pseudospectral solution of the two dimensional navier stokes equations in a disk an efficient and accurate algorithm for solving the two dimensional 2d incompressible navier stokes equations on a disk with no slip boundary conditions is described the vorticity stream function formulation of these equations is used and spatially the vorticity and stream functions are expressed as fourier chebyshev expansions the poisson and helmholtz equations which arise from the implicit explicit time marching scheme are solved as banded systems using a postconditioned spectral tau method the polar coordinate singularity is handled by expanding fields radially over the entire diameter using a parity modified chebyshev series and building partial regularity into the vorticity the no slip boundary condition is enforced by transferring one of the two boundary conditions imposed on the stream function onto the vorticity via a solvability constraint significant gains in run times were realized by parallelizing the code in message passage interface mpi

recursive estimation of autoregressions this paper is concerned with the recursive estimation of autoregressive models in particular the realtime determination of the order of such a specification a model selection criterion based on the minimum description length principle due to rissanen is discussed and strong consistency in the stationary situation is shown alternative criteria are also considered and modifications required to introduce forgetting when the procedures are implemented in the non stationary case are presented some simulation evidence on the performance of the criteria when applied to stationary and non stationary processes is given

goal oriented adaptivity of mixed gmsfem for flows in heterogeneous media abstract we present an adaptive goal oriented framework with the mixed generalized multiscale finite element method gmsfem to numerically solve the flow problem in heterogeneous media in this paper three different error indicators are considered two goal oriented and one a standard adaptive method for the global error each is used to approximate a number of quantities of interest given by interior edge fluxes in a high contrast field following the setting of mixed gmsfem on each coarse neighborhood of the computational domain the local error indicator introduced here is computed by the product of the residual norms of the primal and dual variational equations over coarse neighborhoods numerical results demonstrate the efficiency of this goal oriented method in comparison to a multiscale implementation of the dual weighted residual method and a standard adaptive method

an efficient spectral method for ordinary differential equations with rational function coefficients the authors present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients they employ expansions in terms of a large class of orthogonal polynomial families including all the classical orthogonal polynomials these families obey a simple 3 term recurrence relation for differentiation which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse the inverse is an integration operator for the family and it is simply the tridiagonal coefficient matrix for the recurrence since in these families convolution operators i e matrix representations of multiplication by a function are banded for polynomials the authors are able to obtain a banded representation for linear differential operators with rational coefficients this leads to a method of solution of initial or boundary value problems that besides having an operation count that scales linearly with the order of truncation n is computationally well conditioned among the applications considered is the use of rational maps for the resolution of sharp interior layers 19 refs 2 figs 3 tabs

identification and adaptive control of markov chains consider a countable state controlled markov chain whose transition probability is specified up to an unknown parameter alpha taking values in a compact metric space a to each alpha is associated a prespecified stationary control law zeta alpha the adaptive control law selects at each time t the control action zeta alpha t x t where x t is the state and alpha t is the maximum likelihood estimate of alpha the asymptotic behavior of this control scheme is investigated for the cases when the true parameter value alpha 0 does or does not belong to a and for the case when zeta is chosen to minimize an average cost criterion the analysis uses an appropriate extension of the notions of recurrence to nonstationary markov chains

a robust model reference adaptive control without strictly positive real condition this paper considers the model reference adaptive control problem for the system 1 with unmodelled dynamics m n dominated by a small constant k multiplied by a quantity dependent on the input output and noise using bounded external excitation and randomly varying truncation techniques we give design method of a model reference adaptive controller which is similar to that in meyn and brown 1992 it is shown that the closed loop system is globally stable the estimation error for parameter contained in the modelled part is of order k and the closed loop system under the model reference adaptive control law is suboptimal in the sense of lim sup 1 n n a m z y i 1 b m z z i c m z w i 1 2 h o k 2 n 2 b 1 2 while the spr condition usually used in other papers is replaced by a stability condition

