the numerical solution of integro differential equation by means of the sinc method we develop a numerical procedure for solving a class of linear integro differential equation of fredholm type using the globally defined sinc basis functions properties of the sinc procedure are utilized to reduce the computation of the linear integro differential equation to some algebraic equations we used three numerical examples to illustrate the accuracy and to show the implementation of our method

quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions this paper deals with typical problems that arise when using wavelets in numerical analysis applications the first part involves the construction of quadrature formulae for the calculation of inner products of smooth functions and scaling functions several types of quadratures are discussed and compared for different classes of wavelets since their construction using monomials is ill conditioned also a modified well conditioned construction using chebyshev polynomials is presented the second part of the paper deals with pointwise asymptotic error expansions of wavelet approximations of smooth functions they are used to derive asymptotic interpolating properties of the wavelet approximation and to construct a convergence acceleration algorithm this is illustrated with numerical examples

embedding of tori and grids into twisted cubes the hypercube is one of the most popular interconnection networks since it has a simple structure and is easy to implement an n dimensional twisted cube tq n is an important variation of hypercube q n and preserves many of its desirable properties the problem of how to embed a family of disjoint meshes or tori into a host graph has attracted great attention in recent years however there is no systematic method proposed to generate the desired meshes and tori in tq n in this paper we develop two systematic linear time algorithms for embedding disjoint multi dimensional tori into tq n n 7 as follows 1 for a positive integer m with email protected email protected email protected n 4 a family of 2 m disjoint k dimensional tori of size 2 s 1x2 s 2x x2 s k each can be embedded with unit dilation where k 2 and i 1 ks email protected n m and 2 for a positive integer m with email protected email protected n 5 a family of 2 m disjoint k dimensional tori of size 2 s 1x2 s 2x x2 s k each can be embedded with unit dilation where k 2 s i 2 i 1 ks email protected n m and max 1 i k s i n 2m moreover we also provide similar embedding results for meshes and hypercubes our results mean that a family of torus structured mesh structured or hypercube structured parallel algorithms can be executed on the same twisted cube efficiently and in parallel

edge pancyclicity and path embeddability of bijective connection graphs an n dimensional bijective connection graph in brief bc graph is a regular graph with 2 n nodes and n2 n 1 edges the n dimensional hypercube crossed cube mobius cube etc are some examples of the n dimensional bc graphs in this paper we propose a general method to study the edge pancyclicity and path embeddability of the bc graphs first we prove that a path of length l with dist x n x y 2 y in x n where x n n 4 is a n dimensional bc graph satisfying the three specific conditions and v x n is the node set of x n furthermore by this result we can claim that x n is edge pancyclic lastly we show that these results can be applied to not only crossed cubes and mobius cubes but also other bc graphs except crossed cubes and mobius cubes so far the research on edge pancyclicity and path embeddability has been limited in some specific interconnection architectures such as crossed cubes mobius cubes

asymptotic error expansion of wavelet approximations of smooth functions ii we generalize earlier results concerning an asymptotic error expansion of wavelet approximations the properties of the monowavelets which are the building blocks for the error expansion are studied in more detail and connections between spline wavelets and euler and bernoulli polynomials are pointed out the expansion is used to compare the error for different wavelet families we prove that the leading terms of the expansion only depend on the multiresolution subspaces v j and not on how the complementary subspaces w j are chosen consequently for a fixed set of subspaces v j the leading terms do not depend on the fact whether the wavelets are orthogonal or not we also show that daubechies orthogonal wavelets need in general one level more than spline wavelets to obtain an approximation with a prescribed accuracy these results are illustrated with numerical examples

