superior properties of the presb preconditioner for operators on two by two block form with square blocks matrices or operators in two by two block form with square blocks arise in numerous important applications such as in optimal control problems for pdes the problems are normally of very large scale so iterative solution methods must be used thereby the choice of an efficient and robust preconditioner is of crucial importance since some time a very efficient preconditioner the preconditioned square block presb method has been used by the authors and coauthors in various applications in particular for optimal control problems for pdes it has been shown to have excellent properties such as a very fast and robust rate of convergence that outperforms other methods in this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs under certain conditions the condition number of the preconditioned matrix is bounded by 2 or even smaller furthermore under certain assumptions the rate of convergence is superlinear

an analysis of the glvq algorithm generalized learning vector quantization glvq has been proposed in as a generalization of the simple competitive learning scl algorithm the main argument of glvq proposal is its superior insensitivity to the initial values of the weights code vectors in this paper we show that the distinctive characteristics of the definition of glvq disappear outside a small domain of applications glvq becomes identical to scl when either the number of code vectors grows or the size of the input space is large besides that the behavior of glvq is inconsistent for problems defined on very small scale input spaces the adaptation rules fluctuate between performing descent and ascent searches on the gradient of the distortion function

performance advantage of complex lms for controlling narrow band adaptive arrays in narrow band adaptive array applications the mean square convergence of the discrete time real least mean square lms algorithm is slowed by image frequency noises generated in the lms loops the complex lms algorithm proposed by widrow et al is shown to eliminate these noises yielding convergence of the mean squared error mse at slightly over twice the rate this paper includes a comprehensive analysis of the mse of adaptation for lms the analysis is based upon the method developed in the 1968 dissertation by k d senne and it represents the most complete treatment of the subject published to date

a novel kurtosis driven variable step size adaptive algorithm a new variable step size lms filter is introduced the time varying step size sequence is adjusted utilizing the kurtosis of the estimation error therefore reducing performance degradation due to the existence of strong noise the convergence properties of the algorithm are analyzed and an adaptive kurtosis estimator that takes into account noise statistics and optimally adapts itself is also presented simulation results confirm the algorithm s improved performance and flexibility

on the optimum gain parameter in lms adaptation in this correspondence the optimum selection of the adaptation parameter in lms adaptive estimation is discussed for a white data covarianee matrix it is shown via analysis and numerical evaluation that the optimum selection of is a complicated function of the number of filter taps the initial weight setting the wiener weights and the number of learning samples is not chosen in general to yield the most rapid transient response for most cases of interest a smaller value of will be selected for slower adaptation and smaller misadjustment error at the end of the learning phase

fuzzy clustering for data time arrays with inlier and outlier time trajectories in many knowledge discovery and data mining tasks fuzzy clustering is one of the most common tools for data partitioning in this paper dynamic fuzzy clustering models for classifying a set of multivariate time trajectories time series sequences are developed in particular by adopting an exploratory approach based on a geometric algebraic formulation of the data time array different kinds of dynamic fuzzy clustering models based on cross sectional and longitudinal aspects are suggested furthermore a modified version of the previous clustering models that can be seen as a generalization of these models is proposed by utilizing these models we can obtain beneficial effects in the clustering process when anomalous trajectories trajectories with anomalous positions and slopes are present in the dataset in fact the models are suitable for detecting structures of time trajectories with anomalous patterns that are not uniformly distributed over the structure s domains and are characterized by strange slopes in these models the disruptive effect of the anomalous trajectories is neutralized and smoothed and the information on the influence of individual time trajectories on the detected groups is given furthermore some remarks on dynamic three way extensions of a few robust fuzzy clustering models for two way data are suggested demonstrative examples are shown and a comparison assessment based on artificial multivariate time varying data is carried out

