on time integration of groundwater flow equations by spectral methods a study of the computational performance of the recently introduced spectral approach for the time integration of finite element flow equations is performed two reduction methods are presented and discussed one method relies on the classical modal decomposition wherein the leftmost eigenpairs of a generalized symmetric eigenvalue problem are evaluated one at a time by a cost effective orthogonal deflation technique the other uses a set of lanczos vectors for the coordinate transformation matrix and involves a recursive product between the inverse of the stiffness matrix and a vector an extensive analysis of the behavior of the two methods is made with a representative sample problem of subsurface flow solved over a regular and an irregular mesh the results show that the spectral approach cannot be competitive from a computational viewpoint with a more traditional time stepping or direct integration scheme e g the crank nicolson scheme the eigenvector technique is slow to converge and a large portion if not all of the flow modes need to be determined to accurately describe the desired solution the lanczos algorithm may converge faster in the lanczos vector space however its actual performance depends to a large extent on the initial guessed vector and is adversely influenced by the requirement to solve an equivalent steady state problem at each iteration it is concluded that for a robust and efficient finite element code of transient ground water flow direct integration methods are generally to be preferred

covariance regularization by thresholding this paper considers regularizing a covariance matrix of p variables estimated from n observations by hard thresholding we show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense the variables are gaussian or sub gaussian and log p n 0 and obtain explicit rates the results are uniform over families of covariance matrices which satisfy a fairly natural notion of sparsity we discuss an intuitive resampling scheme for threshold selection and prove a general cross validation result that justifies this approach we also compare thresholding to other covariance estimators in simulations and on an example from climate data 1 introduction estimation of covariance matrices is important in a number of areas of statistical analysis including dimension reduction by principal component analysis pca classification by linear or quadratic discriminant analysis lda and qda establishing independence and conditional independence relations in the context of graphical models and setting confidence intervals on linear functions of the means of the components in recent years many application areas where these tools are used have been dealing with very high dimensional datasets and sample sizes can be very small relative to dimension examples include genetic data brain imaging spectroscopic imaging climate data and many others it is well known by now that the empirical covariance matrix for samples of size n from a p variate gaussian distribution np p is not a good estimator of the population covariance if p is large many results in random matrix theory illustrate this from the classical mary law 29 to the more recent work of johnstone and his students on the theory of the largest eigenvalues 12 23 30 and associated eigenvectors 24 however with the exception of a method for estimating the covariance spectrum 11 these probabilistic results do not offer alternatives to the sample covariance matrix alternative estimators for large covariance matrices have therefore attracted a lot of attention recently two broad classes of covariance estimators have emerged those that rely on a natural ordering among variables and assume that variables

visual multiple secret sharing based upon turning and flipping the secret sharing schemes in conventional visual cryptography are capable of sharing one secret image into a set of random transparencies called shares in the form of rectangles which reveal the secret image to the human visual system when they are superimposed recently visual secret sharing schemes involving multiple secrets have attracted much attention by adopting rotations on one of the two encoded circle shares more than two secrets could be shared yet the encoding and decoding processes of circle shares need more sophisticated mechanisms than those of rectangular or square ones in this paper we explore the possibilities of visual multiple secret sharing using simply two rectangular or square shares specifically we define some operations onto a transparency based upon turning over or flipping around then we propose visual cryptographic schemes that are able to encode two or four secrets into two rectangular shares and up to eight secrets into two square shares such that the secrets cannot be obtained from any single share whereas they are revealed by stacking the two shares under various combinations of turning or flipping operations the proposed schemes which solidly elaborate the relationship between the encoded shares and the shared secrets broaden the research scope and enrich the flexibility and applicability of visual cryptography or image encryption theoretically and practically

on the security of a visual cryptography scheme for color images hou visual cryptography for color images pattern recognition 36 2003 1619 1629 proposed a four share visual cryptography scheme for color images the scheme splits a dithered eight color secret image into four shares the black mask and other three shares it was claimed that without knowing the black mask no information about the secret image can be obtained even if all the other three shares are known in this paper we show that this may be true for a few specific two color secret images only in all other cases however security cannot be guaranteed we show that an attacker can compromise a randomly chosen two color secret image from any two of the other three shares with probability 47 by completely recovering the shape and pattern of the secret image the advantage will increase to 67 if all the three shares are known if the secret image has three or four colors we show that the attacker can compromise it with probability 47 and 835 respectively finally we show that our technique can be extended to compromising secret images with more than four colors