embedding meshes into crossed cubes crossed cubes are important variants of hypercubes in this paper we consider embeddings of meshes in crossed cubes the major research findings in this paper are 1 for any integer n 1 a 2x2 n 1 mesh can be embedded in the n dimensional crossed cube with dilation 1 and expansion 1 2 for any integer n 4 two node disjoint 4x2 n 3 meshes can be embedded in the n dimensional crossed cube with dilation 1 and expansion 2 the obtained results are optimal in the sense that the dilations of the embeddings are 1 the embedding of the 2x2 n 1 mesh is also optimal in terms of expansion because it has the smallest expansion 1

an efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the daubechies wavelet basis an efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with daubechies wavelet and scaling function basis sets our quadrature is also applicable in the case of adaptive spatial resolution our theoretical error estimates are confirmed by numerical test calculations of the ground state energy and wavefunction of the harmonic oscillator in one dimension with and without adaptive resolution as a byproduct we derive a filter which upon application on the scaling function coefficients of a smooth function renders the approximate grid values of this function this also allows for a fast calculation of the charge density from the wavefunction

spectral projected gradient method with inexact restoration for minimization with nonconvex constraints this work takes advantage of the spectral projected gradient direction within the inexact restoration framework to address nonlinear optimization problems with nonconvex constraints the proposed strategy includes a convenient handling of the constraints together with nonmonotonic features to speed up convergence the numerical performance is assessed by experiments with hard spheres problems pointing out that the inexact restoration framework provides an adequate environment for the extension of the spectral projected gradient method for general nonlinearly constrained optimization

on the linear convergence of descent methods for convex essentially smooth minimization consider the problem of minimizing over a polyhedral set the composition of an affine mapping with a strictly convex essentially smooth function a general result on the linear convergence of descent methods for solving this problem is presented by applying this result the linear convergence of both the gradient projection algorithm of goldstein and levitin and polyak and a matrix splitting algorithm using regular splitting is established the results do not require that the cost function be strongly convex or that the optimal solution set be bounded the key to the analysis lies in a new error bound for estimating the distance from a feasible point to the optimal solution set

solving second kind fredholm integral equations by periodic wavelet galerkin method in this paper we use the periodized daubechies wavelets based galerkin method pwgm to solve linear nonlinear and singular fredholm integral equations of the second kind a main advantage of the present pwgm over the existing wavelet galerkin methods lies in that the wavelet expansion coefficients are exactly obtained without calculating the wavelet integrations therefore the computational cost is low whereas the accuracy is high after discretization the linear and nonlinear integral equations is converted into a system of linear and nonlinear equations respectively and for the linear case the matrix can be converted into a sparse and symmetrical one by fast wavelet transform fwt numerical experiments show that the pwgm has a good degree of accuracy

weak sharp solutions of variational inequalities xuexiang huang pointed out that the statement on line 5 of page 184 of p marcotte and d zhu siam j optim 9 1999 pp 179 189 is invalid and supplied an alternative proof of the inequality that appears on line 10 here is a simple proof of this result due to an anonymous referee the substitution starts at line 4 and ends at line 11

the barzilai and borwein gradient method for the large scale unconstrained minimization problem the barzilai and borwein gradient method for the solution of large scale unconstrained minimization problems is considered this method requires few storage locations and very inexpensive computations furthermore it does not guarantee descent in the objective function and no line search is required recently the global convergence for the convex quadratic case has been established however for the nonquadratic case the method needs to be incorporated in a globalization scheme in this work a nonmonotone line search strategy that guarantees global convergence is combined with the barzilai and borwein method this strategy is based on the nonmonotone line search technique proposed by grippo lampariello and lucidi siam j numer anal 23 1986 pp 707 716 numerical results to compare the behavior of this method with recent implementations of the conjugate gradient method are presented these results indicate that the global barzilai and borwein method may allow some significant reduction in the number of line searches and also in the number of gradient evaluations

a wavelet multilevel method for ill posed problems stabilized by tikhonov regularization an additive schwarz iteration is described for the fast resolution of linear ill posed problems which are stabilized by tikhonov regularization the algorithm and its analysis are presented in a general framework which applies to integral equations of the first kind discretized either by spline functions or daubechies wavelets numerical experiments are reported on to illustrate the theoretical results and to compare both discretization schemes