superlinearly convergent cg methods via equivalent preconditioning for nonsymmetric elliptic operators the convergence of the conjugate gradient method is studied for preconditioned linear operator equations with nonsymmetric normal operators with focus on elliptic convection diffusion operators in sobolev space superlinear convergence is proved first for equations whose preconditioned form is a compact perturbation of the identity in a hilbert space then the same convergence result is verified for elliptic convection diffusion equations using different preconditioning operators the convergence factor involves the eigenvalues of the corresponding operators for which an estimate is also given the above results enable us to verify the mesh independence of the superlinear convergence estimates for suitable finite element discretizations of the convection diffusion problems

adaptive lms l filters for noise suppression in images several adaptive least mean squares lms l filters both constrained and unconstrained ones are developed for noise suppression in images and compared in this paper first the location invariant lms l filter for a nonconstant signal corrupted by zero mean additive white noise is derived it is demonstrated that the location invariant lms l filter can be described in terms of the generalized linearly constrained adaptive processing structure proposed by griffiths and jim 1982 subsequently the normalized and the signed error lms l filters are studied a modified lms l filter with nonhomogeneous step sizes is also proposed in order to accelerate the rate of convergence of the adaptive l filter finally a signal dependent adaptive filter structure is developed to allow a separate treatment of the pixels that are close to the edges from the pixels that belong to homogeneous image regions

switching regression models and fuzzy clustering a family of objective functions called fuzzy c regression models which can be used too fit switching regression models to certain types of mixed data is presented minimization of particular objective functions in the family yields simultaneous estimates for the parameters of c regression models together with a fuzzy c partitioning of the data a general optimization approach for the family of objective functions is given and corresponding theoretical convergence results are discussed the approach is illustrated by two numerical examples that show how it can be used to fit mixed data to coupled linear and nonlinear models

general c means clustering model partitional clustering is an important part of cluster analysis based on various theories numerous clustering algorithms have been developed and new clustering algorithms continue to appear in the literature it is known that occam s razor plays a pivotal role in data based models and partitional clustering is categorized as a data based model however no relation had previously been discovered between occam s razor and partitional clustering as we discuss in this paper the three main contributions of this paper can be summarized as follows 1 according to a novel definition of the mean a unifying generative framework for partitional clustering algorithms called a general c means clustering model gcm is presented and studied and 2 based on the local optimality test of the gcm the connection between occam s razor and partitional clustering is established for the first time as its application a comprehensive review of the existing objective function based clustering algorithms is presented based on gcm 3 under a common assumption about partitional clustering a theoretical guide for devising and implementing clustering algorithm is discovered these conclusions are verified by numerical experimental results

alternating cluster estimation a new tool for clustering and function approximation many clustering models define good clusters as extrema of objective functions optimization of these models is often done using an alternating optimization ao algorithm driven by necessary conditions for local extrema we abandon the objective function model in favor of a generalized model called alternating cluster estimation ace ace uses an alternating iteration architecture but membership and prototype functions are selected directly by the user virtually every clustering model can be realized as an instance of ace out of a large variety of possible instances of non ao models we present two examples 1 an algorithm with a dynamically changing prototype function that extracts representative data and 2 a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions we illustrate these non ao instances on three problems a simple clustering of plane data where we show that creating an unmatched ace algorithm overcomes some problems of fuzzy c means fcm ao and possibilistic c means pcm ao b functional approximation by clustering on a simple artificial data set and c functional approximation on a 12 input 1 output real world data set ace models work pretty well in all three cases

the complex lms adaptive algorithm transient weight mean and covariance with applications to the ale the transient and steady state mean and covariance of the complex valued lms adaptive element weights are investigated when the inputs are samples from circularly normal processes it is shown that the data covariance diagonalizing matrix also diagonalizes the weight covariance matrix this result permits describing the complete transient behavior of the adaptive line enhancer ale weight covariance matrix in closed form for the case of multiple equal power narrow band statistically independent orthogonal rayleigh fading sinusoids in broad band noise based on these transient covariance results it is shown that for any stage of adaptation there exists an optimum ale gain constant that minimizes the excess mean squared prediction error this result is of particular significance when processing time limited data

