a new rigorous expansion for the velocity potential of a circular piston source in the case of boundary value problems such as the sound scattering from a sphere placed in the nearfield of a plane piston source it is sometimes essential to express the velocity potentials in terms of the orthogonal expansion it is demonstrated in the present work that the rayleigh surface integral giving the velocity potential for a plane piston source surrounded by an infinite rigid flange reduces to a rigorous expansion of the simplest form for a circular piston as series of spherical surface harmonics the resulting equation is valid for any field points even on the piston surface sample calculations made with a microcomputer are presented with three dimensional and contour plots

isogeometric collocation methods with generalized b splines we introduce isogeometric collocation methods based on generalized b splines and we analyze their performance through numerical examples for univariate and multivariate scalar and vector valued problems in particular advection diffusion and linear elasticity model problems are addressed the resulting method combines the favorable properties of isogeometric collocation and the geometrical and analytical problem oriented advantages of generalized b splines

a family of non uniform subdivision schemes with variable parameters for curve design in this paper we present non uniform subdivision schemes with variable parameter sequences a locally different tension parameter is set at each edge of the initial control polygon to control locally the shape of the resulting curve such that the scheme becomes non uniform due to the variable parameters the scheme can reproduce locally different analytic curves such as conics lissajous trigonometric and catenary curves hence blending curves including such analytic components can be successfully generated we discuss the convergence and smoothness of the proposed non uniform schemes and present some numerical results to demonstrate their advantages in geometric modeling furthermore as an application we propose a chamfering algorithm which can be used in designing automobile and mechanical products

cardinal exponential splines part i theory and filtering algorithms causal exponentials play a fundamental role in classical system theory starting from those elementary building blocks we propose a complete and self contained signal processing formulation of exponential splines defined on a uniform grid we specify the corresponding b spline basis functions and investigate their reproduction properties green function and exponential polynomials we also characterize their stability riesz bounds we show that the exponential b spline framework allows an exact implementation of continuous time signal processing operators including convolution differential operators and modulation by simple processing in the discrete b spline domain we derive efficient filtering algorithms for multiresolution signal extrapolation and approximation extending earlier results for polynomial splines finally we present a new asymptotic error formula that predicts the magnitude and the nth order decay of the l sub 2 approximation error as a function of the knot spacing t

some estimates for h p k refinement in isogeometric analysis in this paper we propose a theoretical study of the approximation properties of nurbs spaces which are used in isogeometric analysis we obtain error estimates that are explicit in terms of the mesh size h the degree p and the global regularity measured by the parameter k our approach covers the approximation with global regularity from c 0 up to c k 1 with 2k 1 p notice that the interesting case of higher regularity up to k p is still open however our results give an indication of the role of the smoothness k in the approximation properties and offer a first mathematical justification of the potential of isogeometric analysis based on globally smooth nurbs

robust image hashing based on random gabor filtering and dithered lattice vector quantization in this paper we propose a robust hash function based on random gabor filtering and dithered lattice vector quantization lvq in order to enhance the robustness against rotation manipulations the conventional gabor filter is adapted to be rotation invariant and the rotation invariant filter is randomized to facilitate secure feature extraction particularly a novel dithered lvq based quantization scheme is proposed for robust hashing the dithered lvq based quantization scheme is well suited for robust hashing with several desirable features including better tradeoff between robustness and discrimination higher randomness and secrecy which are validated by analytical and experimental results the performance of the proposed hashing algorithm is evaluated over a test image database under various content preserving manipulations the proposed hashing algorithm shows superior robustness and discrimination performance compared with other state of the art algorithms particularly in the robustness against rotations of large degrees

on axis and far field sound radiation from resilient flat and dome shaped radiators on axis and far field series expansions are developed for the sound pressure due to an arbitrary circular symmetric velocity distribution on a flat radiator in an infinite baffle these expansions are obtained by expanding the velocity distributions in terms of orthogonal polynomials r 2n 0 sigma a p n 2 sigma a 2 1 with p n the legendre polynomials the terms r 2n 0 give rise to a closed form expression for the pressure on axis as well as for the far field pressure furthermore for a large number of velocity profiles including those associated with the rigid piston the simply supported radiator and the clamped radiators as well as gaussian radiators there are closed form expressions for the required expansion coefficients in particular for the rigid simply supported and clamped radiators this results in explicit finite series expressions for both the on axis and far field pressures in the reverse direction a method of estimating velocity distributions from measured on axis pressures by matching in terms of expansion coefficients is proposed together with the forward far field computation scheme this yields a method for far field loudspeaker assessment from on axis data generalized keele scheme the forward computation scheme is extended to dome shaped radiators with arbitrary velocity distributions