secret sharing schemes from binary linear codes in principle every linear code can be used to construct a secret sharing scheme however in general determining the access structure of the scheme is very hard on the other hand finding error correcting codes that produce secret sharing schemes with efficient access structures is also difficult in this paper we study a set of minimal codewords for certain classes of binary linear codes and then determine the access structure of secret sharing schemes based on these codes furthermore we prove that the secret sharing schemes obtained are democratic in the sense that every participant is involved in the same number of minimal access sets

sharing a verifiable secret image using two shadows in this paper we propose a novel 2 2 verifiable secret sharing vss scheme which not only protects a secret image but also allows users to verify the restored secret image in the revealing and verifying phase for all binary grayscale and color images error diffusion and image clustering techniques are adopted to achieve our objective experimental results and discussions show that the proposed scheme with its smaller shadow size and lower computational complexity obviously outperforms previous vss schemes designed either with or without the cheating prevention mechanism moreover the use of a halftone logo gives an efficient solution to verifying whether the restored secret image is correct by using a halftone logo

minimal eigenvalue of large sparse matrices by an efficient reverse power conjugate gradient scheme in the assessment of the minimal eigenvalue of large sparse positive definite matrices the shift method easily fails to give successful results since its rate of convergence may prove unacceptably slow a very efficient alternative approach is provided by a double iterative scheme wherein external and internal iterations are performed by the reverse power and the modified conjugate gradients respectively the wider the spectral interval the greater the success of this technique whose efficiency in engineering practice therefore increases with the problem size n the results obtained with large 800 n 2200 space positive definite matrices arising from the finite element integration of flow and elasticity equations show that an accurate estimate of the minimal eigenvalue is achieved after very few 10 external iterations and a number of internal iterations of the order of n

a trace minimization algorithm for the generalized eigenvalue problem an algorithm for computing a few of the smallest or largest eigenvalues and associated eigenvectors of the large sparse generalized eigenvalue problem ax lambda bx is presented the matrices a and b are assumed to be symmetric and haphazardly sparse with b being positive definite the problem is treated as one of constrained optimization and an inverse iteration is developed which requires the solution of linear algebraic systems only to the accuracy demanded by a given subspace the rate of convergence of the method is established and a technique for improving it is discussed numerical experiments and comparisons with other methods are presented

on linearly constrained minimum variance beamforming beamforming is a widely used technique for source localization in signal processing and neuroimaging a number of vector beamformers have been introduced to localize neuronal activity by using magnetoencephalography meg data in the literature however the existing theoretical analyses on these beamformers have been limited to simple cases where no more than two sources are allowed in the associated model and the theoretical sensor covariance is also assumed known the information about the effects of the meg spatial and temporal dimensions on the consistency of vector beamforming is incomplete in the present study we consider a class of vector beamformers defined by thresholding the sensor covariance matrix which include the standard vector beamformer as a special case a general asymptotic theory is developed for these vector beamformers which shows the extent of effects to which the meg spatial and temporal dimensions on estimating the neuronal activity index the performances of the proposed beamformers are assessed by simulation studies superior performances of the proposed beamformers are obtained when the signal to noise ratio is low we apply the proposed procedure to real meg data sets derived from five sessions of a human face perception experiment finding several highly active areas in the brain a good agreement between these findings and the known neurophysiology of the meg response to human face perception is shown

accelerated simultaneous iterations for large finite element eigenproblems abstract an accelerated simultaneous iteration method is presented for the solution of the generalized eigenproblem ax bx where a and b are real sparse symmetric positive definite matrices the approach is well suited for the determination of the leftmost eigenpairs of problems with large size n the procedure relies on the optimization of the rayleigh quotient over a subspace of orthogonal vectors by a conjugate gradient technique effectively preconditioned with the pointwise incomplete cholesky factorization the method is applied to the evaluation of the smallest 15 eigenpairs of finite element models with size ranging between 150 and 2300 the numerical experiments show that while the simultaneous conjugate gradient scheme fails to converge the accelerated iterations yield accurate results in a number of steps which is much smaller than n the new approach does not require the a priori estimate of any empirical parameter and appears to be a robust reliable and efficient tool for the partial eigensolution of large finite element problems