solving linear integro differential equation system by galerkin methods with hybrid functions in this paper we use the hybrid legendre and block pulse functions on interval 0 1 to solve the linear integro differential equation system and construct the quadrature formulae for the calculation of inner products of any functions which are required in the galerkin methods for integro differential equation system

a multivariate spectral projected gradient method for bound constrained optimization in this paper we consider a multivariate spectral projected gradient mspg method for bound constrained optimization combined with a quasi newton property the multivariate spectral projected gradient method allows an individual adaptive step size along each coordinate direction on the basis of nonmonotone line search global convergence is established a numerical comparison with the traditional spg method shows that the method is promising

embedding of meshes in mobius cubes the hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement mobius cubes form a class of hypercube variants that give better performance with the same number of edges and vertices in this paper we consider embedding of meshes in mobius cubes the main results obtained in this paper are 1 for n 1 there exists a 2x2 n 1 mesh that can be embedded in the n dimensional mobius cube with dilation 1 and expansion 1 2 for n 4 there exists a 4x2 n 2 mesh that can be embedded in the n dimensional mobius cube with dilation 2 and expansion 1 3 for n 4 there are two disjoint 4x2 n 3 meshes that can be embedded in the 0 type n dimensional mobius cube with dilation 1 4 for n 4 there are two disjoint 4x2 n 3 meshes that can be embedded in the 1 type n dimensional mobius cube with dilation 2 results of 1 and 3 are optimal in the sense that the dilations of the embeddings are 1

mapping cycles and trees on wrap around butterfly graphs we give a new algebraic representation for the wrap around butterfly interconnection network this new representation is based on the direct product of groups and finite fields and allows an algebraic expression of the network connectivity the abstract algebraic tools may then be employed to explore the structural properties of the butterfly in this paper we exploit this model to map guest graphs on the butterfly in particular we provide designs of unit dilation mappings of all possible length cycles on butterflies we also map the largest possible binary trees on butterfly networks with a dilation 2 if the network degree is less than 16 3 if it is less than 32 and 4 if it is less than 64 this is a great improvement over previous results

weak sharp minima in mathematical programming the notion of a sharp or strongly unique minimum is extended to include the possibility of a nonunique solution set these minima will be called weak sharp minima conditions necessary for the solution set of a minimization problem to be a set of weak sharp minima are developed in both the unconstrained and constrained cases these conditions are also shown to be sufficient under the appropriate convexity hypotheses the existence of weak sharp minima is characterized in the cases of linear and quadratic convex programming and for the linear complementarity problem in particular a result of mangasarian and meyer is reproduced that shows that the solution set of a linear program is always a set of weak sharp minima whenever it is nonempty consequences for the convergence theory of algorithms are also examined especially conditions yielding finite termination

randomized algorithms for binary search and load balancing on fixed connection networks with geometric applications there are now a number of fundamental problems in computational geometry that have optimal algorithms on pram models this paper presents randomized parallel algorithms that execute on an n processor butterfly interconnection network in o log n time for the following problems of input size n trapezoidal decomposition visibility triangulation and two dimensional convex hull these algorithms involve tackling some of the very basic problems like binary search and load balancing that are taken for granted in pram models apart from a two dimensional convex hull algorithm these are the first nontrivial geometric algorithms that attain this performance on fixed connection networks these techniques use a number of ideas from flashsort that have to be modified to handle more difficult situations it seems likely that they will have wider applications

numerical solution of linear integro differential equation by using sine cosine wavelets abstract we use the continuous sine cosine wavelets on the interval 0 1 to solve the linear integro differential equation to do so we construct the quadrature formulae for the calculation of inner products of any functions which are required in the approximation for the integro differential equation then we reduced the integro differential equation to the solution of linear algebraic equations

