the decomposition method applied to systems of fredholm integral equations of the second kind in this paper the adomian decomposition method is applied to solve systems of linear and nonlinear fredholm integral equations of the second kind convergence of the method is proved and some examples are presented to illustrate the method

a comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations in this paper we conduct a comparative study between the modified decomposition method and two of the traditional methods for analytic treatment of nonlinear integral and integro differential equations the proper implementation of the modified method can dramatically minimize the size of work if compared to existing traditional techniques the analysis is accompanied by examples that demonstrate the comparison and show the pertinent features of the modified technique

robust stabilization of linear multivariable systems relations to approximation the stabilization of a linear system modelled as g a where g is a known rational transfer function and a is a perturbation satisfying w a2 g1 or equivalently there does not exist g with fewer poles in c than g such that w1 g g w2 a simple characterization of all robustly stabilizing controllers is then derived and state space formulae for maximally robust controllers are given finally reduced order controllers are considered

fredholm volterra integral equation with singular kernel in this paper under certain conditions a series in the legendre polynomials form is used to obtain the solution of fredholm volterra integral equation of the second kind in l 2 1 1 xc 0 t t the uniqueness of the solution is considered the kernel of fredholm integral term is established in a logarithmic form in position while the kernel of volterra integral term is a positive continuous function in time and belongs to the class c 0 t t the solution by series leads us to obtain an infinite system of linear algebraic equations where the convergence of this system is studied in the end of this paper the fredholm volterra integral equation of the first kind is established and its solution is discussed

numerical solution of volterra fredholm integral equations using the collocation method based on a special form of the muntz legendre polynomials abstract this paper presents a computational technique based on a special family of the muntz legendre polynomials to solve a class of volterra fredholm integral equations the relationship between the jacobi polynomials and muntz legendre polynomials in a particular state are expressed the proposed method reduces the integral equation into algebraic equations via the chebyshev gauss lobatto points so that the system matrix coefficients are obtained by the least squares approximation method the useful properties of the jacobi polynomials are exploited to analyze the approximation error the performance and accuracy of our method are examined with some illustrative examples

spillover stabilization in finite dimensional control and observer design for dissipative evolution equations we consider the problem of global stabilization of a semilinear dissipative evolution equation by finite dimensional control with finite dimensional outputs coupling between the system modes occurs directly through the nonlinearity and also through the control influence functions similar modal coupling occurs in the infinite dimensional error dynamics through the nonlinearity and measurements for both the control and observer designs rather than decompose the original system into fourier modes we consider lyapunov functions based on the infinite dimensional dynamics of the state and error systems respectively the inner product terms of the lyapunov derivative are decomposed into fourier modes upper bounds on the terms representing control and observation spillover are obtained linear quadratic regulator lqr designs are used to stabilize the state and error systems with these upper bounds relations between system and lqr design parameters are given to ensure global stability of the state and error dynamics with robustness with respect to control and observation spillover respectively it is shown that the control and observer designs can be combined to yield a globally stabilizing compensator the control and observer designs are numerically demonstrated on the problem of controlling stall in a model of axial compressors

compressive sensing on manifolds using a nonparametric mixture of factor analyzers algorithm and performance bounds nonparametric bayesian methods are employed to constitute a mixture of low rank gaussians for data x rn that are of high dimension n but are constrained to reside in a low dimensional subregion of rn the number of mixture components and their rank are inferred automatically from the data the resulting algorithm can be used for learning manifolds and for reconstructing signals from manifolds based on compressive sensing cs projection measurements the statistical cs inversion is performed analytically we derive the required number of cs random measurements needed for successful reconstruction based on easily computed quantities drawing on block sparsity properties the proposed methodology is validated on several synthetic and real datasets