generalized fuzzy c means clustering strategies using l sub p norm distances fuzzy c means fcm is a useful clustering technique modifications of fcm using l sub 1 norm distances increase robustness to outliers object and relational data versions of fcm clustering are defined for the more general case where the l sub p norm p spl ges 1 or semi norm 0 0 in order to facilitate the empirical examination of the object data models both object and relational approaches are included in a numerical study

efficient dynamic finite element method for 3d objects with uniform cross section an efficient implicit dynamic finite element method fem for elastic 3d objects with uniform cross sections was developed in this method the finite element mesh is generated in such a way that the object to be analysed is at first sliced into layers with the same thickness along its generatrix and then each layer is discretized into finite elements of the same pattern this way of discretization makes the mass viscosity and stiffness matrices into the repetitive block tridiagonal matrices the repetitive block tridiagonal matrix has the characteristic that the sequence of matrices which appears in the gaussian elimination for the repetitive block tridiagonal matrix is a rapid convergent sequence the process of the gaussian elimination can be terminated when the sequence converges the rest of the sequence is not necessary to be stored the present method can save the computational time and memory by utilising this characteristic of the repetitive block tridiagonal matrix a few examples of analyses including whole hopkinson bar analysis were performed to demonstrate the effectiveness of the present method the present method is applicable not only to the elasto dynamics but also to many other problems such as thermal problems electrical problems and plastic problems without geometric non linearity copyright 2005 john wiley sons ltd

a new extrapolation algorithm for band limited signals using the regularization method the ill posedness of the extrapolation problem in the presence of noise is considered a stable algorithm is constructed by solving a fredholm equation based on a regularization method the algorithm appears relatively robust since the noise eta sub delta t is taken as a function in l sup 2 t t t 0 such that the error energy integral mod eta sub delta t mod sup 2 dt

efficient subspace based algorithm for adaptive bearing estimation and tracking in some practical applications of array processing the directions of the incident signals should be estimated adaptively and or the time varying directions should be tracked promptly in this paper an adaptive bearing estimation and tracking abest algorithm is investigated for estimating and tracking the uncorrelated and correlated narrow band signals impinging on a uniform linear array ula based on the subspace based method without eigendecomposition sumwe where a linear operator is obtained from the array data to form a basis for the null space by exploiting the array geometry and its shift invariance property specifically the null space is estimated using the least mean square lms or normalized lms nlms algorithm and the directions are updated using the approximate newton method the transient analyses of the lms and nlms algorithms are studied where the weight i e the linear operator is in the form of a matrix and there is a correlation between the additive noise and input data that involve the instantaneous correlations of the received array data in the updating equation and the step size stability conditions are derived explicitly in addition the analytical expressions for the mean square error mse and mean square deviation msd learning curves of the lms algorithm are clarified the effectiveness of the abest algorithm is verified and the theoretical analyses are corroborated through numerical examples simulation results show that the abest algorithm is computationally simple and has good adaptation and tracking abilities

a methodology for constructing fuzzy algorithms for learning vector quantization this paper presents a general methodology for the development of fuzzy algorithms for learning vector quantization falvq the design of specific falvq algorithms according to existing approaches reduces to the selection of the membership function assigned to the weight vectors of an lvq competitive neural network which represent the prototypes the development of a broad variety of falvq algorithms can be accomplished by selecting the form of the interference function that determines the effect of the nonwinning prototypes on the attraction between the winning prototype and the input of the network the proposed methodology provides the basis for extending the existing falvq 1 falvq 2 and falvq 3 families of algorithms this paper also introduces two quantitative measures which establish a relationship between the formulation that led to falvq algorithms and the competition between the prototypes during the learning process the proposed algorithms and competition measures are tested and evaluated using the iris data set the significance of the proposed competition measure is illustrated using falvq algorithms to perform segmentation of magnetic resonance images of the brain