brief papers linear identification of arma processes a new method for estimating the parameters of an arma process is presented the method consists of three linear least squares estimations in the first an autoregressive model is fitted to the observation sequence yielding an estimate of the values of the driving white noise sequence linear least squares is then used to fit an arma model to the observation and estimated white noise sequences this model is used to filter the observation and estimated white noise sequences finally an arma model is fitted to the filtered sequences it is shown that the resultant estimator is p consistent the asymptotic bias tends to zero as the degree p of the autoregressive model tends to infinity and is p efficient the asymptotic efficiency approaches the theoretical maximum as p tends to infinity

a robust stochastic adaptive controller the adaptive tracking problem is considered for discrete time stochastic systems consisting of a modeled part being a stable armax process and unmodeled dynamics dominated by a small constant epsilon multiplied by a quantity independent of epsilon but tending to infinity as the past input output and noise grow the adaptive control law proposed is switched at stopping times and is disturbed by a sequence of random vectors bounded by an arbitrary small but fixed constant sigma it is shown that the closed loop system is globally stable the estimation errors for parameters contained in the modeled part of the order epsilon and the tracking error differs from the minimum tracking error for systems without unmodeled dynamics by value of o epsilon sup 2 o sigma sup 2

discrete time stochastic adaptive control this paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems it is shown that with probability one the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control thus asymptotically the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known

multiscale modeling using goal oriented adaptivity and numerical homogenization part ii algorithms for the moore penrose pseudoinverse this paper is the second in this series to develop a numerical homogenization method for heterogeneous media and integrate it with goal oriented finite element mesh adaptivity the first paper developed the mathematical formulation of local homogenization this was done using an appropriate averaging of the moore penrose pseudoinverse of the element stiffness matrix we also presented numerical verification of this approach and other numerical results in the current paper we present four algorithms to compute the moore penrose pseudoinverse that also exploit the sparsity these are based on qr factorization a priori knowledge of the null space a regularization based characterization and lastly an iterative algorithm based on proper splittings of matrices we analyze some of these algorithms in detail for homogenizing hexahedral elements in the molecular base model of densification in step and flash imprint lithography

robust methods for recursive autoregressive moving average estimation in this paper we consider the problem of fitting recursively in time an autoregressive moving average arma model to time series data where outliers may be present although many recursive estimation procedures are available for fitting arma models they are based on the recursive least squares algorithm which is known to be badly affected by additive outliers to minimize the impact of these sort of outliers we investigate some robustified versions of the recursive maximum likelihood procedure the problem of incorporating robust scale recursion is discussed and asymptotic properties of the procedures are examined

goal oriented adaptivity using unconventional error representations for the multidimensional helmholtz equation in goal oriented adaptivity goa the error in the quantity of interest qoi is represented using the error functions of the direct and adjoint problems this error representation is subsequently bounded above by element wise error indicators that are used to drive optimal refinements in this work we propose to replace in the error representation the adjoint problem by an alternative operator the main advantage of the proposed approach is that when judiciously selecting such alternative operator the corresponding upper bound of the error representation becomes sharper leading to a more efficient goa while the method can be applied to a variety of problems we focus here on two and threedimensional 2d and 3d helmholtz problems we show via extensive numerical experimentation that the upper bounds provided by the alternative error representations are sharper than the classical ones and lead to a more robust p adaptive process we also provide guidelines for finding operators delivering sharp error representation upper bounds we further extend the results to a convectiondominated diffusion problem as well as to problems with discontinuous material coefficients finally we consider a sonic logging while drilling lwd problem to illustrate the applicability of the proposed method

adaptive control with recursive identification for stochastic linear systems this paper presents a stochastic adaptive control algorithm which is shown to possess the following properties when applied to a possibly unstable inverse stable linear stochastic system with unknown parameters whenever that system satisfies a certain positive real condition on its moving average noise dynamics 1 the adaptive control part of the algorithm stabilizes and asymptotically optimizes the behavior of the system in the sense that the limit of the sample mean square variation of the output around a given demand level equals that of a minimum variance control strategy implemented with known parameters this optimal behavior is subject to an offset 2where 2is the variance of a dither signal added to the control action in order to produce a continually disturbed control for mu 2 0 it is shown that the input output process satisfies a persistent excitation property and hence subject to a simple identifiability condition the next property holds 2 the observed input and output of the controlled system may be taken as inputs to an approximate maximum likelihood algorithm aml which generates strongly consistent estimates of the system s parameters results are presented for the scalar and multivariable cases