on local intrinsic dimension estimation and its applications in this paper we present multiple novel applications for local intrinsic dimension estimation there has been much work done on estimating the global dimension of a data set typically for the purposes of dimensionality reduction we show that by estimating dimension locally we are able to extend the uses of dimension estimation to many applications which are not possible with global dimension estimation additionally we show that local dimension estimation can be used to obtain a better global dimension estimate alleviating the negative bias that is common to all known dimension estimation algorithms we illustrate local dimension estimation s uses towards additional applications such as learning on statistical manifolds network anomaly detection clustering and image segmentation

the semiparametric bernstein von mises theorem in a smooth semiparametric estimation problem the marginal posterior for the parameter of interest is expected to be asymptotically normal and satisfy frequentist criteria of optimality if the model is endowed with a suitable prior it is shown that under certain straightforward and interpretable conditions the assertion of le cam s acclaimed but strictly parametric bernstein von mises theorem univ california publ statist 1 1953 277 329 holds in the semiparametric situation as well as a consequence bayesian point estimators achieve efficiency for example in the sense of hajek s convolution theorem z wahrsch verw gebiete 14 1970 323 330 the model is required to satisfy differentiability and metric entropy conditions while the nuisance prior must assign nonzero mass to certain kullback leibler neighborhoods ghosal ghosh and van der vaart ann statist 28 2000 500 531 in addition the marginal posterior is required to converge at parametric rate which appears to be the most stringent condition in examples the results are applied to estimation of the linear coefficient in partial linear regression with a gaussian prior on a smoothness class for the nuisance

galerkin approximation in modeling of controlled distributed parameter flexible systems abstract numerical study of control problems for linear distributed parameter flexible mechanical systems requires finite dimensional modeling of the system we study the conditions for h covergence of the transfer functions of finite dimensional galerkin approximations this convergence ensures that control problems can be solved by using a galerkin model a stabilization problem for the angular position of a bernoulli euler beam illustrates the theoretical consideration the beam with an inertial drive represents a flexible manipulator link

robust stabilization of infinite dimensional systems by finite dimensional controllers abstract the problem of robustly stabilizing an infinite dimensional system with transfer function g subject to an additive perturbation is considered it is assumed that g b 0 of systems introduced by callier and desoer 3 the perturbation satisfies w1 w2 c now write w1gw2 g1 g1 where g1 is rational and totally unstable and g2 is stable generalizing the finite dimensional results of glover 12 this family of perturbed systems is shown to be stabilizable if and only if min g 1 the smallest hankel singular value of g 1 a finite dimensional stabilizing controller is then given by k w 2 k 1 i g 2 k 1 1 w 1 where 2 is a rational approximation of g2 such that g 2 g 2 min g 1 and k1 robustly stabilizes g1 to margin the feedback system g k will then be stable if w1 w2

the theoretical foundation of the adomian method abstract in this paper we work out the theoretical basis of the adomian method this powerful method that g adomian has developed in the beginning of the 1980 s supplies analytical approximations to the solution of many kinds of equations thanks to our decomposition theory we justify the practical method and we generalize the convergence results obtained by y cherruault afterward we explain how to solve rigorously equations with linear nonlinear or composed operator and also equations with several terms or with a second member

adaptive nonparametric regression with the k nearest neighbour fused lasso the fused lasso also known as total variation denoising is a locally adaptive function estimator over a regular grid of design points in this article we extend the fused lasso to settings in which the points do not occur on a regular grid leading to a method for nonparametric regression this approach which we call the formula see text nearest neighbours fused lasso involves computing the formula see text nearest neighbours graph of the design points and then performing the fused lasso over this graph we show that this procedure has a number of theoretical advantages over competing methods specifically it inherits local adaptivity from its connection to the fused lasso and it inherits manifold adaptivity from its connection to the formula see text nearest neighbours approach in a simulation study and an application to flu data we show that excellent results are obtained for completeness we also study an estimator that makes use of an formula see text graph rather than a formula see text nearest neighbours graph and contrast it with the formula see text nearest neighbours fused lasso