numerical comparison of iterative eigensolvers for large sparse symmetric positive definite matrices abstract the jacobi davidson jd method has been recently proposed for the evaluation of the partial eigenspectrum of large sparse matrices in this work we report a set of numerical experiments that compare this method with other previously proposed techniques deflation accelerated conjugate gradient dacg and lanczos arpack on large sparse symmetric matrices the results obtained by jd and dacg are benchmarked against those obtained with arpack in terms of computational time for the evaluation of s s 100 leftmost eigenpairs the comparison is performed on a number of matrices with dimensions up to a few hundred thousands arising from the discretization of the diffusion equation by means of finite element mixed finite element and finite difference techniques the results show that dacg and jd are equally more efficient than arpack for a small number of eigenpairs with dacg more performing for small s and particularly for s 1 while arpack tends to become competitive when 40 or more eigenpairs are sought for the largest and worst conditioned matrix dacg proves the only viable alternative

block subspace projection preconditioned conjugate gradient method in modal structural analysis abstract this paper considers the preconditioned block conjugate gradient method for solving the algebraic generalized partial eigenvalue problem which arises when the finite element method is applied to dynamic analysis in structural and solid mechanics the focus is on the development of an algorithm that keeps constant the iterable subspace dimension independently of the number of eigenpairs required novelties in this approach include a preconditioning strategy based on block incomplete factorization of the shifted stiffness matrix and analysis of unremovable errors which accumulate with increasing numbers of eigenpairs

application of the lanczos algorithm to the solution of the groundwater flow equation the solution to the finite element matrix differential equations resulting from the discretization of the groundwater flow equation is normally carried out by a finite difference approximation to the time derivative the total computational effort in solving a fluid flow problem is then directly related to the number of unknowns and the number of time steps required to obtain accurate and stable solutions the lanczos algorithm uses an orthogonal matrix transformation to reduce the finite element equations to a much smaller tridiagonal system of first order differential equations this new system can be solved by a standard tridiagonal solution algorithm with very little computational effort a matrix vector multiplication is then used to obtain the original solution at desired time steps the algorithm is used to accurately simulate the drawdown of synthetic two dimensional aquifers including ones with substantial hydraulic conductivity contrasts the method affords an efficient means of solving large problems particularly when time durations are long

parallel preconditioned conjugate gradient optimization of the rayleigh quotient for the solution of sparse eigenproblems a parallel algorithm based on the multidimensional minimization of the rayleigh quotient is proposed to evaluate the leftmost eigenpairs of the generalized symmetric positive definite eigenproblem the minimization is performed via a conjugate gradient like procedure accelerated by a factorized approximate inverse preconditioner fsai and by a number of block preconditioners the resulting code obtains a high level of parallel efficiency and proves to be comparable with the parpack package on a set of large matrices arising from various discretizations of pdes of elliptic parabolic type

two verifiable multi secret sharing schemes based on nonhomogeneous linear recursion and lfsr public key cryptosystem we shall propose two new efficient verifiable multi secret sharing schemes based on linear feedback shift register lfsr public key and new nonhomogeneous linear recursions compared with previous schemes these schemes have better performance and shorter private public key length moreover they have fewer public values and simpler construction as well as various methods for the reconstruction phase altogether they are easy to use and provide great capabilities for many applications

a novel secret image sharing scheme in color images using small shadow images over the past several years secret image sharing techniques have become another branch of the effort to prevent secret images from being eavesdropped on in addition to traditional cryptography because smaller shadows can speed up the transmission of a secret color image in this paper we combine chang and wu s gradual search algorithm for a single bitmap btc gsbtc and shamir s k n threshold concept to propose a novel secret color image sharing scheme that generates smaller shadows experimental results confirm that the proposed scheme successfully reduces shadow size and that each shadow behaves as a random like image that prevents leakage of information about the secret color image furthermore the correlation between two vertically or horizontally adjacent pixels in each shadow is significantly less than those in a color secret image and the presented scheme also achieves on average an npcr 0 414 and auci 32 78 thus with our scheme one pixel difference could cause a significant difference in the corresponding shadows therefore the security of the presented scheme is also confirmed

an improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices abstract an accelerated optimization technique combined with a stepwise deflation procedure is presented for the efficient evaluation of the p p 20 leftmost eigenvalues and eigenvectors of finite element symmetric positive definite p d matrices of very large size the optimization is performed on the rayleigh quotient of the deflated matrices by the aid of a conjugate gradient cg scheme effectively preconditioned with the incomplete cholesky factorization no a priori estimate of acceleration parameters is required numerical experiments on large arbitrarily sparse problems taken from the engineering finite elements f e practice show a very fast convergence rate for any value of p within the explored interval and particularly so for the minimal eigenpair in this case the number of iterations needed to achieve an accurate solution may be as much as 2 orders of magnitude smaller than the problem size several results concerning the spectral behavior of the cg preconditioning matrices are also given and discussed

new efficient and practical verifiable multi secret sharing schemes in 2006 zhao et al proposed a practical verifiable multi secret sharing based on yang et al s and feldman s schemes in this paper we propose two efficient computationally secure t n and verifiable multi secret sharing schemes based on homogeneous linear recursion the first scheme has the advantage of better performance a new simple construction and various techniques for the reconstruction phase the second scheme requires fewer public values with respect to zhao et al s and shao and cao schemes these schemes are easy to implement and provide great capabilities for many applications

solution of the partial eigenproblem by iterative methods a combined iterative method is formulated for the partial solution of the eigenproblem ax bx that arises from the application of the finite element method the method is a combination of the conjugate gradient cg method and the symmetric successive co ordinate overrelaxation sscor method both of these methods belong to the same family of iterative methods which retain their vectorial form and approach the solution by seeking stationary points of the rayleigh quotient the formulation consists in splitting a characteristic matrix into the sum of two matrices one of which corresponds to the sscor matrix and then accelerating the associated iteration using the cg the behaviour of the method is illustrated for five test cases and comparisons are made with other iterative methods the influence of the relaxation parameter on the computational efficiency of the methods is also studied

the lanczos algorithm with partial reorthogonalization the lanczos algorithm is becoming accepted as a powerful tool for finding the cigenvalues and for solving linear systems of equations any practical implementation of the algorithm suffers however from roundoff errors which usually cause the lanczos vectors to lose their mutual orthogonality in order to maintain some level of orthogonality full reorthogonalization fro and selective orthogonalization so have been used in the past as a remedy here partial reorthogonalization pro is proposed as a new method for maintain ing semiorthogonality among the lanczos vectors pro is based on a simple recurrence which allows us to monitor the loss of orthogonality among the lanczos vectors directly wvithout computing the inner products based on the information from the recurrence reorthogonalizations occur only when necessary thus substantial savings are made as compared to fro in some numerical examples we apply the lanczos algorithm with pro to the solution of large symmetric systems of linear equations and show that it is a robust and efficient algorithm for maintaining semiorthogonality among the lanczos vectors the results obtained compare favorably with the conjugate gradient method

a multisecret sharing scheme for color images based on cellular automata in this work a new multisecret sharing scheme for secret color images among a set of users is proposed the protocol allows that each participant in the scheme to share a secret color image with the rest of participants in such a way that all of them can recover all the secret color images only if the whole set of participants pools their shadows the proposed scheme is based on the use of bidimensional reversible cellular automata with memory the security of the scheme is studied and it is proved that the protocol is ideal and perfect and that it resists the most important statistical attacks

an orthogonal accelerated deflation technique for large symmetric eigenproblems abstract an improvement in accelerated conjugate gradient iterations is presented for the evaluation of several of the leftmost eigenpairs of large sparse symmetric positive definite matrices the approach relies on an orthogonal deflation procedure and is based on the subsequent preconditioned conjugate gradient optimization of rayleigh quotients over the restricted space orthogonal to the set of eigenvectors previously computed comparison with the accelerated simultaneous iterations performed over large finite element problems with size up to 4500 shows that storage requirement is significantly less and cpu times may be reduced by a factor of two or more

high dimensional covariance matrix estimation in approximate factor models the variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems classical methods of estimating the covariance matrices are based on the strict factor models assuming independent idiosyncratic components this assumption however is restrictive in practical applications by assuming sparse error covariance matrix we allow the presence of the cross sectional correlation even after taking out common factors and it enables us to combine the merits of both methods we estimate the sparse covariance using the adaptive thresholding technique as in cai and liu j amer statist assoc 106 2011 672 684 taking into account the fact that direct observations of the idiosyncratic components are unavailable the impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied

preconditioning constrained eigenvalue problems abstract the purpose of our paper is to introduce a robust preconditioning scheme for the numerical solution of the leftmost eigenvalues and corresponding eigenvectors of a constrained eigenvalue problem this constrained eigenvalue problem is congruent to a nonsymmetric eigenvalue problem with nontrivial jordan blocks associated with infinite eigenvalues the proposed preconditioning scheme is relevant to the application of krylov subspace methods and preconditioned eigensolvers the two key results are a semi orthogonal decomposition and a transformation process that implicitly combines a preconditioning step followed by abstract projection onto the subspace associated with the finite eigenvalues numerical results demonstrate the effectiveness of the preconditioning scheme

lanczos versus subspace iteration for solution of eigenvalue problems in this paper we consider solution of the eigen problem in structural analysis using a recent version of the lanczos method and the subspace method the two methods are applied to examples and we conclude that the lanczos method has advantages which are too good to overlook

adaptive thresholding for sparse covariance matrix estimation in this article we consider estimation of sparse covariance matrices and propose a thresholding procedure that is adaptive to the variability of individual entries the estimators are fully data driven and demonstrate excellent performance both theoretically and numerically it is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covariance matrices under the spectral norm in contrast the commonly used universal thresholding estimators are shown to be suboptimal over the same parameter spaces support recovery is discussed as well the adaptive thresholding estimators are easy to implement the numerical performance of the estimators is studied using both simulated and real data simulation results demonstrate that the adaptive thresholding estimators uniformly outperform the universal thresholding estimators the method is also illustrated in an analysis on a dataset from a small round blue cell tumor microarray experiment a supplement to this ar

a multiple level visual secret sharing scheme without image size expansion in traditional vss schemes the size of the share image is substantially expanded since each pixel of the secret image is mapped onto a block consisting of several pixels in addition the quality of the reconstructed secret image is normally degraded in contrast especially for halftone images this study proposes a vss scheme that maps a block in a secret image onto one corresponding equal sized block in each share image without image size expansion two types of techniques including histogram width equalization and histogram depth equalization are proposed to generate the corresponding share blocks containing multiple levels rather than two levels based on the density of black pixels on the blocks for a secret block in the former technique the gray scale image histogram is obtained by uniformly splitting the range of the pixel gray levels in the secret image while in the latter the buckets are created so that the area of each bucket is roughly constant by containing approximately the same number of pixels the proposed schemes significantly improve the quality of the reconstructed secret image compared to several previous investigations

probabilistic visual secret sharing schemes for grey scale images and color images visual secret sharing vss scheme is an encryption technique that utilizes the human visual system in recovering the secret image and does not require any cryptographic computation pixel expansion has been a major issue of vss schemes a number of probabilistic vss schemes with minimum pixel expansion have been proposed for binary secret images this paper presents a general probabilistic k n vss scheme for grey scale images and another scheme for color images with our schemes the pixel expansion can be set to a user defined value when this value is 1 there is no pixel expansion at all the quality of reconstructed secret images measured by average contrast or average relative difference is equivalent to the contrast of existing deterministic vss schemes previous probabilistic vss schemes for black and white images can be viewed as special cases in the schemes proposed here

source localization with meg data a beamforming approach based on covariance thresholding summary reconstructing neural activities using non invasive sensor arrays outside the brain is an ill posed inverse problem since the observed sensor measurements could result from an infinite number of possible neuronal sources the sensor covariance based beamformer mapping represents a popular and simple solution to the above problem in this article we propose a family of beamformers by using covariance thresholding a general theory is developed on how their spatial and temporal dimensions determine their performance conditions are provided for the convergence rate of the associated beamformer estimation the implications of the theory are illustrated by simulations and a real data analysis

a numerical study of various algorithms related to the preconditioned conjugate gradient method we present the results of a numerical study of the preconditioned conjugate gradient algorithm the minimal residual algorithm the biconjugate gradient algorithm and the bi minimal residual algorithm using both simple test matrices and more realistic test matrices derived from physical problems the application of the methods to unsymmetric matrices is considered we emphasize the importance of a good preconditioning look at various methods including icgg n and incomplete block factorization and make some practical recommendations some of the folk lore surrounding the semi iterative methods is dispelled