adaptive fuzzy c shells clustering and detection of ellipses several generalizations of the fuzzy c shells fcs algorithm are presented for characterizing and detecting clusters that are hyperellipsoidal shells an earlier generalization the adaptive fuzzy c shells afcs algorithm is examined in detail and is found to have global convergence problems when the shapes to be detected are partial new formulations are considered wherein the norm inducing matrix in the distance metric is unconstrained in contrast to the afcs algorithm the resulting algorithm called the afcs u algorithm performs better for partial shapes another formulation based on the second order quadrics equation is considered these algorithms can detect ellipses and circles in 2d data they are compared with the hough transform ht based methods for ellipse detection existing ht based methods for ellipse detection are evaluated and a multistage method incorporating the good features of all the methods is used for comparison numerical examples of real image data show that the afcs algorithm requires less memory than the ht based methods and it is at least an order of magnitude faster than the ht approach

fast direct solution of the helmholtz equation with a perfectly matched layer or an absorbing boundary condition we consider the efficient numerical solution of the helmholtz equation in a rectangular domain with a perfectly matched layer pml or an absorbing boundary condition abc standard bilinear trilinear finite element discretization on an orthogonal mesh leads to a separable system of linear equations for which we describe a cyclic reduction type fast direct solver we present numerical studies to estimate the reflection of waves caused by an absorbing boundary and a pml and we optimize certain parameters of the layer to minimize the reflection copyright 2003 john wiley sons ltd

mesh independent superlinear pcg rates via compact equivalent operators the subject of the paper is the mesh independent convergence of the preconditioned conjugate gradient pcg method for nonsymmetric elliptic problems the approach of equivalent operators is involved in which one uses the discretization of another suitable elliptic operator as preconditioning matrix by introducing the notion of compact equivalent operators it is proved that for a wide class of elliptic problems the superlinear convergence of the obtained pcg method is mesh independent under finite element discretizations that is the rate of superlinear convergence is given in the form of a sequence which is mesh independent and is determined only by the elliptic operators

an integrated approach to fuzzy learning vector quantization and fuzzy c means clustering derives an interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c means and fuzzy learning vector quantization these algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent a close relationship between the resulting algorithms and fuzzy c means is revealed by investigating the functionals involved it is also shown that the fuzzy c means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition

on the probability density function of the lms adaptive filter weights the joint probability density function of the weight vector in least mean square lms adaptation is studied for gaussian data models an exact expression is derived for the characteristic function of the weight vector at time n 1 conditioned on the weight vector at time n the conditional characteristic function is expanded in a taylor series and averaged over the unknown weight density to yield a first order partial differential difference equation in the unconditioned characteristic function of the weight vector the equation is approximately solved for small values of the adaption parameter and the weights are shown to be jointly gaussian with time varying mean vector and covariance matrix given as the solution to well known difference equations for the weight vector mean and covariance matrix the theoretical results are applied to analyzing the use of the weights in detection and time delay estimation simulations that support the theoretical results are also presented

finite time balanced truncation for linear systems via shifted legendre polynomials abstract in this paper we present a finite time model order reduction method for linear systems via shifted legendre polynomials the main idea of the approach is to use finite time empirical gramians which are constructed from impulse responses by solving block tridiagonal linear systems to generate approximate balanced system for the large scale system the balancing transformation is directly computed from the expansion coefficients of impulse responses in the space spanned by shifted legendre polynomials without individual reduction of the gramians and a separate eigenvector solve then the reduced order model is constructed by truncating the states corresponding to the small approximate hankel singular values hsvs the stability preservation of the reduced model is briefly discussed and in combination with the dominant subspace projection method we modify the reduction procedure to alleviate the shortcomings of the above method which may unexpectedly lead to unstable systems even though the original one is stable furthermore the properties of the resulting reduced models are considered finally numerical experiments are given to demonstrate the effectiveness of the proposed methods

microstatistic lms filtering adaptive microstatistic filters are developed for applications in which the second order statistics of the thresholded signals are not known or may be nonstationary a multilevel threshold decomposition such that real valued stochastic processes can be filtered is used and the computational complexity of the algorithm can be arbitrarily specified by the designer the adaptation uses the least mean squares error approach of the least mean square lms algorithm the convergence of the adaptive algorithm is proved due to the nonhomogeneous statistical characteristic of the threshold signals a different step size adaptation parameter can be assigned to each threshold level simple design guidelines are developed for finding the set of nonhomogeneous step sizes which in practice yield better convergence characteristics