an efficient method for the numerical solution of hammerstein mixed vf integral equations on 2d irregular domains abstract in this work we adapt the implicity linear collocation method for solving nonlinear two dimensional mixed volterra fredholm integral equations of hammerstein type by using imq rbfs on a non rectangular domain the proposed method is mesh free and it is independent of the geometry of domain convergence analysis of the proposed method together with some benchmark examples is provided which support its reliability and numerical stability

numerical solution of the neural field equation in the two dimensional case we are concerned with the numerical solution of a class of integro differential equations known as neural field equations which describe the large scale dynamics of spatially structured networks of neurons these equations have many applications in neuroscience and robotics we describe a numerical method for the approximation of solutions in the two dimensional case including a space dependent delay in the integrand function compared with known algorithms for this type of equation we propose a scheme with higher accuracy in the time discretization since computational efficiency is a key issue in this type of calculation we use a new method for reducing the complexity of the algorithm the convergence issues are discussed in detail and a number of numerical examples are presented which illustrate the performance of the method

iterative method and convergence analysis for a kind of mixed nonlinear volterra fredholm integral equation in this paper the iterative method is presented for numerically solving the nonlinear volterra fredholm integral equation first considering some conditions on k i and l i i 1 2 of the integral equation then we define the equidistance collocation points and the integral part of equation is discretized by newton cotes integration formula finally the approximate solutions of integral equation are obtain by iterative method the convergence analysis of the integral equation is given some numerical examples are given to illustrate the accuracy and dependability of the method

anisotropic function estimation using multi bandwidth gaussian processes in nonparametric regression problems involving multiple predictors there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones our focus is on defining a bayesian procedure that leads to the minimax optimal rate of posterior contraction up to a log factor adapting to the unknown dimension and anisotropic smoothness of the true surface we propose such an approach based on a gaussian process prior with dimension specific scalings which are assigned carefully chosen hyperpriors we additionally show that using a homogenous gaussian process with a single bandwidth leads to a sub optimal rate in anisotropic cases

discrete time waveform relaxation volterra runge kutta methods convergence analysis the discrete time relaxation methods based on volterra runge kutta methods for solving large system of second kind volterra integral equations are proposed convergence of the discrete time iteration process with particular attention to parallel methods is investigated

a modified homotopy perturbation method for solving the nonlinear mixed volterra fredholm integral equation the purpose of this paper is to obtain the approximation solution of the strongly nonlinear mixed volterra fredholm integral equation vfie for some strongly nonlinear problems the traditional homotopy perturbation method is divergent so we propose a modified homotopy perturbation method which is still convergent when solving the strongly nonlinear mixed vfie by means of this method an algorithm is successfully established for solving the strongly nonlinear mixed vfie and the convergence of the algorithm is proved strictly finally several examples are presented to illustrate the application of the algorithm

numerical solution of volterra fredholm integral equations using parameterized pseudospectral integration matrices the main purpose of this work is to provide parameterized pseudospectral integration matrices ppims for solving volterra fredholm integral equations we present an exact efficient and stable approach for computing ppims furthermore we provide a rigorous convergence analysis for the pseudospectral scheme with collocation at the jacobi type points in both l and l 2 spaces numerical results confirm the spectral rate of convergence for the proposed pseudospectral schemes

compressed gaussian process for manifold regression nonparametric regression for large numbers of features p is an increasingly important problem if the sample size n is massive a common strategy is to partition the feature space and then separately apply simple models to each partition set this is not ideal when n is modest relative to p and we propose an alternative approach relying on random compression of the feature vector combined with gaussian process regression the proposed approach is particularly motivated by the setting in which the response is conditionally independent of the features given the projection to a low dimensional manifold conditionally on the random compression matrix and a smoothness parameter the posterior distribution for the regression surface and posterior predictive distributions are available analytically running the analysis in parallel for many random compression matrices and smoothness parameters model averaging is used to combine the results the algorithm can be implemented rapidly even in very large p and moderately large n nonparametric regression has strong theoretical justification and is found to yield state of the art predictive performance