an annular superposition integral for axisymmetric radiators a fast integral expression for computing the nearfield pressure is derived for axisymmetric radiators this method replaces the sum of contributions from concentric annuli with an exact double integral that converges much faster than methods that evaluate the rayleigh sommerfeld integral or the generalized king integral expressions are derived for plane circular pistons using both continuous wave and pulsed excitations several commonly used apodization schemes for the surface velocity distribution are considered including polynomial functions and a smooth piston function the effect of different apodization functions on the spectral content of the wave field is explored quantitative error and time comparisons between the new method the rayleigh sommerfeld integral and the generalized king integral are discussed at all error levels considered the annular superposition method achieves a speed up of at least a factor of 4 relative to the point source method and a factor of 3 relative to the generalized king integral without increasing the computational complexity

multi iterative methods abstract a general class of iterative methods is introduced for solving positive definite linear systems ax b these methods use two or more different iterative techniques and each of them reduces the error by a constant factor in a different subspace of r n the multigrid as an example of a multi iterative method combines these partial results and we reach a reduction of the error by at each step where is the number of applications of the first scheme and gt 1 is a constant independent of n in the second part we consider the prolongation operator p with a special antidiagonal structure and we show that the multigrid method for toeplitz matrices 1 is an example of a method of this class in a third part we extend the multigrid method to block toeplitz matrices obtaining a block antidiagonal structure for toeplitz and block toeplitz cases the choice of p which maximizes convergence speed simply depends on the coefficients of matrix a the numerical results on 1 d and 2 d elliptic differential problems confirm the effectiveness of this multi iterative method in fact its spectral radius is very small and independent of the mesh spacing h

the low frequency axisymmetric modal sound radiation efficiency of an elastically supported annular plate abstract this paper deals with the sound radiation efficiency of a vibrating thin elastically supported annular plate embedded into a flat rigid baffle the free axisymmetric time harmonic vibrations have been considered for a single mode it has been assumed that the influence of the air column above the plate on the plate s vibrations is negligible first the sound radiation efficiency has been formulated as an integral further rigorous mathematical manipulations have been carried out based on the theory of summation of multiple expansion series containing the hypergeometric functions as a result the formulations have been expressed as some fast convergent expansion series containing only the bessel and struve functions of integer order and the spherical bessel functions the presented formulations of sound radiation efficiency of an elastically supported annular plate are useful for numerical calculations within the low frequency range what is important for practical reasons the formulations are valid for axisymmetric boundary conditions and they enable changing the values of boundary stiffness constants consequently the analysis of influence of the plate s edge attachment on the sound radiation efficiency has been performed the limiting transitions have also been performed from formulations valid for the elastically supported annular plates to the formulations valid for annular plates with classical boundary conditions clamped simply supported and free at one edge or at both edges

unified and extended form of three types of splines the three types refer to polynomial trigonometric and hyperbolic splines in this paper we unify and extend them by a new kind of spline ue spline for short defined over the space cos wt sin wt 1 t t l where l is an arbitrary nonnegative integer w is a frequency sequence w i a i a i r existing splines such as usual polynomial b splines cb splines hb splines nuat splines ah splines fb splines and the third form fb splines etc are all special cases of ue splines ue splines inherit most properties of usual polynomial b splines and enjoy some other advantageous properties for modelling they can exactly represent classical conics the catenary the helix and even the eight curve a kind of snake like curves etc