strongly consistent coefficient estimate for errors in variables models for the single input single output siso errors in variables system it is assumed that the system input is an arma process and that the driven noise of the system input and the observation noise are jointly gaussian the two dimensional observation made on system input and output is represented as a two dimensional 2d arma system of minimum phase driven by a sequence of 2d i i d gaussian random vectors innovation representation it is shown that the resulting arma system is identifiable i e its coefficients are uniquely defined under reasonable conditions recursive algorithms are proposed for estimating coefficients of the arma representation including those contained in the original siso system the estimates are proved to be convergent to the true values with probability one and the convergence rate is derived as well the theoretical results are justified by numerical simulation

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

robust estimation without positive real condition the strictly positive real spr condition on the noise model is necessary for a discrete time linear stochastic control system with unmodeled dynamics even so for a time invariant armax system in the past robust analysis of parameter estimation however this condition is hardly satisfied for a high order and or multidimensional system with correlated noise the main work in this paper is to show that for robust parameter estimation and adaptive tracking as well as closed loop system stabilization the spr condition is replaced by a stable matrix polynomial the main method is to design a two step recursive least squares algorithm with or without a weighted factor and with a fixed lag regressive vector and to define an adaptive control with bounded external excitation and with randomly varying truncation

a multi time scale generalization of recursive identification algorithm for armax systems recently chen 2010 presented a new approach to recursive identification for armax systems which is a three stage recursive scheme and assumes independent and identically distributed input signals here we observe that unless the time scale of the algorithm at one stage is reasonably faster than those at the previous stages convergence to the true value may not take place to remedy this issue this note proposes a multi time scale modification of the algorithm in 5 such that convergence is achieved in addition the new scheme handles a wider class of input signals so that the input can be designed for some purpose the advantage of the multi time scale algorithm is verified with numerical examples

the aastrom wittenmark self tuning regulator revisited and els based adaptive trackers although considerable progress has been made in stochastic adaptive control the problem concerning the convergence of the original self tuning regulator proposed by k j aastrom and b wittenmark 1973 is still open since it is attractive in theory and important in applications this problem is examined and a rigorous proof of its stability and optimality is given related problems such as convergence of the extended least squares els based adaptive tracker are also considered

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

multidomain spectral method for the helically reduced wave equation we consider the 2 1 and 3 1 scalar wave equations reduced via a helical killing field respectively referred to as the 2 dimensional and 3 dimensional helically reduced wave equation hrwe the hrwe serves as the fundamental model for the mixed type pde arising in the periodic standing wave psw approximation to binary inspiral we present a method for solving the equation based on domain decomposition and spectral approximation beyond describing such a numerical method for solving strictly linear hrwe we also present results for a nonlinear scalar model of binary inspiral the psw approximation has already been theoretically and numerically studied in the context of the post minkowskian gravitational field with numerical simulations carried out via the eigenspectral method despite its name the eigenspectral technique does feature a finite difference component and is lower order accurate we intend to apply the numerical method described here to the theoretically well developed post minkowski psw formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation

self tuning trackers we examine the problem of obtaining adaptive control laws which tune themselves to control laws minimizing the variance of the tracking error between the output of the linear armax system and a specified reference trajectory if the reference trajectory is sufficiently rich of order greater than or equal to the sum of the degrees of the control and noise polynomials in the armax system then an adaptive controller is exhibited for which the parameter estimates are strongly consistent for the linear model following problem where the trajectory to be tracked is generated as the output of a linear system it is enough for the order of sufficient richness to be greater than the degree of the noise polynomial alone further if the order of sufficient richness is even smaller as is often the case then a lower dimensional adaptive controller which does not attempt to estimate all the coefficients of the noise polynomial is self tuning

