fuzzy s irresolute mappings in this paper the concepts of fuzzy s irresolute semi s irresolute and s precontinuous mappings in fuzzy topological spaces in sostak sense are introduced and studied some of their characteristic properties are considered also fuzzy s connectedness is introduced and studied with the help of r fuzzy strongly semi open sets

corrigendum finite element galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems math comp 52 1989 no 186 275 297 mr0962210 89k 65132

convergence rates in stochastic adaptive tracking abstract for stochastic control systems described by the armax model with unknown matrix coefficients the stochastic adaptive control is designed so that the parameter estimates converge to the true values with a rate of convergence o log n log log n c n a with a 0 c 1 and the tracking error tends to its minimum value at a speed of o n 1 2e with e 0

on characterizations of some covering properties in l fuzzy topological spaces in sostak s sense in this work various characterizations of some weaker and stronger forms of l fuzzy compactness are obtained in l fuzzy topological spaces in sostak s sense where l is a fuzzy lattice

a two grid finite difference scheme for nonlinear parabolic equations we present a two level finite difference scheme for the approximation of nonlinear parabolic equations discrete inner products and the lowest order raviart thomas approximating space are used in the expanded mixed method in order to develop the finite difference scheme analysis of the scheme is given assuming an implicit time discretization in this two level scheme the full nonlinear problem is solved on a coarse grid of size h the nonlinearities are expanded about the coarse grid solution and an appropriate interpolation operator is used to provide values of the coarse grid solution on the fine grid in terms of superconvergent node points the resulting linear but nonsymmetric system is solved on a fine grid of size h some a priori error estimates are derived which show that the discrete l infty l2 and l2 h1 errors are o h 2 h 4 d 2 delta t where d geq 1 is the spatial dimension

fuzzy smooth preproximity spaces abstract the concept of a fuzzy smooth preproximity space is introduced and studied also some particular constructions of fuzzy smooth preproximity are given a natural link is established between this concept and the concept of fuzzy pretopological spaces and fuzzy preuniform spaces

k fan s theorem in fuzzifying topology in this paper we offer an application of ukasiewicz logic in topology by ukasiewicz logic we introduce a new definition of connectivity in fuzzifying topology and prove k fan s theorem of connectivity in fuzzifying topology

finite element galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems abstract this paper establishes some refined estimates for the approximation of the eigenvalues and eigenvectors of selfadjoint eigenvalue problems by finite element or more generally galerkin methods suppose lambda is an eigenvalue of multiplicity q of a selfajoint problem and let m lambda denote the space of eigenvectors corresponding to lambda keywords hilbert space

three topological structures of smooth topological spaces abstract various concepts related to smooth topological spaces have been introduced and relations among them studied by several authors 2 6 in this paper we introduce the notions of smooth quasi smooth and weak smooth structure showing that various properties of a smooth topological space can be expressed in terms of these structures in particular the definitions and the results of 2 6 may be expressed in terms of the smooth and quasi smooth structures then we will set out the fundamental concepts of these three structures and the relations between them

adaptive control via consistent estimation for deterministic systems abstract for multidimensional discrete time deterministic systems the optimal adaptive control has been derived by use of a probabilistic method so that when the reference signal is an arbitrary bounded random sequence the tracking error and the estimation error based on a projection algorithm go to zero with a near exponential convergence rate for this the basic step is to prove the consistency of estimates when the condition number of the matrix consisting of regressors diverges to infinity in other words when the persistent excitation condition is not satisfied

iterative two grid methods for semilinear elliptic equations abstract we design and analyze a new finite element discretization technique based on iterative two grid methods for semilinear elliptic partial differential equations pdes we first present an iterative two grid method that just applies the classical two grid for semilinear elliptic pdes in a successive fashion namely to solve a semilinear problem on the coarse space and then to solve a symmetric positive definite problem on the fine space thus we only need to deal with semilinear problems in the coarse space in the first algorithm secondly we replace the semilinear term by using the corresponding first order taylor expansion in the second iterative two grid we provide the error estimates for the second iterative algorithm and present numerical experiments to show the efficiency of our methods