ultrasonic field modeling by distributed point source method for different transducer boundary conditions several investigators have modeled ultrasonic fields in front of transducers by huygens fresnel superposition principle that integrates the contributions of a number of point sources distributed on the transducer face this integral solution also known as the rayleigh integral or rayleigh sommerfeld integral solution assumes the strengths of the point sources distributed over the transducer face a newly developed technique called distributed point source method dpsm offers an alternative approach for modeling ultrasonic fields dpsm is capable of modeling the field for prescribed source strength distribution as well as for prescribed interface conditions with unknown source strengths it is investigated how the ultrasonic field in front of the transducer varies in different situations 1 when the point source strengths are known 2 when the point source strengths are unknown but obtained from the interface condition that only the normal component of the transducer velocity is continuous across th

generalized spline spaces over t meshes univariate generalized splines are smooth piecewise functions with sections in certain extended tchebycheff spaces they are a natural extension of univariate algebraic polynomial splines and enjoy the same structural properties as their polynomial counterparts in this paper we consider generalized spline spaces over planar t meshes and we deepen their parallelism with polynomial spline spaces over the same partitions first we extend the homological approach from polynomial to generalized splines this provides some new insights into the dimension problem of a generalized spline space defined on a prescribed t mesh for a given degree and smoothness second we extend the construction of lr splines to the generalized spline context

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

from approximating subdivision schemes for exponential splines to high performance interpolating algorithms in this work we construct three novel families of approximating subdivision schemes that generate piecewise exponential polynomials and we show how to convert these into interpolating schemes of great interest in curve design for their ability to reproduce important analytical shapes and to provide highly smooth limit curves with a controllable tension in particular throughout this paper we will focus on the derivation of 6 point interpolating schemes that turn out to be unique in combining vital ingredients like c 2 continuity simplicity of definition ease of implementation user independency tension control and ability to reproduce salient trigonometric and transcendental curves

on the sound field of a circular membrane in free space and an infinite baffle an enhanced method for calculating the radiation characteristics of a tensioned circular membrane in free space is presented using an analytical solution to the infinite integral in the free space green s function in cylindrical coordinates this enables direct calculation of the surface pressure series coefficients by equating the coefficients of the resulting bessel series in a set of simultaneous equations eliminating both numerical integration and least squares minimization improves calculation speed and accuracy an infinite baffle is introduced to provide an indication of what the theoretical limit of the bass performance would be using a very large enclosure furthermore analytical solutions to the pressure field integrals are presented a force transmission coefficient is introduced which is the ratio of the total radiation impedance to the motional impedance the motional radiation and diaphragm impedances of the damped membrane are calculated together with the near and far field pressure responses and efficiency a comparison is made between the on axis response without damping calculated using this method and using a finite element model it is demonstrated that good correlation between the two calculation methods can be achieved provided the elements are small enough and a sufficiently large model is used at the frequency extremes

simplified expansions for radiation from a baffled circular piston computation of acoustic radiation from a baffled circular piston continues to be an active area of investigation both as a canonical problem and because of numerous practical applications for time harmonic radiation exact series expansions are an attractive approach because they do not require numerical integration or limiting approximations here series expansions due to hasegawa inoue and matsuzawa j acoust soc am 74 1044 1047 1983 75 1048 1051 1984 are shown to reduce to simpler expressions suitable for numerical computations for the region r a where a is the piston radius and r is the distance from the piston center an exact solution is given by a series of spherical hankel functions and legendre polynomials with explicit closed form position independent coefficients for the paraxial region w a where w is the distance from the piston axis a second exact series expansion is valid for all axial distances z and reduces to the known analytic solution for w 0 these two expansions allow the radiated field to be computed at any point with rapid convergence except for points near the circle bounding the piston example numerical results illustrate application of this method to ultrasonic sources

the rate of convergence of toeplitz based pcg methods for second order nonlinear boundary value problems in previous works 21 23 we proposed the use of tau 5 and band toeplitz based preconditioners for the solution of 1d and 2d boundary value problems bvp by means of the preconditioned conjugate gradient pcg methods as tau and band toeplitz linear systems can be solved 4 by using fast sine transforms 8 these methods become especially attractive in a parallel environment of computation in this paper we extend this technique to the nonlinear nonsymmetric case and in addition we prove some clustering properties for the spectra of the preconditioned matrices showing why these methods exhibit a convergence speed which results to be more than linear therefore these methods work much finer than those based on separable preconditioners 18 45 on incomplete lu factorizations 36 13 27 and on circulant preconditioners 9 30 35 since the latter two techniques do not assure a linear rate of convergence on the other hand the proposed technique has a wider range of application since it can be naturally used for nonlinear nonsymmetric problems and for bvp in which the coefficients of the differential operator are not strictly positive and only piecewise smooth finally the several numerical experiments performed here and in 22 23 confirm the effectiveness of the theoretical analysis