space time event sparse penalization for magneto electroencephalography this article presents a new spatio temporal method for m eeg source reconstruction based on the assumption that only a small number of events localized in space and or time are responsible for the measured signal each space time event is represented using a basis function expansion which reflects the most relevant or measurable features of the signal this model of neural activity leads naturally to a bayesian likelihood function which balances the model fit to the data with the complexity of the model where the complexity is related to the number of included events a novel expectation maximization algorithm which maximizes the likelihood function is presented the new method is shown to be effective on several meg simulations of neurological activity as well as data from a self paced finger tapping experiment

polynomial preconditioners for conjugate gradient calculations dubois greenbaum and rodrigue proposed using a truncated neumann series as an approximation to the inverse of a matrix a for the purpose of preconditioning conjugate gradient iterative approximations to ax b if we assume that a has been symmetrically scaled to have unit diagonal and is thus of the form i g then the neumann series is a power series in g with unit coefficients the incomplete inverse was thought of as a replacement of the incomplete cholesky decomposition suggested by meijerink and van der vorst in the family of methods iccg n the motivation for the replacement was the desire to have a preconditioned conjugate gradient method which only involved vector operations and which utilized long vectors we here suggest parameterizing the incomplete inverse to form a preconditioning matrix whose inverse is a polynomial in g we then show how to select the parameters to minimize the condition number of the product of the polynomial and i g theoretically the resulting algorithm

generalized thresholding of large covariance matrices we propose a new class of generalized thresholding operators that combine thresholding with shrinkage and study generalized thresholding of the sample covariance matrix in high dimensions generalized thresholding of the covariance matrix has good theoretical properties and carries almost no computational burden we obtain an explicit convergence rate in the operator norm that shows the tradeoff between the sparsity of the true model dimension and the sample size and shows that generalized thresholding is consistent over a large class of models as long as the dimension p and the sample size n satisfy log p n 0 in addition we show that generalized thresholding has the sparsistency property meaning it estimates true zeros as zeros with probability tending to 1 and under an additional mild condition is sign consistent for nonzero elements we show that generalized thresholding covers as special cases hard and soft thresholding smoothly clipped absolute deviation and adaptive lasso and comp

verifiable multi secret sharing based on lfsr sequences in verifiable multi secret sharing schemes vmsss many secrets can be shared but only one share is kept by each user and this share is verifiable by others in this paper we propose two secure efficient and verifiable t n multi secret sharing schemes namely scheme i and scheme ii scheme i is based on the lagrange interpolating polynomial and the lfsr based public key cryptosystem the lagrange interpolating polynomial is used to split and reconstruct the secrets and the lfsr based public key cryptosystem is employed to verify the validity of the data scheme ii is designed according to the lfsr sequence and the lfsr based public key cryptosystem we compare our schemes with the state of the art in terms of attack resistance computation complexity and so on and conclude that our schemes have better performance and incur less computation overhead our schemes can effectively detect a variety of forgery or cheating actions to ensure that the recovery of the secrets is secure and creditable and the length of the private key is only one third of that of others for the same security level

computational experience with sequential and parallel preconditioned jacobi davidson for large sparse symmetric matrices the jacobi davidson jd algorithm was recently proposed for evaluating a number of the eigenvalues of a matrix jd goes beyond pure krylov space techniques it cleverly expands its search space by solving the so called correction equation thus in principle providing a more powerful method preconditioning the jacobi davidson correction equation is mandatory when large sparse matrices are analyzed we considered several preconditioners classical block jacobi and ic 0 together with approximate inverse ainv or fsai preconditioners the rationale for using approximate inverse preconditioners is their high parallelization potential combined with their efficiency in accelerating the iterative solution of the correction equation analysis was carried on the sequential performance of preconditioned jd for the spectral decomposition of large sparse matrices which originate in the numerical integration of partial differential equations arising in physical and engineering problems it was found that jd is highly sensitive to preconditioning and it can display an irregular convergence behavior we parallelized jd by data splitting techniques combining them with techniques to reduce the amount of communication data our own parallel preconditioned code was executed on a dedicated parallel machine and we present the results of our experiments our jd code provides an appreciable parallel degree of computation its performance was also compared with those of parpack and parallel dacg

a bernstein type inequality and moderate deviations for weakly dependent sequences in this paper we present a bernstein type tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that is not necessarily bounded the class considered includes geometrically and subgeometrically strongly mixing sequences the result is then used to derive asymptotic moderate deviation results applications are given for classes of markov chains iterated lipschitz models and functions of linear processes with absolutely regular innovations