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

consistent order estimation for linear stochastic feedback control systems carma model abstract a new criterion cic is introduced to estimate orders p0 q0 r0 of the linear stochastic feedback control system with correlated noise described by a carma model it is proved that the estimate is strongly consistent when the upper bounds for p0 q0 and r0 are available but neither the stability condition nor the ergodicity of the input and output are imposed on the system

an iv based criterion for model order selection a new criterion for estimating the order of an arx model is presented the proposed criterion is defined for replacing the ls loss function in traditional criteria for model order selection by an estimate of the noiseless value of the ls loss function the estimate is computed by means of the instrumental variable technique the consistency of the estimate is proved for a relatively general condition upon the noise the transfer function of the noise may be time varying and of infinite order the relation with the rank test is shown simulation results are included for illustration

convergence in i fuzzy topological spaces the purpose of this work is to combine the fuzzy q neighborhood system of fuzzy points introduced by sostak with the convergence structures of lee et al using the l filter approach of gahler and eklund

on fuzzy convergence abstract we propose and examine two concepts of convergence for sequences of elements of a set x with respect to a fuzzy topology on x such concepts are obtained by interpreting in a multivalued logic two different first order formulas expressing the classical convergence

acceleration of a two grid method for eigenvalue problems this paper provides a new two grid discretization method for solving partial differential equation or integral equation eigenvalue problems in 2001 xu and zhou introduced a scheme that reduces the solution of an eigenvalue problem on a finite element grid to that of one single linear problem on the same grid together with a similar eigenvalue problem on a much coarser grid by solving a slightly different linear problem on the fine grid the new algorithm in this paper significantly improves the theoretical error estimate which allows a much coarser mesh to achieve the same asymptotic convergence rate numerical examples are also provided to demonstrate the efficiency of the new method

on several types of degree of fuzzy compactness abstract sostak 1985 defined a fuzzy topology on a set x as a fuzzy subset of the family i x of fuzzy subsets of x satisfying some axioms the concept of the degree of compactness of a fuzzy set was first introduced by sostak 1985 in this paper we discuss the degrees of almost compactness near compactness countable compactness light compactness and strong compactness of a fuzzy set also we investigate the behavior of the degrees of compactness under several types of fuzzy continuous functions

on smooth topological spaces ii separation axioms in the present paper we introduce the notions of smooth separation axioms in several ways and investigate some of their properties and the relations between them in the general framework of smooth topological spaces

a two grid discretization method for decoupling systems of partial differential equations in this paper we propose a two grid finite element method for solving coupled partial differential equations e g the schrodinger type equation with this method the solution of the coupled equations on a fine grid is reduced to the solution of coupled equations on a much coarser grid together with the solution of decoupled equations on the fine grid it is shown both theoretically and numerically that the resulting solution still achieves asymptotically optimal accuracy

almost compactness and near compactness in smooth topological spaces abstract this paper discusses almost compactness in fuzzy topology and we introduce near compactness for fuzzy topological spaces we give some characterizations of almost compactness in terms of regular open or regular closed fuzzy sets we show that the weakly continuous image of a compact fuzzy topological space is almost compact and that the fuzzy strongly continuous image of an almost compact fuzzy topological space is compact moreover nearly compact fuzzy topological spaces are defined and we characterize near compactness we show that the almost continuous and almost open image of a nearly compact space is nearly compact

identification and adaptive control for systems with unknown orders delay and coefficients an analysis that gives recursive estimates for time delay system orders and coefficients of single input single output linear discrete time deterministic and stochastic systems with uncorrelated noise is presented it is assumed that a lower bound for the time delay and upper bounds for system order are known the optimal adaptive control is designed for both tracking and linear quadratic regulation when the system parameters including time delay orders and coefficients are unknown the rates of convergence are derived the coefficient estimates to their true values and the loss functions to their minima