robust recursive identification of multidimensional linear regression models stochastic adaptive estimation and control algorithms involving recursive prediction estimates have guaranteed convergence rates when the noise is not too coloured as when a positive real condition on the noise mode is satisfied moreover the whiter the noise environment the more robust are the algorithms this paper shows that for linear regression signal models the suitable introduction of while noise into the estimation algorithm can make it more robust without compromising on convergence rates indeed there are guaranteed attractive convergence rates independent of the process noise colour no positive real condition is imposed on the noise model

coulomb and bessel functions of complex arguments and order abstract the coulomb wavefunctions originally constructed for real 0 real and integer 0 are defined for and all complex we examine the complex continuation of a variety of series and continued fraction expansions for the coulomb functions and their logarithmic derivatives and then see how these expansions may be selectively combined to calculate both the regular and irregular functions and their derivatives the resulting algorithm 46 is a complex generalisation of steed s method 6 7 as it appears in the real procedure coulfg 10 complex whittaker confluent hypergeometric and bessel functions can also be calculated

nonstationary time series identification abstract in this paper strongly consistent estimates are given for both unknown parameters and orders of the nonstationary time series where the nonstationarity arises because 1 at any time n a feedback control is added to the usual arma process which is successfully applied to modelling economic systems and 2 det a z may have zeros on the unit circle in addition to those located outside the unit disk where a z is the matrix polynomial corresponding to the ar part of the arma process

persistency of excitation sufficient richness and parameter convergence in discrete time adaptive control abstract the main result of this paper is to give new techniques for deriving explicit conditions on the exogenously specified reference trajectory to guarantee parameter convergence for a class of either single input single output or multi input multi output discrete time adaptive control schemes other interesting results are relations between persistently exciting signals and sufficiently rich signals

goal oriented adaptivity using unconventional error representations for the 1d helmholtz equation in this work the error of a given output functional is represented using bilinear forms that are different from those given by the adjoint problem these representations can be employed to design novel h p and h p energy norm and goal oriented adaptive algorithms numerical results in 1d show that for wave propagation problems the advantages of this new representation are notorious when selecting the laplace equation as the dual problem specifically the computed upper bounds of the new error representation are sharper than the classical ones used in both energy norm and goal oriented adaptive methods especially when the dispersion pollution error is significant

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

persistence of excitation conditions and the convergence of adaptive schemes in the study of the behavior of adaptive filtering algorithms persistence of excitation of the input process arises as a sufficient condition for convergence and perhaps more importantly for convergence rate of the parameter estimates in this paper the underlying nature of the persistence requirement is presented and discussed relating its normal specification in terms of moment conditions with covariance decays etc to sample path properties deterministic and stochastic persistence conditions and persistence measures are treated as well as persistence conditions for output error equation error and adaptive control schemes

a method for autoregressive moving average estimation summary the problem considered is that of estimating an autoregressive moving average system including estimating the degrees of the autoregressive and moving average lag operators the basic method is that introduced by hannan rissanen 1982 however that method may sometimes overestimate the degrees and modifications are here introduced to correct this the problem is itself due to the use of a long autoregression of order clog t when t is large in the first stage of the process the effect of this is investigated and in particular its effect on the speed of convergence of the estimates

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

strongly consistent estimation of the order of stochastic control systems carma model abstract in this paper a variant of the plc predictive least squares criterion for order estimation is combined with an adaptive control strategy and applied to multidimensional carma systems it is shown that with this combination we can estimate recursively and in a strongly consistent way both the order and coefficients of the controlled system while achieving asymptotically optimal cost

convergence of adaptive minimum variance algorithms via weighting coefficient selection weighted least squares and related stochastic approximation algorithms are studied for parameter estimation adaptive state estimation adaptive n step ahead prediction and adaptive control in both white and colored noise environments for the fundamental algorithm which is the basis for the various applications the step size in the stochastic approximation versions and the weighting coefficient in the weighted least squares schemes are selected according to a readily calculated stability measure associated with the estimator the selection is guided by the convergence theory in this way strong global convergence of the parameter estimates state estimates and prediction or tracking errors is not only guaranteed under the appropriate noise passivity and stability or minimum phase conditions but the convergence is also as fast as it appears reasonable to achieve given the simplicity of the adaptive scheme