a new computational method for volterra fredholm integral equations abstract the main purpose of this article is to demonstrate the use of the adomian decomposition method for mixed nonlinear volterra fredholm integral equations a bound is also given for the adomian decomposition series finally numerical examples are presented to illustrate the implementation and accuracy of the decomposition method

asymptotic expansion for the trapezoidal nystro m method of linear volterra fredholm equations abstract integral equations of mixed volterra fredholm type arise in various physical and biological problems in the present paper we study the particular trapezoidal nystrom method and we obtain the asymptotic error expansion for the trapezoidal nystrom solution of the linear volterra fredholm equation so the richardson extrapolation can be applied this will increase the accuracy of the numerical solution greatly some numerical examples are given to illustrate this theory

numerical solution of a class of mixed two dimensional nonlinear volterra fredholm integral equations using multiquadric radial basis functions an efficient numerical method is proposed for solving the mixed nonlinear volterra fredholm two dimensional integral equations ies using two dimensional radial basis functions rbfs this method is based on interpolation by radial basis functions including multiquadrics mqs using legendre gauss lobatto nodes and weights also a theorem is proved for convergence analysis some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

continuous time collocation methods for volterra fredholm integral equations integral equations of mixed volterra fredholm type arise in various physical and biological problems in the present paper we study continuous time collocation time discretization and their global and discrete convergence properties

numerical solution of volterra fredholm integral equations via modification of hat functions abstract in this paper a new numerical approach is developed for solving linear and nonlinear volterra fredholm integral equations the fundamental structure of the presented method is based on the modification of hat functions the properties of modification of hat functions mhfs are first presented after implementation of our scheme the solution of the main problem would be transformed into the solution of a system of linear or nonlinear algebraic equations also an error analysis is provided under several mild conditions in addition examples are presented to illustrate the pertinent features of the method and the results are discussed

a hybrid legendre block pulse method for mixed volterra fredholm integral equations abstract mixed volterra fredholm integral equations can arise from mathematical modelling of the spatio temporal development of an epidemic in this paper a hybrid legendre block pulse method is used to provide solutions to a general integral equation of this type the main idea of this approach is to reduce a volterra fredholm integral equation to a system of algebraic equations an order convergence analysis is provided the accuracy of the proposed method is then confirmed by solving some problems the first being a nonlinear epidemic problem

on a method for solving an integral equation in the displacement contact problem in this paper the solution in a series form of the integral equation of the mixed type in the space l w xc 0 t is obtained where w x y z

numerical solution for three dimensional nonlinear mixed volterra fredholm integral equations via three dimensional block pulse functions we are concerned here with a three dimensional nonlinear mixed volterra fredholm integral equations of the second kind which include many key integral that appear in the theory of nonlinear parabolic boundary value problems the existence of a unique solution will be proved a new numerical method for solving these type of equations will be presented the method is based upon three dimensional block pulse functions approximation in addition convergence analysis of the method is discussed illustrative examples are included to demonstrate the validity and applicability of the technique

an approximate method for solving a class of weakly singular volterra integro differential equations abstract in this paper we present a new approach to resolve linear and nonlinear weakly singular volterra integro differential equations of first or second order by first removing the singularity using taylor s approximation and then transforming the given first or second order integro differential equations into an ordinary differential equation such as the well known legendre degenerate hypergeometric euler or abel equations in such a manner that adomian s asymptotic decomposition method can be applied which permits convenient resolution of these equations some examples with closed form solutions are studied in detail to further illustrate the proposed technique and the results obtained demonstrate this approach is indeed practical and efficient

solving second kind integral equations by galerkin methods with hybrid legendre and block pulse functions in this paper we use a combination of legendre 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

asymptotic error expansion for the nystro m method for a nonlinear volterra fredholm integral equation in this paper we study the numerical solution of general nonlinear mixed volterra fredholm integral equations by the trapezoidal nystrom method it focuses on the derivation and analysis of asymptotic error expansion of the nystrom solution providing the basis for richardson s extrapolation this will greatly increase the accuracy of the numerical solution some numerical results are given to illustrate this theory