a variable step size lms algorithm a least mean square lms adaptive filter with a variable step size is introduced the step size increases or decreases as the mean square error increases or decreases allowing the adaptive filter to track changes in the system as well as produce a small steady state error the convergence and steady state behavior of the algorithm are analyzed the results reduce to well known results when specialized to the constant step size case simulation results are presented to support the analysis and to compare the performance of the algorithm with the usual lms algorithm and another variable step size algorithm they show that its performance compares favorably with these existing algorithms

a parallel fictitious domain method for the three dimensional helmholtz equation the application of a fictitious domain domain embedding method to the three dimensional helmholtz equation with absorbing boundary conditions is considered the finite element discretization is performed by using locally fitted meshes and an algebraic fictitious domain method with a separable preconditioner is used in the iterative solution of the resultant linear systems such a method is based on embedding the original domain into a larger one with a simple geometry with this approach it is possible to realize the gmres iterations in a low dimensional subspace and use the partial solution method to solve the linear systems with the preconditioner an efficient parallel implementation of the iterative algorithm is introduced results of numerical experiments demonstrate good scalability properties on distributed memory parallel computers and the ability to solve high frequency acoustic scattering problems

a domain decomposition solver for acoustic scattering by elastic objects in layered media a finite element solution procedure is presented for accurately computing time harmonic acoustic scattering by elastic targets buried in sediment an improved finite element discretization based on trilinear basis functions leading to fourth order phase accuracy is described for sufficiently accurate discretizations 100 million to 1 billion unknowns are required the resulting systems of linear equations are solved iteratively using the gmres method with a domain decomposition preconditioner employing a fast direct solver due to the construction of the discretization and preconditioner iterations can be reduced onto a sparse subspace associated with the interfaces numerical experiments demonstrate capability to evaluate the scattered field with hundreds of wavelengths

a parallel fast direct solver for block tridiagonal systems with separable matrices of arbitrary dimension a parallel fast direct solution method for linear systems with separable block tridiagonal matrices is considered such systems appear for example when discretizing the poisson equation in a rectangular domain using the five point finite difference scheme or the piecewise linear finite elements on a triangulated possibly nonuniform rectangular mesh the method under consideration has the arithmetical complexity mathcal o n log n and it is closely related to the cyclic reduction method but instead of using the matrix polynomial factorization the so called partial solution technique is employed hence in this paper the method is called the partial solution variant of the cyclic reduction method pscr method the method is presented and analyzed in a general radix q framework and based on this analysis the radix 4 variant is chosen for parallel implementation using the mpi standard the generalization of the method to the case of arbitrary block dimension is described the numerical experiments show the sequential efficiency and numerical stability of the pscr method compared to the well known blktri implementation of the generalized cyclic reduction method the good scalability properties of the parallel pscr method are demonstrated in a distributed memory cray t3e 750 computer

stochastic gradient adaptation under general error criteria examines a family of adaptive filter algorithms of the form w sub k 1 w sub k spl mu f d sub k w sub k sup t x sub k x sub k in which f spl middot is a memoryless odd symmetric nonlinearity acting upon the error such algorithms are a generalization of the least mean square lms adaptive filtering algorithm for even symmetric error criteria for this algorithm family the authors derive general expressions for the mean and mean square convergence of the filter coefficients for both arbitrary stochastic input data and gaussian input data they then provide methods for optimizing the nonlinearity to minimize the algorithm misadjustment for a given convergence rate using the calculus of variations it is shown that the optimum nonlinearity to minimize misadjustment near convergence under slow adaptation conditions is independent of the statistics of the input data and can be expressed as p x p x where p x is the probability density function of the uncorrelated plant noise for faster adaptation under the white gaussian input and noise assumptions the nonlinearity is shown to be x 1 spl mu spl lambda x sup 2 spl sigma sub k sup 2 where spl lambda is the input signal power and spl sigma sub k sup 2 is the conditional error power thus the optimum stochastic gradient error criterion for gaussian noise is not mean square it is shown that the equations governing the convergence of the nonlinear algorithm are exactly those which describe the behavior of the optimum scalar data nonlinear adaptive algorithm for white gaussian input simulations verify the results for a host of noise interferences and indicate the improvement using non mean square error criteria

