hilbert space frames containing a riesz basis and banach spaces which have no subspace isomorphic toc0 abstract we prove that a hilbert space frame fi i icontains a riesz basis if every subfamily fi i j j i is a frame for its closed span secondly we give a new characterization of banach spaces which do not have any subspace isomorphic toc0 this result immediately leads to an improvement of a recent theorem of holub concerning frames consisting of a riesz basis plus finitely many elements

frames and pseudo inverses abstract we point out some connections between the existing theories for frames and pseudo inverses in particular using the pseudo inverse of an unbounded operator we show how to make frame like decompositions with respect to some sequences which do not satisfy the upper frame condition as a special case this approach immediately gives nontrivial results for usual frames

a new bayesian recursive technique for parameter estimation 1 the performance of any model depends on how well its associated parameters are estimated in the current application a localized bayesian recursive estimation lobare approach is devised for parameter estimation the lobare methodology is an extension of the bayesian recursive estimation bare method it is applied in this paper on two different types of models an artificial intelligence ai model in the form of a support vector machine svm application for forecasting soil moisture and a conceptual rainfall runoff crr model represented by the sacramento soil moisture accounting sac sma model support vector machines based on statistical learning theory slt represent the modeling task as a quadratic optimization problem and have already been used in various applications in hydrology they require estimation of three parameters sac sma is a very well known model that estimates runoff it has a 13 dimensional parameter space in the lobare approach presented here bayesian inference is used in an iterative fashion to estimate the parameter space that will most likely enclose a best parameter set this is done by narrowing the sampling space through updating the parent bounds based on their fitness these bounds are actually the parameter sets that were selected by bare runs on subspaces of the initial parameter space the new approach results in faster convergence toward the optimal parameter set using minimum training calibration data and fewer sets of parameter values the efficacy of the localized methodology is also compared with the previously used bare algorithm

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

on a riesz basis of exponentials related to the eigenvalues of an analytic operator and application to a non selfadjoint problem deduced from a perturbation method for sound radiation in the present paper we prove that the family of exponentials associated to the eigenvalues of the perturbed operator t t0 t1 2t2 ktk forms a riesz basis in l2 0 t t 0 where c t0 is a closed densely defined linear operator on a separable hilbert space h with domain d t0 having isolated eigenvalues with multiplicity one while t1 t2 are linear operators on h having the same domain d d t0 and satisfying a specific growing inequality after that we generalize this result using a h lipschitz function as application we consider a non selfadjoint problem deduced from a perturbation method for sound radiation

streamline design of stability parameters for advection diffusion problems the dependence of the computation of advective diffusive transport phenomena on the orientation of the mesh with respect to the flow direction is analyzed poor performance of the classical galerkin finite element method in the convection dominated regime is alleviated by stabilization we propose definitions of the stability parameter that rationally incorporate the flow direction numerical tests compare the performance of the proposed methods with established techniques

further considerations on residual free bubbles for advective diffusive equations abstract we further consider the galerkin method for advective diffusive equations in two dimensions the finite dimensional space employed is of piecewise polynomials enriched with residual free bubbles rfb we show that in general this method does not coincide with the supg method unless the piecewise polynomials are spanned by linear functions furthermore a simple stability analysis argument displays the effect of the rfb on the reduced space of piecewise polynomials which in some situations is not equivalent to streamline diffusion for bilinears

angle criteria for frame sequences and frames containing a riesz basis we obtain a condition implying that the union of two frame sequences is also a frame sequence christensen found a condition for this in terms of orthogonal projections we phrase our condition by use of the angle between closed subspaces also a lower bound formula is obtained we then apply the results to find conditions for a frame containing a riesz basis to be a riesz frame