convergence of adomian s method applied to differential equations this paper deals with a new proof of convergence of adomian s method applied to differential equations we also give new formulae and properties and we suggest a simple computational form for adomian s polynomials

solution of physical problems by decomposition recent generalizations are discussed and results are presented for the theory and applications of the decomposition method application is made to the duffing equation with an error of 0 0001 in only four terms and less than 10 16 in thirteen terms of the decomposition series application is also made to a dissipative wave equation a matrix riccati equation and advection diffusion nonlinear transport

thomas bayes walk on manifolds convergence of the bayes posterior measure is considered in canonical statistical settings where observations sit on a geometrical object such as a compact manifold or more generally on a compact metric space verifying some conditions a natural geometric prior based on randomly rescaled solutions of the heat equation is considered upper and lower bound posterior contraction rates are derived

two scale boolean galerkin discretizations for fredholm integral equations of the second kind in this paper some two scale boolean galerkin discretizations are proposed and analyzed for a class of fredholm integral equations of the second kind in multidimensions it is shown by both theory and numerics that this type of multiscale discretization algorithm not only significantly reduces the number of degrees of freedom but also produces very accurate approximations

iterated collocation methods and their discretizations for volterra integral equations it is known that the numerical solution of volterra integral equations of the second kind by polynomial spline collocation at the gauss legendre points does not lead to local superconvergence at the knots of the approximating function in the present paper we show that iterated collocation approximation restores optimal local superconvergence at the knots but does not yield global superconvergence on the entire interval of integration in contrast to fredholm integral equations with smooth kernels we also analyze the discretized versions obtained by suitable numerical quadrature of the collocation and iterated collocation methods

representation of exact solution for the nonlinear volterra fredholm integral equations abstract in this paper the representation of the exact solution for the nonlinear volterra fredholm integral equations will be obtained in the reproducing kernel space the exact solution is given by the form of series its approximate solution is obtained by truncating the series and a new numerical approximate method is obtained the error of the approximate solution is monotone deceasing in the sense of w 2 1 a b the intrinsic merit of the method given in the paper lies in its speedy convergence in addition it must be pointed out that additional conditions as linearization or unjustified assumptions are not required for nonlinear cases

hybrid legendre block pulse functions for the numerical solutions of system of nonlinear fredholm hammerstein integral equations in this paper the numerical technique based on hybrid legendre block pulse function has been developed to approximate the solution of system of nonlinear fredholm hammerstein integral equations these functions are formed by the hybridization of legendre polynomials and block pulse functions these functions are orthonormal and have compact support on 0 1 the proposed method reduces the system of integral equations to a system of nonlinear algebraic equations that can be solved easily by any usual numerical method the numerical results obtained by the presented method have been compared with those obtained by legendre wavelet method lwm numerical examples are presented to illustrate the accuracy of the method

bayesian manifold regression there is increasing interest in the problem of nonparametric regression with high dimensional predictors when the number of predictors d is large one encounters a daunting problem in attempting to estimate a d dimensional surface based on limited data fortunately in many applications the support of the data is concentrated on a d dimensional subspace with d ll d manifold learning attempts to estimate this subspace our focus is on developing computationally tractable and theoretically supported bayesian nonparametric regression methods in this context when the subspace corresponds to a locally euclidean compact riemannian manifold we show that a gaussian process regression approach can be applied that leads to the minimax optimal adaptive rate in estimating the regression function under some conditions the proposed model bypasses the need to estimate the manifold and can be implemented using standard algorithms for posterior computation in gaussian processes finite sample performance is illustrated in a data analysis example

applications and numerical analysis of partial differential volterra equations a brief survey this article contains a concise survey of the numerical analysis of volterra equations and leads up to some recent results on a posteriori error estimation for finite element approximations