gb splines of arbitrary order explicit formulae and recurrence relations for the calculation of generalized b splines gb splines of arbitrary order are given we derive main properties of gb splines and their series i e partition of unity shape preserving properties invariance with respect to ane transformations etc it is shown that such splines have the variation diminishing property and are chebyshevian splines c 1999 elsevier science b v all rights reserved

effortless quasi interpolation in hierarchical spaces we present a general and simple procedure to construct quasi interpolants in hierarchical spaces such spaces are composed of a hierarchy of nested spaces and provide a flexible framework for local refinement the proposed hierarchical quasi interpolants are described in terms of the so called truncated hierarchical basis assuming a quasi interpolant is selected for each space associated with a particular level in the hierarchy the hierarchical quasi interpolants are obtained without any additional manipulation the main properties like polynomial reproduction of the quasi interpolants selected at each level are locally preserved in the hierarchical construction we show how to construct hierarchical local projectors and the local approximation order of the underling hierarchical space is also investigated the presentation is detailed for the truncated hierarchical b spline basis and we discuss its extension to a more general framework

critical length an alternative approach abstract we provide a numerical method to determine the critical lengths of linear differential operators with constant real coefficients the need for such a procedure arises when the orders increase the interest of this article is clearly on the practical side since knowing the critical lengths permits an optimal use of the associated kernels the efficiency of the procedure is due to its being based on crucial features of extended chebyshev spaces on closed bounded intervals

on the sound field of a resilient disk in an infinite baffle the rayleigh integral describing the near field pressure of an axisymmetric planar monopole source with an arbitrary velocity distribution is solved with a method similar to that used by mast and yu j acoust soc am 118 6 3457 3464 2005 for a rigid disk in an infinite baffle the closed form solution is in the form of a double expansion which is valid for distances from the observation point to the center of the source that are greater than its radius however for the remaining immediate near field the king integral is solved using a combination of gegenbauer s summation theorem and the lommel expansion resulting in a solution which is in the form of a triple expansion reducing to a double expansion along the source s axis of symmetry these relatively compact solutions in analytic form do not require numerical integration and therefore present no numerical difficulties except for a singularity at the rim as an example of a monopole source with an arbitrary velocity distribution equations

robust extrema features for time series data analysis the extraction of robust features for comparing and analyzing time series is a fundamentally important problem research efforts in this area encompass dimensionality reduction using popular signal analysis tools such as the discrete fourier and wavelet transforms various distance metrics and the extraction of interest points from time series recently extrema features for analysis of time series data have assumed increasing significance because of their natural robustness under a variety of practical distortions their economy of representation and their computational benefits invariably the process of encoding extrema features is preceded by filtering of the time series with an intuitively motivated filter e g for smoothing and subsequent thresholding to identify robust extrema we define the properties of robustness uniqueness and cardinality as a means to identify the design choices available in each step of the feature generation process unlike existing methods which utilize filters x201c inspired x201d from either domain knowledge or intuition we explicitly optimize the filter based on training time series to optimize robustness of the extracted extrema features we demonstrate further that the underlying filter optimization problem reduces to an eigenvalue problem and has a tractable solution an encoding technique that enhances control over cardinality and uniqueness is also presented experimental results obtained for the problem of time series subsequence matching establish the merits of the proposed algorithm

on a class of weak tchebycheff systems in this paper we study the approximation power the existence of a normalized b basis and the structure of a degree raising process for spaces of the form requiring suitable assumptions on the functions u and v the results about degree raising are detailed for special spaces of this form which have been recently introduced in the area of cagd