recursive estimation of linear systems on compare par simulation deux algorithmes bien connus avec une methode liee a l algorithme de hannan et rissanen 1982

brief paper recursive identification for multivariate errors in variables systems the recursive algorithm is given for estimating matrix coefficients of the multivariate errors in variables eiv systems it is shown that under mild conditions the estimate given by the algorithm converges to a limit belonging to the solution set of the yule walker equation satisfied by the true coefficients of the system the sufficient conditions guaranteeing the uniqueness of the solution to the yule walker equation are given in this case the estimate provided by the recursive algorithm is strongly consistent

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

new approach to recursive identification for armax systems for the multivariate armax system a z yk b z uk 1 c z wk recursive algorithms are proposed for estimating coefficients of a z b z and c z and the covariance matrix rw of wk assuming that the orders of a z b z and c z are known and the control uk can be arbitrarily chosen the new method consists in on line solving the algebraic equations associated with armax on the basis of observed data the algorithms are easily computable and the almost sure convergence of the algorithms is proved under reasonable conditions

a framework for fft based homogenization on anisotropic lattices abstract in order to take structural anisotropies of a given composite and different shapes of its unit cell into account we generalize the basic scheme in homogenization by moulinec and suquet to arbitrary sampling lattices and tilings of the d dimensional euclidean space we employ a fourier transform for these lattices by introducing the corresponding set of sample points the so called pattern and its frequency set the generating set the pattern and the generating set represent the anisotropy of both the shape of the unit cell and the chosen preferences in certain sampling directions in several cases this fourier transform is of lower dimension than the space itself for the so called rank 1 lattices it reduces to a one dimensional fourier transform having the same leading coefficient as the fastest fourier transform implementation available we illustrate the results using the generalized basic scheme on an anisotropic laminate and on a generalized ellipsoidal hashin structure for both we give an analytical solution to the elasticity problem in two and three dimensions respectively we then illustrate the possibilities of choosing a pattern compared to classical grids this introduces both a reduction of computation time and a reduced error of the numerical method it also allows for anisotropic subsampling i e choosing a sub lattice of a pixel or voxel grid based on anisotropy information of the material at hand

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

least squares identification for armax models without the positive real condition recursive identification problems of linear stochastic feedback control systems described by armax models are studied without imposing the strictly positive real condition on the noise model an increasing lag least squares is used in the first step to estimate the noise process while the parameter estimate is formed in the second step by an extended least squares in the algorithm there is an increase in computational cost in comparison to traditional algorithms however the results of this note do not need any a priori information or conditions on the noise model except that of stability and they are applicable to the identification of general feedback control systems

adaptive control with a compact parameter set we consider the problem of the adaptive control of a markov chain with unknown transition probabilities we suppose the transition probabilities p i j u alpha to be dependent on an unknown parameter alpha at each time instant t a maximum likelihood estimate hat alpha t of the unknown parameter is made and a control input u t phi x t hat alpha t is applied where for each alpha phi cdot alpha is a good feedback control law it is shown that if a ranges over a compact set s then hat alpha t may diverge with probability one in the event however that the parameter estimates converge or more generally just the control laws phi cdot hat alpha t converge to some psi then under psi the closed loop transition probabilities for the true model are indistinguishable from those of any limit point of the parameter estimates

sparse spectral tau method for the three dimensional helically reduced wave equation on two center domains we describe a multidomain spectral tau method for solving the three dimensional helically reduced wave equation on the type of two center domain that arises when modeling compact binary objects in astrophysical applications a global two center domain may arise as the union of cartesian blocks cylindrical shells and inner and outer spherical shells for each such subdomain our key objective is to realize certain differential and multiplication physical space operators as matrices acting on the corresponding set of modal coefficients we then achieve sparse realizations through the integration preconditioning of coutsias hagstrom hesthaven and torres since ours is the first three dimensional multidomain implementation of the technique we focus on the issue of convergence for the global solver here the alternating schwarz method accelerated by gmres our methods may prove relevant for numerical solution of other mixed type or elliptic problems and in particular for the generation of initial data in general relativity