information rates of nonparametric gaussian process methods we consider the quality of learning a response function by a nonparametric bayesian approach using a gaussian process gp prior on the response function we upper bound the quadratic risk of the learning procedure which in turn is an upper bound on the kullback leibler information between the predictive and true data distribution the upper bound is expressed in small ball probabilities and concentration measures of the gp prior we illustrate the computation of the upper bound for the matern and squared exponential kernels for these priors the risk and hence the information criterion tends to zero for all continuous response functions however the rate at which this happens depends on the combination of true response function and gaussian prior and is expressible in a certain concentration function in particular the results show that for good performance the regularity of the gp prior should match the regularity of the unknown response function

a reliable treatment for mixed volterra fredholm integral equations the main goal of this paper is to demonstrate the use of the modified decomposition method for mixed nonlinear volterra fredholm integral equations the modified method combined with the noise terms phenomena may provide the exact solution by using two iterations only two numerical illustrations are given to show the pertinent features of the technique

on the numerical solution of linear and nonlinear volterra integral and integro differential equations abstract sinc bases are developed to approximate the solutions of linear and nonlinear volterra integral and integro differential equations properties of these sinc bases and some operational matrices are first presented these properties are then used to reduce the integral and integro differential equations to systems of linear or nonlinear algebraic equations numerical examples illustrate the pertinent features of the method and its applicability to a large variety of problems the examples include convolution type singular as well as singularly perturbed problems

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

he s variational iteration method for solving nonlinear mixed volterra fredholm integral equations in this paper he s variational iteration method is used to give the approximate solution of nonlinear mixed volterra fredholm integral equations the method constructs a convergent sequence of functions which approximates the exact solution with few iterations numerical results and a comparison with the exact solution are given which reveal its efficiency

estimating the intrinsic dimension of data with a fractal based method in this paper the problem of estimating the intrinsic dimension of a data set is investigated a fractal based approach using the grassberger procaccia algorithm is proposed since the grassberger procaccia algorithm 1983 performs badly on sets of high dimensionality an empirical procedure that improves the original algorithm has been developed the procedure has been tested on data sets of known dimensionality and on time series of santa fe competition

on the numerical solution of nonlinear volterra fredholm integral equations by collocation methods particular cases of nonlinear mixed volterra fredholm integral equations of the second kind arise in the mathematical modeling of the spatio temporal development of an epidemic this paper is concerned with the numerical solution of general integral equations of this type by continuous time and discrete time spline collocation methods its focus is on the derivation and analysis of methods of high order of convergence

an efficient numerical approximation for the linear class of mixed integral equations in this paper an efficient numerical and analytical method for the linear class of mixed integral equations is presented the bivariate chebyshev collocation method for solving the linear volterra fredholm integral equations of the second kind is examined theoretically and numerically its focus lies mainly on the truncated bivariate chebyshev expansion and chebyshev collocation points

a relationship between sensitivity and stability of multivariable feedback systems both comparison sensitivity and robust stability analysis attempt to extend concepts which are well understood in scalar feedback systems to multivariable control system design although the two bodies of work have developed about a decade apart the basic philosophies are similar both attempt to maintain a system property sensitivity reduction versus stability in the presence of plant modeling errors this paper demonstrates how the similarity in philosophy translates into a similarity in results and interpretations

numerical solution of the mixed volterra fredholm integro differential multi term equations of fractional order abstract this paper aims to introduce two effective numerical approaches for solving the mixed volterra fredholm integro differential equation of fractional order and multi order with initial values despite the fact that the second approach transfers the integro differential equations into a system of algebraic equations through the usage of operational matrices these problems can be transferred to a system of algebraic equations by expanding the solution s highest order derivative through the block pulse functions bpfs this is done by using the generalized operational matrices of bpfs for differentiation along with the fractional calculus properties in the first scheme in which convergence of the solution obtained has been shown in the following the accuracy and applicability of two proposed approaches will be compared by some relevant numerical examples for which the exact solution is known

numerical solution of volterra fredholm integral equations using legendre collocation method a numerical method for solving the volterra fredholm integral equations is presented the method is based upon shifted legendre polynomials approximation the properties of shifted legendre polynomials are first presented these properties together with the shifted gauss legendre nodes are then utilized to reduce the volterra fredholm integral equations to the solution of a matrix equation an estimation of the error is given illustrative examples are included to demonstrate the validity and applicability of the technique