a radial propagator for axisymmetric pressure fields the concept of a propagator is central to the angular spectrum formulation of diffraction theory which expresses the pressure field diffracted by a two dimensional aperture as a superposition of a continuum of plane waves in the conventional form an exponential term known as a propagator is multiplied by the wavenumber spectrum obtained from a two dimensional spatial fourier transform of the aperture boundary condition to obtain the wavenumber spectrum in a plane parallel to the boundary offset by some distance specified in the propagator by repeated use of this propagator and fourier inversion it is possible to completely construct the homogeneous part of the pressure field in the positive half space beyond the planar boundary containing the aperture drawing upon preceding work relating the boundary condition to the axial pressure pees j acoust soc am 127 3 1381 1390 2010 it is shown in this article that when the aperture is axially symmetric an alternative type of propagator can b

robust and optimal multi iterative techniques for iga galerkin linear systems we consider fast solvers for the large linear systems coming from the isogeometric analysis iga collocation approximation based on b splines of full elliptic d dimensional partial differential equations pdes we are interested in designing iterative algorithms which are optimal and robust the former property implies that the computational cost is linear with respect to the number of degrees of freedom i e the matrix size the latter property means that the convergence rate is completely independent of or only mildly dependent on all the relevant parameters in our setting we can mention the coefficients of the pde the dimensionality d the geometric map g describing the physical domain the matrix size related to the fineness parameters and the spline degrees associated with the iga approximation order our approach is based on the spectral symbol which describes the global eigenvalue behavior of the iga collocation matrices it is precisely the spectral information contained in the symbol that is exploited for the design of an optimal and robust multi iterative solver of multigrid type several numerical experiments are presented and discussed in view of recent theoretical findings concerning the symbol and its properties

fitting scattered data on spherelike surfaces using tensor products of trigonometric and polynomial splines a method is presented for fitting a function defined on a general smooth spherelike surfaces given measurements on the function at a set of scattered points lying ons the approximating surface is constructed by mapping the surface onto a rectangle and using a tensor product of polynomial splines with periodic trigonometric splines the use of trigonometric splines allows a convenient solution of the problem of assuring that the resulting surface is continuous and has continuous tangent planes at all points ons two alternative algorithms for computing the coefficients of the tensor fit are presented one based on global least squares and the other on the use of local quasi interpolators the approximation order of the method is established and the numerical performance of the two algorithms is compared

analysis of preconditioning strategies for collocation linear systems in the past few years several authors have studied the preconditioning of collocation matrices by finite differences fds matrices arising from the associated collocation points here we discuss how to solve in an efficient way nonuniform grid fd linear systems including those related to a generic fd collocation preconditioner the main idea is based on a further step of preconditioning defined in terms of diagonal and toeplitz matrices first we identify the limit spectral distributions of the involved fd collocation matrix sequences and then we prove that the proposed toeplitz based preconditioners assure a clustering at the unity with respect to the eigenvalues in the 1d case in the 2d case the situation is different so that more appropriate strategies are discussed a wide numerical experimentation emphasizing the correctness of the theoretical results is also reported

a unifying approach to some old and new theorems on distribution and clustering abstract a unifying approach is proposed to studying the distributions of eigenvalues and singular values of toeplitz matrices associated with a fourier series and multilevel toeplitz matrices associated with a multidimensional fourier series obtained are the extensions of the szego and avram parter theorems where the generating function is now required to belong to l 2 and not necessarily to l analogous extensions are given for multilevel toeplitz matrices in particular it is proved that if f x 1 x p l 2 then the p level complex toeplitz matrices allied with f have their singular values distributed as f x 1 x p the distribution results for the cesaro optimal circulants hold even if f l 1 also suggested are new theorems on clustering that have to do with the preconditioning of multilevel toeplitz matrices by multilevel circulants

trigonometric generalized t splines abstract the paper s main aim consists of extending the t spline approach to trigonometric generalized b splines a particularly relevant case of non polynomial splines such goal can be achieved by a careful revision of some results concerning the basic properties of the trigonometric generalized b splines and by a formalization of the concept of t splines in the trigonometric setting moreover fundamental for the use of this new tool is the study of the noteworthy case with constant frequencies and of the linear independence of the corresponding blending functions which can be proved to be strongly linked to the linear independence of the polynomial blending functions associated to the same t mesh