repairs to glvq a new family of competitive learning schemes first we identify an algorithmic defect of the generalized learning vector quantization glvq scheme that causes it to behave erratically for a certain scaling of the input data we show that glvq can behave incorrectly because its learning rates are reciprocally dependent on the sum of squares of distances from an input vector to the node weight vectors finally we propose a new family of models the glvq f family that remedies the problem we derive competitive learning algorithms for each member of the glvq f model and prove that they are invariant to all scalings of the data we show that glvq f offers a wide range of learning models since it reduces to lvq as its weighting exponent a parameter of the algorithm approaches one from above as this parameter increases glvq f then transitions to a model in which either all nodes may be excited according to their inverse distances from an input or in which the winner is excited while losers are penalized and as this parameter increases without limit glvq f updates all nodes equally we illustrate the failure of glvq and success of glvq f with the iris data

a mesh independent superlinear algorithm for some nonlinear nonsymmetric elliptic systems the numerical solution of nonlinear elliptic transport systems is considered an outer inner damped inexact newton plus pcg type iteration is proposed for the finite element discretization of the problem and mesh independent superlinear convergence is proved for both the outer and inner iterations numerical experiments are enclosed

exponential convergence through linear finite element discretization of stratified subdomains motivated by problems where the response is needed at select localized regions in a large computational domain we devise a novel finite element discretization that results in exponential convergence at pre selected points the key features of the discretization are a use of midpoint integration to evaluate the contribution matrices and b an unconventional mapping of the mesh into complex space named complex length finite element method cfem the technique is linked to pade approximants that provide exponential convergence of the dirichlet to neumann maps and thus the solution at specified points in the domain exponential convergence facilitates drastic reduction in the number of elements this combined with sparse computation associated with linear finite elements results in significant reduction in the computational cost the paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving laplace helmholtz and elastodynamics equations

competitive algorithms for the clustering of noisy data abstract in this paper we consider the issue of clustering when outliers exist the outlier set is defined as the complement of the data set following this concept a specially designed fuzzy membership weighted objective function is proposed and the corresponding optimal membership is derived unlike the membership of fuzzy c means the derived fuzzy membership does not reduce with the increase of the cluster number with the suitable redefinition of the distance metric we demonstrate that the objective function could be used to extract c spherical shells a hard clustering algorithm alleviating the prototype under utilization problem is also derived artificially generated data are used for comparisons

optimization of clustering criteria by reformulation various hard fuzzy and possibilistic clustering criteria objective functions are useful as bases for a variety of pattern recognition problems at present many of these criteria have customized individual optimization algorithms because of the specialized nature of these algorithms experimentation with new and existing criteria can be very inconvenient and costly in terms of development and implementation time this paper shows how to reformulate some clustering criteria so that specialized algorithms can be replaced by general optimization routines found in commercially available software we prove that the original and reformulated versions of each criterion are fully equivalent finally two numerical examples are given to illustrate reformulation

preconditioning operators and sobolevgradients for nonlinear elliptic problems a preconditioning framework is presented for the iterative solution of nonlinear elliptic problems based on the preconditioning operator approach various fixed preconditioning operators are used in the iteration which can be interpreted as a weighted sobolev gradient method

convergence analysis of lms filters with uncorrelated gaussian data statistical analysis of the least mean squares lms adaptive algorithm with uncorrelated gaussian data is presented exact analytical expressions for the steady state mean square error mse and the performance degradation due to weight vector misadjustment are derived necessary and sufficient conditions for the convergence of the algorithm to the optimal wiener solution within a finite variance are derived it is found that the adaptive coefficient which controls the rate of convergence of the algorithm must be restricted to an interval significantly smaller than the domain commonly stated in the literature the outcome of this paper therefore places fundamental limitations on the mse performance and rate of convergence of the lms adaptive scheme