a computational method for system of volterra fredholm integral equations adomian decomposition method has been applied for solving volterra fredholm equation by maleknejad k maleknejad m hadizadeh a new computational method for volterra fredholm integral equations comput math appl 37 1999 1 8 in 1999 in this paper we solve the system of nonlinear volterra fredholm integral equations by adomian decomposition method some examples are solved to illustrate the accuracy of this method

bayesian monotone regression using gaussian process projection shape constrained regression analysis has applications in dose response modelling environmental risk assessment disease screening and many other areas incorporating the shape constraints can improve estimation efficiency and avoid implausible results we propose a novel method focusing on monotone curve and surface estimation which uses gaussian process projections our inference is based on projecting posterior samples from the gaussian process we develop theory on continuity of the projection and rates of contraction our approach leads to simple computation with good performance in finite samples the proposed projection method can also be applied to other constrained function estimation problems including those in multivariate settings

numerical solutions of integrodifferential systems by hybrid of general block pulse functions and the second chebyshev polynomials in this paper integrodifferential systems are converted into a system of algebraic equations by hybrid of general block pulse functions and the second chebyshev polynomials the approximate solutions of integrodifferential systems are derived the numerical examples illustrate that the algorithm is valid

convergence rates of posterior distributions we consider the asymptotic behavior of posterior distributions and bayes estimators for infinite dimensional statistical models we give general results on the rate of convergence of the posterior measure these are applied to several examples including priors on finite sieves log spline models dirichlet processes and interval censoring

posteriori error estimates for the nonlinear volterra fredholm integral equations abstract we study the numerical approximation of the nonlinear volterra fredholm integral equations by combining the discrete time collocation method 1 and the new formulation of kumar and sloan 2 which converts an integral equation of the conventional hammerstein form into a conductive form for approximation by a collocation method the intrinsic merit of this alternative formulation lies in its computational savings posteriori error estimates of the method for two typical nonlinearities i e algebraic and exponential nonlinearity are obtained some remarks on the generalization of the method to higher dimensional cases are offered and finally some numerical examples are given

a fast iterative method for discretized volterra fredholm integral equations solving the nonlinear systems arising in the discretization in space and time of volterra fredholm integral equations by newton iteration leads to dense linear systems whose dimension depends on the spatial mesh the solution of these linear systems can hence be very costly here we try to reduce these costs by solving each newton iteration by a non stationary inner iteration process each inner iteration again requires the solution of a linear system however since the splitting matrix is diagonal now the components or sets of components can be computed in parallel the performance of this iteration method is illustrated by means of a few significative examples

a note on spillover and robustness for flexible systems many stabilizer designs for infinite dimensional systems for example flexible systems are based on a finite dimensional approximation of the original system it is shown that whether or not this approach leads to a stabilizing controller for the infinite dimensional system is in fact a robustness question lack of robustness can lead to a spillover effect from the neglected dynamics which destroys the stability this phenomenon is illustrated by an example of a damped flexible system

numerical solution of nonlinear volterrafredholmhammerstein integral equations in two dimensional spaces based on block pulse functions in this paper the numerical technique based on block pulse functions bpfs has been developed to approximate the solutions of nonlinear volterrafredholmhammerstein integral equations in two dimensional spaces these functions are orthogonal and have compact support on 0 1 the proposed method reduces the integral equations to a system of nonlinear algebraic equations that can be easily solved by any numerical method also the convergence of the proposed approach is discussed furthermore in order to show the accuracy and reliability of the above mentioned algorithm the new approach is verified through some numerical examples a numerical technique based on block pulse functions is proposed two dimensional nonlinear volterrafredholmhammerstein integral equations are firstly numerically solved the proposed method is to transform the volterrafredholm integral equations into a system of algebraic equations the main characteristic behind the algorithm is operator theory