investigations on two kinds of two grid mixed finite element methods for the elliptic eigenvalue problem two kinds of two grid new mixed finite element schemes for the elliptic eigenvalue problem based on less regularity of flux are considered in the new mixed variational formulation the flux belongs to the square integrable space instead of the classical h div and the choices of finite element pairs become simple and easy the two grid methods consist of solving a small elliptic eigenvalue problem on the coarse mesh and then solving a linear algebraic system on the fine mesh which can still maintain asymptotically optimal accuracy finally the performance of two kinds of two grid schemes are compared in efficiency and precision aspects by a series of numerical experiments numerical results show that the accelerated two grid method is a viable choice for the lowest order approximations of the elliptic eigenvalue problem

on several types of compactness in smooth topological spaces abstract the smooth closure and smooth interior of a fuzzy set w r t a smooth topology were defined by gayyar et al 1994 and some relations between a few types of compactness were established in the presence of strong restrictions in this paper by constructing new definitions of smooth closure and smooth interior which have more desirable properties than those of gayyar et al 1994 we prove that several hypothesis in the results of gayyar et al 1994 can be weakened and show that the relations which hold between various types of compactness in fuzzy topological spaces in chang s sense cfts for short di concilio and gerla 1984 haydar es 1987 can be extended to smooth topological spaces

a two grid discretization scheme for eigenvalue problems a two grid discretization scheme is proposed for solving eigenvalue problems including both partial differential equations and integral equations with this new scheme the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid and the resulting solution still maintains an asymptotically optimal accuracy

error estimates on a new nonlinear galerkin method based on two grid finite elements a new nonlinear galerkin method based on finite element discretization is presented in this paper for semilinear parabolic equations the new scheme is based on two different finite element spaces defined respectively on one coarse grid with grid size h and one fine grid with grid size h ll h nonlinearity and time dependence are both treated on the coarse space and only a fixed stationary equation needs to be solved on the fine space at each time with linear finite element discretizations it is proved that the difference between the new nonlinear galerkin solution and the standard galerkin solution in h 1 omega norm is of the order of h 3

similarity of fuzzy sets application to r n as a substratum in this paper we apply to real spaces the concept of similarity relation on fuzzy sets the underlying topological space is said to play the role of an expression substratum these relations can be used to define relative positions of expression of fuzzy sets groups of homeomorphisms of a topological space are important they are representative of the symmetries of the space we give very simple examples to clarify these rather abstract notions

consistent estimation of the order of stochastic control systems a consistent estimate of the order of feedback control systems with unknown matrix coefficients estimated by the least squares method is derived by minimizing a modified version of the bayesian information criterion

a higher order correlation method for model order and parameter estimation abstract the identification of linear systems with unknown orders is considered the observed input and output signals are corrupted by the gaussian random coloured noise or other non gaussian random coloured noise with zero third order statistics it is also assumed that a priori statistical information of these two kinds of noise input and output is unknown the input signal to the identified system is a zero mean stationary non gaussian random sequence by applying a proposed estimation algorithm the system orders and parameters can be estimated accurately finally two simulation results are presented to illustrate the proposed algorithm

the multilevel mixed finite element discretizations based on local defect correction for the stokes eigenvalue problem abstract based on the work of xu and zhou 2000 this paper combines mixed finite element method and the local defect correction technique to establish new local and parallel multilevel discretization schemes for the stokes eigenvalue problem theoretical analysis and numerical experiments show that the computational approach proposed in this paper is simple and easy to carry out in parallel and can be used to solve singular stokes eigenvalue problem efficiently this paper also discusses local error estimates of mixed finite element approximations it is a new feature here that the estimates apply to the local domains containing corner points

two level additive preconditioners for edge element discretizations of time harmonic maxwell equations two level additive preconditioners are presented for edge element discretizations of time harmonic maxwell equations the key is to construct a special coarse mesh space which adds the kernel of the curl operator in a fine space to a coarse mesh space to solve the original problem and then uses the fine mesh space to solve the h curl elliptic problem it is shown that the generalized minimal residual gmres method applied to the preconditioned system converges uniformly provided that the coarsest mesh size is reasonably small but independent of the fine mesh size and the parameter for the coarse mesh space solver is sufficiently large numerical experiments show the efficiency of the proposed approach

smooth topological spaces abstract in 1986 badard introduced the concept of a smooth topological space in this paper we give some links between smooth topological spaces and the corresponding results in chang s fuzzy topological spaces the concepts of subspace continuity and compactness are studied