solving second kind integral equations with hybrid chebyshev and block pulse functions in this paper we use a combination of chebyshev and block pulse functions on the interval 0 1 to solve the linear integral equation of the second kind we convert the integral equation to a system of linear equations we show that our estimates have a good degree of accuracy

the numerical solution of the non linear integro differential equations based on the meshless method this article investigates the numerical solution of the nonlinear integro differential equations the numerical scheme developed in the current paper is based on the moving least square method the moving least square methodology is an effective technique for the approximation of an unknown function by using a set of disordered data it consists of a local weighted least square fitting valid on a small neighborhood of a point and only based on the information provided by its n closet points hence the method is a meshless method and does not need any background mesh or cell structures the error analysis of the proposed method is provided the validity and efficiency of the new method are demonstrated through several tests

optimal emulations by butterfly like networks the power of butterfly like networks as multicomputer interconnection networks is studied by considering how efficiently the butterfly can emulate other networks emulations are studied formally via graph embeddings so the topic here becomes how efficiently can one embed the graph underlying a given interconnection network in the graph underlying the butterfly network within this framework the slowdown incurred by an emulation is measured by the sum of the dilation and the congestion of the corresponding embedding respectively the maximum amount that the embedding stretches an edge of the guest graph and the maximum traffic across any edge of the host graph the efficiency of resource utilization in an emulation is measured by the expansion of the corresponding embedding the ratio of the sizes of the host to guest graph three main results expose a number of optimal emulations by butterfly networks call a family of graphs balanced if complete binary trees can be embedded in the family with simultaneous dilation congestion and expansion 0 1 1 the family of butterfly graphs is balanced 2 a any graph from a family of maxdegree d graphs having a recursive separator of size s x can be embedded in any balanced graph family with simultaneous dilation o log d i s 2 i g and expansion o 1 b any dilation d embedding of a maxdegree d graph in a butterfly graph can be converted to an embedding having simultaneous dilation o d and congestion o dd 3 any embedding of a planar graph g in a butterfly graph must have dilation log g g where g is the size of the smallest 1 3 2 3 node separator of g and g is the size of g s largest interior face applications of these results include 1 the n node x tree network can be emulated by the butterfly network with slowdown o log log n and expansion 0 1 no embedding has dilation smaller than log log n independent of expansion 2 every embedding of the n x n mesh in the butterfly graph has dilation log n any expansion o 1 embedding in the butterfly graph achieves dilation o log n these applications provide the first examples of networks that can be embedded more efficiently in hypercubes than in butterflies we also show that analogues of these results hold for networks that are structurally related to the butterfly network the upper bounds hold for the hypercube and the de bruijn networks possibly with altered constants the lower bounds hold at least in weakened form for the de bruijn network

a fast adaptive wavelet collocation algorithm for multidimensional pdes a fast multilevel wavelet collocation method for the solution of partial differential equations in multiple dimensions is developed the computational cost of the algorithm is independent of the dimensionality of the problem and is o n where n is the total number of collocation points the method can handle general boundary conditions the multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution high resolution computations are performed only in regions where singularities or sharp transitions occur numerical results demonstrate the ability of the method to resolve localized structures such as shocks which change their location and steepness in space and time the present results indicate that the method has clear advantages in comparison with well established numerical algorithms

using the refinement equation for evaluating integrals of wavelets the wavelet galerkin method for solving partial differential equations leads to the problem of computing integrals of products of derivatives of wavelets this paper studies the problem from the point of view of stationary subdivision schemes one of the main results is to identify these integrals as components of the unique solution of a certain eigenvector moment problem associated with the coefficients of the refinement equation asymptotic expansions for the corresponding subdivision schemes form an important ingredient of our approach