sobolev gradient preconditioning for the electrostatic potential equation sobolev gradient type preconditioning is proposed for the numerical solution of the electrostatic potential equation a constructive representation of the gradients leads to efficient laplacian preconditioners in the iteration thanks to the available fast poisson solvers convergence is then verified for the corresponding sequence in sobolev space implying mesh independent convergence results for the discretized problems a particular study is devoted to the case of a ball due to the radial symmetry of this domain a direct realization without discretization is feasible the simplicity of the algorithm and the fast linear convergence are finally illustrated in a numerical test example

superlinearly convergent pcg algorithms for some nonsymmetric elliptic systems a preconditioned conjugate gradient method is applied to finite element discretizations of some nonsymmetric elliptic systems mesh independent superlinear convergence is proved which is an extension of a similar earlier result from a single equation to systems the proposed preconditioning method involves decoupled preconditioners which yields small and parallelizable auxiliary problems

an efficient algorithm for a model with a bidiagonal coefficient matrix bidiagonal matrices arise directly in the discretization of models using one step methods and indirectly through the factoring of tridiagonal systems with special characteristics we first look at the solution of a bidiagonal system and then relate it to an experimental method that has been used to determine the overall heat transfer coefficient in a concentric tube parallel flow heat exchanger the discretization of the governing partial differential equation with its boundary conditions gives rise to a near toeplitz bidiagonal system here we consider a method for the parallel processing of the resulting systems to provide measurements at fixed spatial and time increments

fuzzy j means a new heuristic for fuzzy clustering abstract a fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership in order to solve it we first propose a new local search heuristic called fuzzy j means where the neighbourhood is defined by all possible centroid to pattern relocations the integer solution is then moved to a continuous one by an alternate step i e by finding centroids and membership degrees for all patterns and clusters to alleviate the difficulty of being stuck in local minima of poor value this local search is then embedded into the variable neighbourhood search metaheuristic results on five standard test problems from the literature are reported and compared with those obtained with the well known fuzzy c means heuristic it appears that solutions of substantially better quality are obtained with the proposed methods than with this former one

complexity optimized data clustering by competitive neural networks data clustering is a complex optimization problem with applications ranging from vision and speech processing to data transmission and data storage in technical as well as in biological systems we discuss a clustering strategy that explicitly reflects the tradeoff between simplicity and precision of a data representation the resulting clustering algorithm jointly optimizes distortion errors and complexity costs a maximum entropy estimation of the clustering cost function yields an optimal number of clusters their positions and their cluster probabilities our approach establishes a unifying framework for different clustering methods like k means clustering fuzzy clustering entropy constrained vector quantization or topological feature maps and competitive neural networks

the aitken like acceleration of the schwarz method on nonuniform cartesian grids in this paper we present a family of domain decomposition based on an aitken like acceleration of the schwarz method seen as an iterative procedure with a linear rate of convergence this paper is a generalization of the method first introduced at the 12th international conference on domain decomposition that was restricted to regular cartesian grids the potential of this method to provide scalable parallel computing on a geographically broad grid of parallel computers was demonstrated for some linear and nonlinear elliptic problems discretized by finite differences on a cartesian mesh the main purpose of this paper is to present a generalization of the method to nonuniform cartesian meshes the salient feature of the method consists of accelerating the sequence of traces on the artificial interfaces generated by the schwarz procedure using a good approximation of the main eigenvectors of the trace transfer operator for linear separable elliptic operators our solver is a direct solver for nonlinear operators we use an approximation of the eigenvectors of the jacobian of the trace transfer operator the acceleration is then applied to the sequence generated by the schwarz algorithm applied directly to the nonlinear operator