optimal adaptive control and consistent parameter estimates for armax model withquadratic cost we consider the multidimensional armax model a z y n b z u n c z w n with loss function j u mathop overline lim limits n to infty frac 1 n sum limits i 1 n left y i tau q 1 y i u i tau q 2 u i right where the coefficients in the matrix polynomials a z b z and c z are unknown conditions used here are 1 stability of a z and full rank of a p 2 strictly positive realness of c z frac 1 2 i and 3 controllability and observability of a matrix triple consisting of coefficients in a z b z and q 1 on the basis of the estimates given by the stochastic gradient algorithm for unknown parameters an adaptive control law is recursively defined it is proved that the parameter estimates are strongly consistent and the quadratic loss function reaches its minimum this paper also includes some general theorems on parameter estimation on which the results about adaptive control are essentially based

minimum variance control of discrete time multivariable armax systems we consider multivariable armax stochastic systems these systems can incorporate the following complicating features general delay structures nonminimum phase transfer functions different dimensions for input and output vectors we obtain the control laws which minimize the variance of the output process while maintaining system stability

a two level method with backtracking for the navier stokes equations we consider a two level method for resolving the nonlinearity in finite element approximations of the equilibrium navier stokes equations the method yields l2 and h1 optimal velocity approximations and an l2 optimal pressure approximation the two level method involves solving one small nonlinear coarse mesh system one oseen problem hence linear with positive definite symmetric part on the fine mesh and one linear correction problem on the coarse mesh the algorithm we study produces an approximate solution with the optimal asymptotic in h accuracy for any fixed reynolds number we do not consider the behavior of the error for fixed h as re rightarrow infty i e for flows in transition to turbulence

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

convergence rate of least squares identification and adaptive control for stochastic systems the strong consistency and the convergence rate of least squares identification for the multidimensional armax model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied the parameter identification results are applied to adaptive control systems with a quadratic loss function the rate of convergence of the loss function to its minimum is also obtained

a multi level correction scheme for eigenvalue problems abstractin this paper a new type of multi level correction scheme is proposed forsolving eigenvalue problems by nite element method with this new scheme the accuracy of eigenpair approximations can be improved after each correc tion step which only needs to solve a source problem on ner nite elementspace and an eigenvalue problem on the coarsest nite element space thiscorrection scheme can improve the e ciency of solving eigenvalue problemsby nite element method keywords eigenvalue problem multi level correction scheme nite ele ment method multi space multi grid ams subject classi cations 65n30 65b99 65n25 65l15 1 introduction the purpose of this paper is to propose a new type of multi level correction schemebased on nite element discretization to solve eigenvalue problems the two gridmethod for solving eigenvalue problems has been proposed and analyzed by xu andzhou in 21 the idea of the two grid comes from 19 20 for nonsymmetric orinde nite problems and nonlinear elliptic equations since then there have existedmany numerical methods for solving eigenvalue problems based on the idea of two grid method 1 6 17

two grid methods for maxwell eigenvalue problems two new two grid algorithms are proposed for solving the maxwell eigenvalue problem the new methods are based on the two grid methodology recently proposed by xu and zhou math comp 70 2001 pp 17 25 and further developed by hu and cheng math comp 80 2011 pp 1287 1301 for elliptic eigenvalue problems the new two grid schemes reduce the solution of the maxwell eigenvalue problem on a fine grid to one linear indefinite maxwell equation on the same fine grid and an original eigenvalue problem on a much coarser grid the new schemes therefore save total computational cost the error estimates reveals that the two grid methods maintain asymptotically optimal accuracy and the numerical experiments presented confirm the theoretical results

a two grid discretization scheme for semilinear elliptic eigenvalue problems we present a two grid finite element discretization scheme with a two loop continuation algorithm for tracing solution branches of semilinear elliptic eigenvalue problems first we use the predictor corrector continuation method to compute an approximating point for the solution curve on the coarse grid then we use this approximating point as a predicted point for the solution curve on the fine grid in the corrector step we solve the first and the second order approximations of the nonlinear pde to obtain corrections for the state variable on the fine grid and the coarse grid respectively the continuation parameter is updated by computing the rayleigh quotient on the fine space to guarantee the approximating point we just obtained lies on the solution curve we perform newton s method we repeat the process described above until the solution curve on the fine space is obtained we show how the singular points such as folds and bifurcation points can be well approximated comprehensive numerical experiments show that the two grid finite element discretization scheme with a two loop continuation algorithm is efficient and robust for solving second order semilinear elliptic eigenvalue problems