a semi analytical approach to solve integro differential equations in this work we present a semi analytical method for solving integro differential equations under multi point or mixed boundary conditions the proposed method solves linear and nonlinear fredholmvolterra integro differential equations a convergence analysis of the proposed method is directly examined numerical examples are worked out to demonstrate the main results moreover proper graphs are provided to confirm the efficiency and the accuracy of the proposed scheme we show that with a few number of obtained approximating terms we achieve a high accuracy level of the obtained results however increasing the number of approximating terms yields a significant decrease of the error of the approximation the proposed method is very useful reliable and flexible for solving different kinds of integro differential equations

wavelet simultaneous approximation from samples affected by noise the authors recently introduced a pth order wavelet regularization method together with the gcv criterion for approximating a function from a finite sample affected by noise convergence results of the method were proven for the l2 norm the present paper addresses the problem of simultaneous approximation which is of interest in applications where derivatives are useful for extracting several features from a signal it is proved that it is not needed to devise a special method to this purpose since the convergence of the method devised by the authors also works for the hq norm 0 q p

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

bessel polynomial solutions of high order linear volterra integro differential equations abstract in this study a practical matrix method which is based on collocation points is presented to find approximate solutions of high order linear volterra integro differential equations vides under the mixed conditions in terms of bessel polynomials numerical examples are included to demonstrate the validity and applicability of the technique and comparisons are made with the existing results the results show the efficiency and accuracy of the present work all of the numerical computations have been performed on the computer using a program written in matlab v7 6 0 r2008a

gauss type quadrature rule with complex nodes and weights for integrals involving daubechies scale functions and wavelets this paper deals with derivation of a gauss type quadrature rule named as gauss daubechies quadrature rule for numerical evaluation of integrals involving product of integrable function and daubechies scale functions wavelets some of the nodes and weights of the quadrature formula may be complex and appear with their conjugates this is in contrast with the standard gauss type quadrature rule for integrals involving products of integrable functions and non negative weight functions this quadrature rule has accuracy as good as the standard gauss type quadrature rule and is also found to be stable the efficacy of the quadrature rule derived here has been tested through some numerical examples

comparison between the homotopy perturbation method and the sine cosine wavelet method for solving linear integro differential equations this paper compares the homotopy perturbation method with the sine cosine wavelet method for solving linear integro differential equations from the computational viewpoint the homotopy perturbation method is more efficient and easier than the sine cosine wavelet method

a new collocation method for solution of mixed linear integro differential difference equations numerical solution of mixed linear integro differential difference equation is presented using chebyshev collocation method the aim of this article is to present an efficient numerical procedure for solving mixed linear integro differential difference equations our method depends mainly on a chebyshev expansion approach this method transforms mixed linear integro differential difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation the reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system maple10

avoiding the maratos effect by means of a nonmonotone line search ii inequality constrained problems feasible iterates when solving inequality constrained optimization problems via sequential quadratic programming sqp it is potentially advantageous to generate iterates that all satisfy the constraints all quadratic programs encountered are then feasible and there is no need for a surrogate merit function feasibility of the successive iterates is in fact required in many contexts such as in real time applications or when the objective function is not defined outside the feasible set it has recently been shown that this is indeed possible by means of a suitable perturbation of the original sqp iteration without losing superlinear convergence in this context the well known maratos effect is compounded by the possible infeasibility of the full step of one even close to a solution these difficulties have been accommodated by making use of a suitable modification of a bending technique proposed by mayne and polak requiring evaluation of the constraints function at an auxiliary point at each iteration in part i

embedding complete binary trees into butterfly networks the authors present embeddings of complete binary trees into butterfly networks with or without wrap around connections let m be an even integer and q m log m 1 the authors show how to embed a 2 sup q 1 1 node complete binary tree t q into a m 1 2 sup m 1 node wrap around butterfly b sub w m 1 with a dilation of 4 and how to embed t q into a m 2 2 sup m 2 node wrap around butterfly b sub w m 2 with an optimal dilation of 2 they also present an embedding of a wrap around butterfly b sub w m into a m 1 2 sup m node no wrap around butterfly b m with a dilation of 3 using this embedding it is shown that t q can be embedded into a no wrap butterfly b m 1 resp b m 2 with a dilation of 8 resp 5