numerical solution of the nonlinear helmholtz equation using nonorthogonal expansions in j comput phys 171 2001 632 677 we developed a fourth order numerical method for solving the nonlinear helmholtz equation which governs the propagation of time harmonic laser beams in media with a kerr type nonlinearity a key element of the algorithm was a new nonlocal two way artificial boundary condition abc set in the direction of beam propagation this two way abc provided for reflectionless propagation of the outgoing waves while also fully transmitting the given incoming beam at the boundaries of the computational domain altogether the algorithm of j comput phys 171 2001 632 677 has allowed for a direct simulation of nonlinear self focusing without neglecting nonparaxial effects and backscattering to the best of our knowledge this capacity has never been achieved previously in nonlinear optics in the current paper we propose an improved version of the algorithm the principal innovation is that instead of using the dirichlet boundary conditions in the direction orthogonal to that of the laser beam propagation we now introduce sommerfeld type local radiation boundary conditions which are constructed directly in the discrete framework numerically implementation of the sommerfeld conditions requires evaluation of eigenvalues and eigenvectors for a non hermitian matrix subsequently the separation of variables which is a key building block of the aforementioned nonlocal abc is implemented through an expansion with respect to the nonorthogonal basis of the eigenvectors numerical simulations show that the new algorithm offers a considerable improvement in its numerical performance as well as in the range of physical phenomena that it is capable of simulating

on the convergence behavior of the lms and the normalized lms algorithms it is shown that the normalized least mean square nlms algorithm is a potentially faster converging algorithm compared to the lms algorithm where the design of the adaptive filter is based on the usually quite limited knowledge of its input signal statistics a very simple model for the input signal vectors that greatly simplifies analysis of the convergence behavior of the lms and nlms algorithms is proposed using this model answers can be obtained to questions for which no answers are currently available using other perhaps more realistic models examples are given to illustrate that even quantitatively the answers obtained can be good approximations it is emphasized that the convergence of the nlms algorithm can be speeded up significantly by employing a time varying step size the optimal step size sequence can be specified a priori for the case of a white input signal with arbitrary distribution

the fuzzy c spherical shells algorithm a new approach the fuzzy c spherical shells fcss algorithm is specially designed to search for clusters that can be described by circular arcs or generally by shells of hyperspheres a new approach to the fcss algorithm is presented this algorithm is computationally and implementationally simpler than other clustering algorithms that have been suggested for this purpose an unsupervised algorithm which automatically finds the optimum number of clusters is not known it uses a cluster validity measure to identify good clusters merges all compatible clusters and eliminates spurious clusters to achieve the final results experimental results on several data sets are presented

acceleration of the schwarz method for elliptic problems in this paper we present a family of domain decomposition methods based on aitken like acceleration of the schwarz method which is an iterative procedure with linear rate of convergence this paper is a generalization of our method first introduced in 2000 that was restricted to cartesian grids we consider the finite volume fv approximation on general quadrangle meshes introduced by faille in 1992 we first present the so called aitken schwarz procedure for a linear differential operator this solver is a direct solver but its computational cost in the general case might be prohibitive second we introduce the steffensen schwarz variant which is an iterative domain decomposition solver that can be applied to linear and nonlinear problems we show that this iterative solver has reasonable numerical efficiency and can be applied successfully to several classes of linear and nonlinear elliptic problems however the salient feature of our method is that our algorithm has high tolerance for slow networks in the context of distributed parallel computing and is attractive to use with computer architectures for which performance is limited by the memory bandwidth rather than the flop performance of the cpu this is currently the case for most parallel computers using risc processor architecture such as beowulf systems

iterative solution methods for modeling multiphase flow in porous media fully implicitly we discuss several fully implicit techniques for solving the nonlinear algebraic system arising in an expanded mixed finite element or cell centered finite difference discretization of two and three phase porous media flow every outer nonlinear newton iteration requires solution of a nonsymmetric jacobian linear system two major types of preconditioners supercoarsening multigrid scmg and two stage are developed for the gmres iteration applied to the solution of the jacobian system the scmg reduces the three dimensional system to two dimensions using a vertical aggregation followed by a two dimensional multigrid the two stage preconditioners are based on decoupling the system into a pressure and concentration equations several pressure preconditioners of different types are described extensive numerical results are presented using the integrated parallel reservoir simulator ipars and indicate that these methods have low arithmetical complexity per iteration and good convergence rates