two grid discretizations and a local finite element scheme for a non selfadjoint stekloff eigenvalue problem abstract in this paper for a new stekloff eigenvalue problem which is non selfadjoint and not h 1 elliptic we establish and analyze two kinds of two grid discretization scheme and a local finite element scheme we present the error estimates of approximations of two grid discretizations we also prove a local error estimate which is suitable for the case that the local refined region contains singular points lying on the boundary of domain numerical experiments are reported finally to show the efficiency of our schemes

brief on line order estimation and parameter identification for linear stochastic feedback control systems carma model this paper presents a new recursive estimate method for orders and coefficients of linear stochastic feedback control systems carma model under the assumption that the upper bounds of system orders are known the strong consistency of the estimates for orders and coefficients is proved and the convergence rate of coefficient estimates to their true values is also obtained the estimate algorithm is applied to adaptive tracking of the systems with unknown orders and unknown coefficients the resulting closed loop systems are then globally stable and the tracking sample mean square error is minimized as well simultaneously the estimates of the adaptive tracking for orders and coefficients are also strongly consistent the simulation results given here show that the new developed algorithms of both system identification and adaptive tracking are effective

expressions on a fuzzy pretopological substratum in this paper we define similarity relations on fuzzy sets of a pretopological space the underlying pretopological space will be said to play the role of an expression substratum we compare these relations with pretopological homeomorphisms these relations can be used to define relative positions of expression of fuzzy sets groups of homeomorphisms of a pretopological space are key concepts they are representative of some symmetries of the space we give very simple examples to clarify these rather abstract notions

a novel two grid method for semilinear elliptic equations a new finite element discretization technique based on two coarse and fine subspaces is presented for a semilinear elliptic boundary value problem the solution of a nonlinear system on the fine space is reduced to the solution of two small one linear and one nonlinear systems on the coarse space and a linear system on the fine space it is shown both theoretically and numerically that the coarse space can be extremely coarse and still achieve asymptotically optimal approximation as a result the numerical solution of such a nonlinear equation is not significantly more expensive than the solution of one single linearized equation

recursive estimation of mixed autoregressive moving average order summary the order p q of an autoregressive moving average sequence y t may be estimated by minimizing a criterion log 2 p q log t t with respect to p and q where 2 is the maximum likelihood estimate of the variance of the innovations t it is suggested that instead a2 be estimated from a series of regressions of y t on y t 1 y t 2 y t p 5 t 1 t q where the t are obtained by fitting a long autoregression to the data it is shown how the sequence of regressions may for p q be economically recursively calculated by embedding them in a sequence of bivariate autoregressions asymptotic properties of the procedure are established under very general conditions

on fuzzy bitopological spaces abstract in this paper we have used the fuzzy topologies 1 and 2 to generate a family s which is a supra fuzzy topology on x using the family s we introduce and study the concepts of separation axioms continuity resp openness closedness of a mapping and compactness for a fuzzy bitopological space x 1 2 our definitions preserve much of the correspondence between concepts of fuzzy bitopological spaces and the associated fuzzy topological spaces we then investigate the relationship between these concepts and their correspondence with the fuzzy bitopological spaces kandil and el shafee 1991

one to one correspondence between fuzzifying topologies and fuzzy preorders this paper is devoted to the discussion of the relationship between fuzzifying topologies and fuzzy relations a saturated fuzzifying topology can be generated by a reflexive fuzzy relation and conversely a fuzzy preorder can be generated by a fuzzifying topology in fact there exists a one to one correspondence between the set of all saturated fuzzifying topologies and that of all fuzzy preorders