symbol based multigrid methods for galerkin b spline isogeometric analysis we consider the stiffness matrices arising from the galerkin b spline isogeometric analysis discretization of classical elliptic problems by exploiting their specific spectral properties compactly described by a symbol we design an efficient multigrid method for the fast solution of the related linear systems the convergence rate of general purpose multigrid methods based on classical stationary smoothers is optimal i e bounded independently of the matrix size but it also worsens exponentially with respect to the spline degree the symbol allows us to give a detailed theoretical explanation of this exponential worsening in the case of the two grid scheme in addition thanks to a specific factorization of the symbol we are able to design an ad hoc multigrid method with an effective preconditioned cg or gmres smoother at the finest level in the spirit of the multi iterative idea the convergence rate of this multi iterative multigrid method is not only optimal but also robust i e bounded su

a new tension b spline method for third order self adjoint singularly perturbed boundary value problems abstract the aim of this paper is to present a new kind of tension b spline called hyperbolic trigonometric tension b spline of order n which is generated over the space span sin t cos t sinh t cosh t 1 t t n 5 n 5 where is tension parameter this kind of b spline has most properties of usual polynomial b splines and enjoys some other advantageous properties as well also hyperbolic trigonometric tension b spline method is applied for solving self adjoint singularly perturbed problems we use some numerical examples to illustrate the accuracy and implementation of the method

generalized locally toeplitz sequences spectral analysis and applications to discretized partial differential equations abstract starting from the finite difference discretization of an elliptic second order pde as i j 1 d x i a i j x x j u x b x over a bounded domain we introduce the notion of generalized locally toeplitz sequence of matrices the singular value distribution the eigenvalue distribution in the hermitian case is studied and characterized for generalized locally toeplitz sequences in terms of weighted multidimensional szeg formulas this extends preceding results attributed to tilli which concern the unilevel case the application of this theoretic analysis to the numerical solution of pdes is finally discussed

convergence analysis of krylov subspace iterations with methods from potential theory krylov subspace iterations are among the best known and most widely used numerical methods for solving linear systems of equations and for computing eigenvalues of large matrices these methods are polynomial methods whose convergence behavior is related to the behavior of polynomials on the spectrum of the matrix this leads to an extremal problem in polynomial approximation theory how small can a monic polynomial of a given degree be on the spectrum this survey gives an introduction to a recently developed technique to analyze this extremal problem in the case of symmetric matrices it is based on global information on the spectrum in the sense that the eigenvalues are assumed to be distributed according to a certain measure then depending on the number of iterations the lanczos method for the calculation of eigenvalues finds those eigenvalues that lie in a certain region which is characterized by means of a constrained equilibrium problem from potential theory the same constrained equilibrium problem also describes the superlinear convergence of conjugate gradients and other iterative methods for solving linear systems

the normalized acoustic power of a thin clamped annular plate vibrating in a flat screen around a perpendicular semi infinite circular cylinder abstract the neumann boundary value problem is presented for the time harmonic excited steady state vibrations of a thin clamped annular plate embedded in a flat rigid baffle around a perpendicular circular cylindrical rigid semi infinite baffle the system of two coupled differential equations is solved for this purpose one of them being the wave equation of the fluid filling the space between the two baffles and the other being the equation of motion of the plate for its excited vibrations first the acoustic pressure is presented in its spectral form using the weber inverse transform then the time averaged acoustic power is presented using the plate s modal impedance coefficients and the coupling factors the modal coefficients are presented as the integrals together with the corresponding asymptotic formulations the influence of the cylindrical baffle on the acoustic power is analyzed numerically the fluid loading and the internal attenuation of the plate s vibrations are both included whereas the attenuation of the acoustic waves in fluid is neglected

