upper and local lower bounds for the error of the finite element solution it can easily be generalized to the stationary incompressible navier stokes equations and to other non conforming finite element methods numerical examples show the efficiency of the proposed error estimator

on integral solutions of some nonlocal fractional differential equations with nondense domain abstract in this paper we prove the existence and uniqueness of integral solution for some nondensely defined fractional semilinear differential equation with nonlocal conditions the results are obtained by means of fixed point methods we also give some examples of such problems

pseudo almost periodic solutions to some differential equations abstract this paper is concerned with the pseudo almost periodic solutions to the abstract differential equations of the form d d s w s aw s bw s f s where a b are densely defined closed linear operators acting in a hilbert space h and f r h is a h valued pseudo almost periodic function using the theory of the invariant subspaces for unbounded linear operators we show that every bounded solution to is a pseudo almost periodic function

improving the readability of time frequency and time scale representations by the reassignment method in this paper the use of the reassignment method first applied by kodera gendrin and de villedary 1976 to the spectrogram is generalized to any bilinear time frequency or time scale distribution this method creates a modified version of a representation by moving its values away from where they are computed so as to produce a better localization of the signal components we first propose a new formulation of this method followed by a thorough theoretical study of its characteristics its practical use for a large variety of known time frequency and time scale distributions is then addressed finally some experimental results are reported to demonstrate the performance of this method

cauchy problem for fractional diffusion equations abstract we consider an evolution equation with the regularized fractional derivative of an order 0 1 with respect to the time variable and a uniformly elliptic operator with variable coefficients acting in the spatial variables such equations describe diffusion on inhomogeneous fractals a fundamental solution of the cauchy problem is constructed and investigated

on svd for estimating generalized eigenvalues of singular matrix pencil in noise several algorithms for estimating generalized eigenvalues ges of singular matrix pencils perturbed by noise are reviewed the singular value decomposition svd is explored as the common structure in the three basic algorithms direct matrix pencil algorithm pro esprit and tls esprit it is shown that several svd based steps inherent in the algorithms are equivalent to the first order approximation in particular the pro esprit and its variant tls pro esprit are shown to be equivalent and the tls esprit and its earlier version ls esprit are shown to be asymptotically equivalent to the first order approximation for the problem of estimating superimposed complex exponential signals the state space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first order approximation the second order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal an improved state space algorithm is found to be the most robust to noise

broadband dispersion extraction using simultaneous sparse penalization in this paper we propose a broadband method to extract the dispersion curves for multiple overlapping dispersive modes from borehole acoustic data under limited spatial sampling the proposed approach exploits a first order taylor series approximation of the dispersion curve in a band around a given center frequency in terms of the phase and group slowness at that frequency under this approximation the acoustic signal in a given band can be represented as a superposition of broadband propagators each of which is parameterized by the slowness pair above we then formulate a sparsity penalized reconstruction framework as follows these broadband propagators are viewed as elements from an overcomplete dictionary representation and under the assumption that the number of modes is small compared to the size of the dictionary it turns out that an appropriately reshaped support image of the coefficient vector synthesizing the signal using the given dictionary representation exhibits column sparsity our main contribution lies in identifying this feature and proposing a complexity regularized algorithm for support recovery with an l1 type simultaneous sparse penalization note that support recovery in this context amounts to recovery of the broadband propagators comprising the signal and hence extracting the dispersion namely the group and phase slownesses of the modes in this direction we present a novel method to select the regularization parameter based on kolmogorov smirnov ks tests on the distribution of residuals for varying values of the regularization parameter we evaluate the performance of the proposed method on synthetic as well as real data and show its performance in dispersion extraction under presence of heavy noise and strong interference from time overlapped modes

asymptotic wavelet and gabor analysis extraction of instantaneous frequencies the behavior of the continuous wavelet and gabor coefficients in the asymptotic limit using stationary phase approximations are investigated in particular it is shown how under some additional assumptions these coefficients allow the extraction of some characteristics of the analyzed signal such as frequency and amplitude modulation laws applications to spectral line estimations and matched filtering are briefly discussed

hybridized globally divergence free ldg methods part i the stokes problem we devise and analyze a new local discontinuous galerkin ldg method for the stokes equations of incompressible fluid flow this optimally convergent method is obtained by using an ldg method to discretize a vorticity velocity formulation of the stokes equations and by applying a new hybridization to the resulting discretization one of the main features of the hybridized method is that it provides a globally divergence free approximate velocity without having to construct globally divergence free finite dimensional spaces only elementwise divergence free basis functions are used another important feature is that it has significantly less degrees of freedom than all other ldg methods in the current literature in particular the approximation to the pressure is only defined on the faces of the elements on the other hand we show that as expected the condition number of the schur complement matrix for this approximate pressure is of order h 2 in the mesh size h finally we present numerical experiments that confirm the sharpness of our theoretical a priori error estimates

asymptotic periodicity for some evolution equations in banach spaces abstract this work deals with the existence and uniqueness of pseudo almost periodic and asymptotically periodic mild solutions to some evolution equations in banach spaces

5d seismic data completion and denoising using a novel class of tensor decompositions abstractwe have developed a novel strategy for simultaneous interpolation and denoising of prestack seismic data most seismic surveys fail to cover all possible source receiver combinations leading to missing data especially in the midpoint offset domain this undersampling can complicate certain data processing steps such as amplitude variation with offset analysis and migration data interpolation can mitigate the impact of missing traces we considered the prestack data as a 5d multidimensional array or otherwise referred to as a 5d tensor using synthetic data sets we first found that prestack data can be well approximated by a low rank tensor under a recently proposed framework for tensor singular value decomposition tsvd under this low rank assumption we proposed a complexity penalized algorithm for the recovery of missing traces and data denoising in this algorithm the complexity regularization was controlled by tuning a single regularization parameter using a statistical test we tested t

on a hierarchical basis multilevel method with nonconforming p1 elements we develop a hierarchical basis multilevel method for symmetric second order elliptic boundary value problems in two dimensional polygonal domains based on nonconforming p1 triangular elements the main result is that the condition number of the hierarchical discretization is bounded byo k wherek is the number of refinement levels for comparison yserentant s result yields the sharp boundo k 2 for the corresponding hierarchical discretization with conforming linear elements