computation of wavelet coefficients from average samples there exist efficient methods to compute the wavelet coefficients of a function f t from its point samples f t email protected email protected n however in many applications the available samples are average samples of the type f t email protected u t dt where the averaging function u t reflects the characteristic of the acquisition device in this work methods to compute the coefficients in a biorthogonal wavelet system from average samples are studied error estimations are obtained and using them the optimal values for the parameters in the proposed approximation rules are calculated the obtained error estimations can also be applied to the rules that compute the coefficients from point samples and thus these estimations can be used to compare and to choose between the different methods proposed in the literature the methods proposed here also allow us to compute the biorthogonal wavelet coefficients from the coefficients in another biorthogonal wavelet system

convergence properties of nonmonotone spectral projected gradient methods in a recent paper a nonmonotone spectral projected gradient spg method was introduced by birgin et al for the minimization of differentiable functions on closed convex sets and extensive presented results showed that this method was very efficient in this paper we give a more comprehensive theoretical analysis of the spg method in doing so we remove various boundedness conditions that are assumed in existing results such as boundedness from below of f boundedness of xk or existence of accumulation point of xk if f is uniformly continuous we establish the convergence theory of this method and prove that the spg method forces the sequence of projected gradients to zero moreover we show under appropriate conditions that the spg method has some encouraging convergence properties such as the global convergence of the sequence of iterates generated by this method and the finite termination etc therefore these results show that the spg method is attractive in theory

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

path embeddings in faulty 3 ary n cubes the class of k ary n cubes represents the most commonly used interconnection topology for distributed memory parallel systems in this paper we study the problem of embedding paths of various lengths into faulty 3 ary n cubes and prove that a faulty 3 ary n cube with f 2n 3 faulty vertices admits a path of every length from 2n 1 to 3 n f 1 connecting any two distinct healthy vertices this result is optimal with respect to the number of vertex faults tolerated

wavelet packet transform initialization for piecewise polynomial and bandlimited inputs this paper considers the problem of initializing the wavelet packet transform when the analog input x t is either bandlimited or else is piecewise polynomial on the dyadic intervals this is accomplished by the construction of certain prefilter sequences that are applied to the samples x sub k x sub k x kt t is the sampling period in the piecewise polynomial case the prefilter sequences are computed with the aid of the interpolatory graphical display algorithm igda which is used to compute the so called incremental moment functions of the scaling function spl phi t on the dyadic points the moments of spl phi t are also employed

approximation power of biorthogonal wavelet expansions this paper looks at the effect of the number of vanishing moments on the approximation power of wavelet expansions the strang fix conditions imply that the error for an orthogonal wavelet approximation at scale a 2 sup i globally decays as a sup n where n is the order of the transform this is why for a given number of scales higher order wavelet transforms usually result in better signal approximations we prove that this result carries over for the general biorthogonal case and that the rate of decay of the error is determined by the order properties of the synthesis scaling function alone we also derive asymptotic error formulas and show that biorthogonal wavelet transforms are equivalent to their corresponding orthogonal projector as the scale goes to zero these results strengthen sweldens earlier analysis and confirm that the approximation power of biorthogonal and semi orthogonal wavelet expansions is essentially the same finally we compare the asymptotic performance of various wavelet transforms and briefly discuss the advantages of splines we also indicate how the smoothness of the basis functions is beneficial in reducing the approximation error

wavelets and dilation equations a brief introduction wavelets are new families of basis functions that yield the representation f x sum b jk w 2 j x k their construction begins with the solution phi x to a dilation equation with coefficients c k then w comes from phi and the basis comes by translation and dilation of w it is shown in part 1 how conditions on the c k lead to approximation properties and orthogonality properties of the wavelets part 2 describes the recursive algorithms also based on the c k that decompose and reconstruct f the object of wavelets is to localize as far as possible in both time and frequency with efficient algorithms