the glt class as a generalized fourier analysis and applications recently the class of generalized locally toeplitz glt sequences has been introduced as a generalization both of classical toeplitz sequences and of variable coefficient differential operators and for every sequence of the class it has been demonstrated that it is possible to give a rigorous description of the asymptotic spectrum in terms of a function the symbol that can be easily identified this generalizes the notion of a symbol for differential operators discrete and continuous or for toeplitz sequences for which it is identified through the fourier coefficients and is related to the classical fourier analysis the glt class has nice algebraic properties and indeed it has been proven that it is stable under linear combinations and products in this paper we prove that the considered class is closed under inversion as well when the sequence which is inverted shows a sparsely vanishing symbol sparsely vanishing symbol a symbol which vanishes at most in a set of zero lebesgue measure furthermore we show that the glt class virtually includes any finite difference or finite element discretization of pdes and based on this we demonstrate that our results on glt sequences can be used in a pde setting in various directions 1 as a generalized fourier analysis for the study of iterative and semi iterative methods when dealing with variable coefficients non rectangular domains non uniform gridding or triangulations 2 in order to provide a tool for the stability analysis of pde numerical schemes e g a necessary von neumann criterium for variable coefficient systems of pdes is obtained uniformly with respect to the boundary conditions 3 for a multigrid analysis of convergence and for providing spectral information on large preconditioned systems in the variable coefficient case etc the final part of the paper deals indeed with problems 1 3 and other possible directions in which the glt analysis can be conveniently employed

superlinear convergence of conjugate gradients we give a theoretical explanation for superlinear convergence behavior observed while solving large symmetric systems of equations using the conjugate gradient method or other krylov subspace methods we present a new bound on the relative error after n iterations this bound is valid in an asymptotic sense when the size n of the system grows together with the number of iterations the bound depends on the asymptotic eigenvalue distribution and on the ratio n n under appropriate conditions we show that the bound is asymptotically sharp our findings are related to some recent results concerning asymptotics of discrete orthogonal polynomials an important tool in our investigations is a constrained energy problem in logarithmic potential theory the new asymptotic bounds for the rate of convergence are illustrated by discussing toeplitz systems as well as a model problem stemming from the discretization of the poisson equation

generalized b splines as a tool in isogeometric analysis the concept of isogeometric analysis has been proposed in 13 where nurbs are considered as basis of the analysis thanks to their ability to construct an exact geometric model in several practical applications and to their popularity in commercial cad systems in this paper we propose an alternative to the rational model presenting an isogeometric analysis approach based on generalized b splines geometric models exactly represented by generalized b splines include those generated by nurbs moreover generalized b splines possess all fundamental properties of algebraic b splines and nurbs including classical refinement processes as h p k refinements finally since generalized b splines are not confined to rational functions they behave completely similar to algebraic b splines with respect to differentiation and integration this seems to be of interest in the treatment of some relevant problems

overlapping schwarz methods for isogeometric analysis based on generalized b splines abstract generalized b splines gb splines are a special class of tchebycheff b splines that are smooth piecewise function with sections in more general spaces gb splines allow for an exact representation of conic sections as well as transcendental curves and thus they become very attractive for geometrical modeling and numerical simulation in this paper we present overlapping schwarz preconditioners for elliptic problems discretized with isogeometric analysis based on gb splines an h analysis of the proposed preconditioners shows an optimal convergence rate bound that is scalable in the number of subdomains and that is linear in the ratio between subdomain and overlap sizes numerical results in two and three dimensional tests confirm this analysis and also illustrate the good convergence properties of the preconditioner with respect to the discretization parameters the domain deformation and the jumping coefficients

perceptual image hashing based on virtual watermark detection this paper proposes a new robust and secure perceptual image hashing technique based on virtual watermark detection the idea is justified by the fact that the watermark detector responds similarly to perceptually close images using a non embedded watermark the hash values are extracted in binary form with a perfect control over the probability distribution of the hash bits moreover a key is used to generate pseudo random noise whose real values contribute to the randomness of the feature vector with a significantly increased uncertainty of the adversary measured by mutual information in comparison with linear correlation experimentally the proposed technique has been shown to outperform related state of the art techniques recently proposed in the literature in terms of robustness with respect to image processing manipulations and geometric attacks

an explicit method for g 3 merging of two bezier curves this paper presents an explicit method for the g 3 merging problem of two bezier curves the main idea is to express the l 2 distance as a quadratic function of some parameters provided by g 3 continuity conditions an efficient non iterative algorithm is proposed to obtain the optimal merged curve when the l 2 distance is minimized the uniqueness of the global minimum is also proven this method can be applied to two adjacent curves with different degrees and has the ability to obtain satisfactory merging results by using curves of lower degree the efficiency and accuracy of the proposed explicit method are illustrated through several comparative examples