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

numerical analysis of the non uniform sampling problem we give an overview of recent developments in the problem of reconstructing a band limited signal from nonuniform sampling from a numerical analysis view point it is shown that the appropriate design of the finite dimensional model plays a key role in the numerical solution of the nonuniform sampling problem in the one approach often proposed in the literature the finite dimensional model leads to an ill posed problem even in very simple situations the other approach that we consider leads to a well posed problem that preserves important structural properties of the original infinite dimensional problem and gives rise to efficient numerical algorithms furthermore a fast multilevel algorithm is presented that can reconstruct signals of unknown bandwidth from noisy nonuniformly spaced samples we also discuss the design of efficient regularization methods for ill conditioned reconstruction problems numerical examples from spectroscopy and exploration geophysics demonstrate the performance of the proposed methods

weighted projections and riesz frames abstract let h be a separable hilbert space and e k k 1 a fixed orthonormal basis of h motivated by many papers on scaled projections angles of subspaces and oblique projections we define and study the notion of compatibility between a subspace and the abelian algebra of diagonal operators in the given basis this is used to refine previous work on scaled projections and to obtain a new characterization of riesz frames

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

frames containing a riesz basis and approximation of the frame coefficients using finite dimensional methods abstract we consider frames which contain a riesz basis among those we find riesz frames i e frames with the property that every subfamily is a frame for its closed linear span with a common lower bound we point out the connection to the projection method which can be used to approximate the frame coefficients for a riesz frame using finitely many elements of the frame under different conditions we show that the projection method even approximates the frame coefficient in l 2 sense

decomposition of riesz frames and wavelets into a finite union of linearly independent sets we characterize riesz frames and prove that every riesz frame is the union of a finite number of riesz sequences furthermore it is shown that for piecewise continuous wavelets with compact support the associated regular wavelet systems can be decomposed into a finite number of linearly independent sets finally for finite sets an equivalent condition for decomposition into a given number of linearly independent sets is presented

continuous and discrete wavelet transforms this paper is an expository survey of results on integral representations and discrete sum expansions of functions in l 2 bf r in terms of coherent states two types of coherent states are considered weyl heisenberg coherent states which arise from translations and modulations of a single function and affine coherent states called wavelets which arise as translations and dilations of a single function in each case it is shown how to represent any function in l 2 bf r as a sum or integral of these states most of the paper is a survey of literature most notably the work of i daubechies a grossmann and j morlet a few results of the authors are included

on the stability of residual free bubbles for convection diffusion problemsand their approximation by a two level finite element method we consider the galerkin finite element method for partial diffferential equations in two dimensions where the finite dimensional space used consists of piecewise isoparametric polynomials enriched with bubble functions writing l for the differential operator we show that for elliptic convection diffusion problems the component of the bubble enrichment that stabilizes the method is essentially equivalent to a petrov galerkin method with an l spline exponentially fitted trial space and piecewise polynomial test space the remaining component of the bubble influences the accuracy of the method a stability inequality recently obtained by brezzi franca and russo for a limiting case of bubbles applied to convection diffusion problems is shown to be slightly weaker than the standard stability inequality that is obtained for the sdfem supg method thereby demonstrating that the bubble approach is in general slightly less stable than the streamline diffusion method when the trial functions are piecewise linear we show that residual free bubbles are as stable as sdfem supg and we extend this stability inequality to include positive mesh peclet numbers in the convection dominated regime approximate computations of the residual free bubbles are performed using a two level finite element method

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

on an improved unusual stabilized finite element method for theadvective reactive diffusive equation an improved unusual finite element method is studied herein for a second order linear scalar differential equation including a zero order term the method consists in subtracting from the standard galerkin method a mesh dependent term suggested by static condensation of the bubbles based on this idea a new stabilized parameter is constructed which improves accuracy of the solution several numerical tests attest the efficiency of the present method and an error analysis is perfomed

nullspaces and frames in this paper we give new characterizations of riesz and conditional riesz frames in terms of the properties of the nullspace of their synthesis operators on the other hand we also study the oblique dual frames whose coefficients in the reconstruction formula minimize different weighted norms

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100