projected newton methods for optimization problems with simple constraints we consider the problem min f x x geqq 0 and propose algorithms of the form x k 1 x k alpha k d k nabla f x k where cdot denotes projection on the positive orthant alpha k is a stepsize chosen by an armijo like rule and d k is a positive definite symmetric matrix which is partly diagonal we show that d k can be calculated simply on the basis of second derivatives of f so that the resulting newton like algorithm has a typically superlinear rate of convergence with other choices of d k convergence at a typically linear rate is obtained the algorithms are almost as simple as their unconstrained counterparts they are well suited for problems of large dimension such as those arising in optimal control while being competitive with existing methods for low dimensional problems the effectiveness of the newton like algorithm is demonstrated via computational examples involving as many as 10 000 variables extensions to general linearly constrained pr

sampling approximation of smooth functions via generalized coiflets we present the sampling approximation power of a newly constructed class of compactly supported orthonormal wavelets called generalized coiflets we study the accuracy of generalized coiflets based sampling approximation of smooth functions by developing convergence rates for the pointwise approximation error as well as its l sup p norm we show i that the l sup 2 error due to the approximation of expansion coefficients by function samples is asymptotically negligible compared with that due to projection and ii that generalized coiflets can achieve asymptotically better approximation than the original coiflets

convergence of the red tower method for removing noise from data by coupling the wavelet transform with a particular nonlinear shrinking function the red telescopic optimal wavelet estimation of the risk tower method is introduced for removing noise from signals it is shown that the method yields convergence of the l sub 2 risk to the actual solution with optimal rate moreover the method is proved to be asymptotically efficient when the regularization parameter is selected by the generalized cross validation criterion gcv or the mallows criterion numerical experiments based on synthetic data are provided to compare the performance of the red tower method with hard thresholding soft thresholding and neigh coeff thresholding furthermore the numerical tests are also performed when the tower method is applied to hard thresholding soft thresholding and neigh coeff thresholding for which the full convergence results are still open

gauss quadrature rules for cauchy principal value integrals with wavelets gauss quadrature rules for cauchy principal value integrals with wavelets are established by the construction of orthogonal polynomials of wavelets and scaling functions as weight functions the wavelet gauss quadrature formulae for cauchy principal value integrals are introduced numerical examples are also presented

new construction of wavelets base on floor function in this paper the properties of the floor function has been used to find a function which is one on the interval 0 1 and is zero elsewhere the suitable dilation and translation parameters lead us to get similar function corresponding to the interval a b these functions and their combinations enable us to represent the stepwise functions as a function of floor function we have applied this method on haar wavelet sine cosine wavelet block pulse functions and hybrid fourier block pulse functions to get the new representations of these functions

an evaluation of clenshaw curtis quadrature rule for integration w r t singular measures this work is devoted to the study of quadrature rules for integration with respect to w r t general probability measures with known moments automatic calculation of the clenshaw curtis rules is considered and analyzed it is shown that it is possible to construct these rules in a stable manner for quadrature w r t balanced measures in order to make a comparison gauss rules and their stable implementation for integration w r t balanced measures are recalled convergence rates are tested in the case of binomial measures

a note on one point quadrature formula for daubechies scale function with partial support abstract this note is concerned with an efficient computation of integrals of products of a smooth function and daubechies scale function with partial support by using a one point quadrature rule the error estimate is obtained the rule is illustrated by considering an example from the literature

integral operators on sparse grids in this paper we are concerned with the construction and use of wavelet approximation spaces for the fast evaluation of integral expressions the spaces are based on biorthogonal anisotropic tensor product wavelets we introduce sparse grid hyperbolic cross approximation spaces which are adapted not only to the smoothness of the kernel but also to the norm in which the error is measured furthermore we introduce compression schemes for the corresponding discretizations numerical examples for the laplace equation with dirichlet boundary conditions and an additional integral term with a smooth kernel demonstrate the validity of our theoretical results