finite element and nurbs approximations of eigenvalue boundary value and initial value problems abstract we study the spectral approximation properties of finite element and nurbs spaces from a global perspective we focus on eigenfunction approximations and discover that the l 2 norm errors for finite element eigenfunctions exhibit pronounced spikes about the transition points between branches of the eigenvalue spectrum this pathology is absent in nurbs approximations by way of the pythagorean eigenvalue error theorem we determine that the squares of the energy norm errors of the eigenfunctions are the sums of the eigenvalue errors and the squares of the l 2 norm eigenfunction errors the spurious behavior of the higher eigenvalues for standard finite elements is well known and therefore inherited by the energy norm errors along with the spikes in the l 2 norm of the eigenfunction errors the eigenvalue pathology is absent for nurbs the implications of these results to the corresponding elliptic boundary value problem and parabolic and hyperbolic initial value problems are discussed

perceptual image hashing via feature points performance evaluation and tradeoffs we propose an image hashing paradigm using visually significant feature points the feature points should be largely invariant under perceptually insignificant distortions to satisfy this we propose an iterative feature detector to extract significant geometry preserving feature points we apply probabilistic quantization on the derived features to introduce randomness which in turn reduces vulnerability to adversarial attacks the proposed hash algorithm withstands standard benchmark e g stirmark attacks including compression geometric distortions of scaling and small angle rotation and common signal processing operations content changing malicious manipulations of image data are also accurately detected detailed statistical analysis in the form of receiver operating characteristic roc curves is presented and reveals the success of the proposed scheme in achieving perceptual robustness while avoiding misclassification

on the spectrum of stiffness matrices arising from isogeometric analysis we study the spectral properties of stiffness matrices that arise in the context of isogeometric analysis for the numerical solution of classical second order elliptic problems motivated by the applicative interest in the fast solution of the related linear systems we are looking for a spectral characterization of the involved matrices in particular we investigate non singularity conditioning extremal behavior spectral distribution in the weyl sense as well as clustering of the eigenvalues to a certain compact subset of mathbb c c all the analysis is related to the notion of symbol in the toeplitz setting and is carried out both for the cases of 1d and 2d problems

comparison of spheroidal and eigenfunction expansion trial functions for a membrane in an infinite baffle the on axis far field pressure response of a circular membrane in an infinite baffle when driven by a uniformly distributed electrostatic force is calculated using two different trial functions for the surface velocity distribution the first is an expansion based upon a solution to the free space wave equation in oblate spheroidal coordinates which has already been derived in a previous paper j acoust soc am 120 5 2460 2477 2006 and the second is a membrane eigenfunction expansion or bessel series which is rigorously derived in this letter although the latter can be used as a basis for calculating a number of different radiation characteristics such as the radiation impedance or directivity etc only the on axis far field sound pressure is considered here the results are compared and discussed

spectral analysis of matrices in galerkin methods based on generalized b splines with high smoothness we present a first step towards the spectral analysis of matrices arising from iga galerkin methods based on hyperbolic and trigonometric gb splines second order differential problems with constant coefficients are considered and discretized by means of sequences of both nested and non nested spline spaces we prove that there always exists an asymptotic eigenvalue distribution which can be compactly described by a symbol just like in the polynomial case there is a complete similarity between the symbol expressions in the hyperbolic trigonometric and polynomial cases this results in similar spectral features of the corresponding matrices we also analyze the iga discretization based on trigonometric gb splines for the eigenvalue problem related to the univariate laplace operator we prove that for non nested spaces the phase parameter can be exploited to improve the spectral approximation with respect to the polynomial case as part of the analysis we derive several fourier properties of cardinal gb splines

isogeometric analysis in advection diffusion problems tension splines approximation we present a novel approach within the new paradigm of isogeometric analysis introduced by hughes et al 2005 6 to deal with advection dominated advection diffusion problems the key ingredient is the use of galerkin approximating spaces of functions with high smoothness as in iga based on classical b splines but particularly well suited to describe sharp layers involving very strong gradients