two level picard and modified picard methods for the navier stokes equations abstract iterative methods of picard type for the navier stokes equations are known to converge only for quite small reynolds numbers however we study methods involving just one such iteration at general reynolds numbers for the initial approximation a coarse mesh of width h0 is used the corrected approximation is computed by just one picard or modified picard step on a fine mesh of width h1 for example h1 may be of order o h 0 2 when linear velocity elements are used the resulting method requires the solution of a small system of nonlinear equations on the coarse mesh and only one larger linear system on the fine mesh this two level picard method is proven to converge for fixed reynolds number as h 0 further the fine mesh solution satisfies a quasi optimal error bound the error constants grow as re as for the usual finite element method one very heuristic explanation why one step of the divergent picard method might work when beginning with a coarse mesh approximation is that the terms neglected involve lower order derivatives thus they are approximated with higher accuracy on the coarse mesh this is linked with a smoothing property of the fine mesh step

local and parallel finite element algorithms based on two grid discretizations a number of new local and parallel discretization and adaptive nite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems these algorithms are motivated by the observation that for a solution to some elliptic problems low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a ne grid by some local and parallel procedure the theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for nite element solutions on general shape regular grids some numerical experiments are also presented to support the theory in this paper we will propose some new parallel techniques for nite element computation these techniques are based on our understanding of the local and global properties of a nite element solution to some elliptic problems simply speaking the global behavior of a solution is mostly governed by low frequency components while the local behavior is mostly governed by high frequency compo nents the main idea of our new algorithms is to use a coarse grid to approximate the low frequencies and then to use a ne grid to correct the resulted residue which contains mostly high frequencies by some local parallel procedures let us now give a somewhat more detailed but informal and hopefully infor mative description of the main ideas and results in this paper we consider the following very simple model problem posed on a convex polygonal domain r 2 u bru f in

long time behavior of the two grid finite element method for fully discrete semilinear evolution equations with positive memory abstract based on two grid discretizations two fully discrete finite element algorithms for semilinear parabolic integro differential equations with positive memory are proposed with the backward euler scheme for the temporal discretization the basic idea of the space two grid finite element algorithms is to approximate the semilinear equations on a coarse space grid and to solve the linearized equations on a finer space grid at each time step to further decreases the amount of computational work a space time two grid algorithm based on a coarse space grid with large time stepsize t and a finer space grid with small time stepsize t for the evolutional equations is proposed in this paper the sharp long time stability and error estimates for the standard finite element method the space two grid finite element method and the space time two grid finite element method are derived it is showed that the two grid algorithms long time stability and error estimates are similar to those of the direct resolution of the semilinear problem on a fine grid

the adaptive finite element method based on multi scale discretizations for eigenvalue problems in this paper adaptive finite element methods for differential operator eigenvalue problems are discussed for multi scale discretization schemes based on rayleigh quotient iteration see scheme 3 in y yang h bi a two grid discretization scheme based on shifted inverse power method siam j numer anal 49 2011 1602 1624 a reliable and efficient a posteriori error indicator is given in addition a new adaptive algorithm based on the multi scale discretizations is proposed and we apply the algorithm to the schrodinger equation for hydrogen atoms the algorithm is performed under the package of chen and satisfactory numerical results are obtained

neighborhood structures of smooth topological spaces abstract smooth topological spaces and their fundamental concepts have been discussed in the literature 2 4 7 in this paper we present the notions of base and two sorts of neighborhood structure of smooth topological spaces and give some of their properties which are results in 3 extended to smooth topological spaces

shifted inverse iteration based multigrid methods for the quad curl eigenvalue problem abstract this paper is devoted to multgrid methods for solving the quad curl eigenvalue problem the multgrid methods based on the rayleigh quotient iteration and the inverse iteration with fixed shift are proposed we prove the error estimates for both methods numerical experiments confirm our theoretical analysis and validate the efficiency of both methods

on statistical properties of a test for model structure selection using the extended instrumental variable approach a procedure for structural estimation using the extended instrumental variable technique is presented the statistical distribution of the test quantity is obtained in the white noise case a criterion is defined by introducing a penalty term on the decreasing rate with the number of parameters of the proposed test quantity the consistency of the estimate is proven monte carlo simulations are included