meaningful secret sharing technique with authentication and remedy abilities lin and tasi yang et al and chang et al s meaningful secret sharing schemes provided authentication mechanisms but none included a remedy ability that would cause the secret image never to be completely obtained while some information of the stego images are losing or tampering with this paper proposes a meaningful secret sharing scheme which includes both authentication and remedy abilities that allow for detection of the corrupted area and use of the hidden information to repair the secret image with reasonable visual quality in comparison with previous schemes this approach results in superior visual qualities of the stego images by an average of more than 3db

preconditioning and two level multigrid methods of arbitrary degree of approximation let h be a mesh parameter corresponding to a finite element mesh for an elliptic problem we describe preconditioning methods for two level meshes which for most prob lems solved in practice behave as methods of optimal order in both storage and computa tional complexity namely per mesh point these numbers are bounded above by relatively small constants for all h ho where ho is small enough to cover all but excessively fine meshes we note that in practice multigrid methods are actually solved on a finite often even a fixed number of grid levels in which case also these methods are not asymptotically optimal as h 0 numerical tests indicate that the new methods are about as fast as the best implementations of multigrid methods applied on general problems variable coefficients general domains and boundary conditions for all but excessively fine meshes furthermore most of the latter methods have been implemented only for difference schemes of second order of accuracy whereas our methods are applicable to higher order approximations we claim that our scheme could be added fairly easily to many existing finite element codes 1 introduction consider the numerical solution of elliptic boundary value prob lems discretized by finite element methods we assume that the boundary is polygonal or consists of planes we note that in practical problems one often has a fine enough grid already after the definition of the boundary and the minimal number of vertices needed for a first coarse triangulation anyhow if not so in most cases one makes only a few steps of mesh refinement hence the power of multigrid methods their optimal order of computational complexity is most often not achieved fully because optimality requires a large number of recursively defined meshes for details see e g 4 and for further references see 7 hence one might as well consider other methods perhaps simpler and more effective on a fixed mesh but which are not asymptotically optimal here we shall describe a method which uses only a fixed mesh but for which one nevertheless achieves a low order of computational complexity and of seemingly optimal order except for from a practical viewpoint excessively small meshes to be more precise the computational cost per mesh point is bounded by clog n for n no where n is the number of mesh points no is large enough to cover most applications and c is small enough that the method is competitive with multigrid methods as is well known the latter need recursion and the usual smoothing followed by corrections of the solutions on the different mesh levels we claim that the new method is more suitable for implementation in existing finite element packages in fact most packages for the multigrid methods are only for second order difference methods

a comparison of lanczos and optimization methods in the partial solution of sparse symmetric eigenproblems in the present paper we analyse the computational performance of the lanczos method and a recent optimization technique for the calculation of the p p 40 leftmost eigenpairs of generalized symmetric eigenproblems arising from the finite element integration of elliptic pdes the accelerated conjugate gradient method is used to minimize successive rayleigh quotients defined in deflated subspaces of decreasing size the pointwise lanczos scheme is employed in combination with both the cholesky factorization of the stiffness matrix and the preconditioned conjugate gradient method for evaluating the recursive lanczos vectors the three algorithms are applied to five sample problems of varying size up to almost 5000 the numerical results show that the lanczos approach with cholesky triangularization is generally faster up to a factor of 5 for small to moderately large matrices while the optimization method is superior for large problems in terms of both storage requirement and cpu time in the large case the lanczos cholesky scheme may be very expensive to run even on modern quite powerful computers

nested iterations for symmetric eigenproblems the evaluation of the leftmost eigenspectrum of large sparse symmetric matrices is of great interest in many physical and engineering applications recently an efficient iterative method called dacg deflation accelerated conjugate gradient based on the conjugate gradient optimization of successive deflated rayleigh quotients was developed in the present paper the authors study the possibility of increasing the efficiency of this scheme by means of a nested iteration ni technique that acts on nested finite element grids and calculates an improved initial guess to be used by the dacg procedure the new ni dacg method is tested on two sample problems of large size which make use of nested regular and irregular finite element grids the results obtained in the calculation of the 40 leftmost eigenpairs for both problems show that the computational efficiency of dacg is increased by a factor of five for the regular mesh and two for the irregular one they also show the limitation of simple low order int