adaptive control with the stochastic approximation algorithm geometry and convergence new geometric properties possessed by the sequence of parameter estimates are exhibited which yield valuable insight into the behavior of the stochastic approximation based algorithm as it is used in minimum variance adaptive control in particular these geometric properties together with certain probabilistic arguments prove that if the system does not have a reduced order minimum variance controller then the parameter estimates converge to a random multiple of the true parameter an explicit expression for the limiting parameter estimate is also available with strictly positive probability the limiting parameter estimate is not the true parameter and in some cases differs from the true parameter with probability one if the system possesses reduced order minimum variance controllers then convergence to a minimum variance controller in a cesaro sense is shown the geometry of the limit set is described sufficient conditions are also given for some of these results to hold for parameter estimation schemes other than stochastic approximation

parallel recursive algorithms in asymptotically efficient adaptive control of linear stochastic systems first a review of some recent developments in stochastic adaptive control of linear stochastic systems is given by integrating and refining several basic ideas in these developments a relatively complete asymptotic solution to the adaptive control problem is then provided for such systems the solution involves parallel implementation of a few basic recursive identification algorithms that serve to complement each other it also involves occasional use of a dither signal to probe the system for information

multiscale modeling using goal oriented adaptivity and numerical homogenization part i mathematical formulation and numerical results abstract this paper is the first in this series to develop a numerical homogenization method for heterogeneous media and integrate it with goal oriented finite element mesh adaptivity we describe the physical application step and flash imprint lithography in brief and present the mathematical ideas and numerical verification the method requires the moore penrose pseudoinverse of element stiffness matrices algorithms for efficiently computing the pseudoinverse of sparse matrices will be presented in the second paper the purpose of numerical homogenization is to reduce the number of degrees of freedom find locally optimal effective material properties and perform goal oriented mesh refinement traditionally a finite element mesh is designed after obtaining material properties in different regions the mesh has to resolve material discontinuities and rapid variations in the solution in our approach however we generate a sequence of coarse meshes possibly 1 irregular and homogenize material properties on each coarse mesh element using a locally posed constrained convex quadratic optimization problem this upscaling is done using the moore penrose pseudoinverse of the linearized fine scale element stiffness matrices and a material independent interpolation operator numerical verification is done using a two dimensional conductivity problem with known analytical limit finally we present results for two and three dimensional geometries the results show that this method uses orders of magnitude fewer degrees of freedom to give fast and approximate solutions of the original fine scale problem

integration preconditioning of pseudospectral operators i basic linear operators this paper develops a family of preconditioners for pseudospectral approximations of pth order linear differential operators subject to various types of boundary conditions the approximations are based on ultraspherical polynomials with special attention being paid to legendre and chebyshev polynomial methods based on gauss lobatto quadrature points the eigenvalue spectrum of the preconditioned operators are obtained in closed analytic form and the weakly enforced boundary conditions are shown to result in a rank 2p perturbation of the identity operator i e the majority of the preconditioned eigenvalues are unity the spectrum of the preconditioned advective operator is shown to be bounded independent of the order of the approximation n however the preconditioned diffusive operator is in general indefinite with four real eigenvalues for dirichlet boundary conditions the spectral radius grows as sqrt n while it scales as n for the case of neumann boundary conditions these results are shown to be asymptotically optimal within the present framework generalizations to higher order differential operators general boundary conditions and arbitrary polynomial basis and quadrature nodes are discussed

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

paper a new algorithm for recursive estimation of parameters in controlled arma processes a recursive algorithm for estimating the constant but unknown parameters of a controlled arma process is presented the algorithm is a recursive version of an off line algorithm using three stages of standard least squares in the first stage the parameters of a controlled ar model of degree p are estimated the residuals used in this stage are employed in the second stage to estimate the parameters of a controlled arma process the first two stages constitute a recursive version of durbin s algorithm the model obtained in the second stage is used to filter the input output and residuals and these filtered variables are used in the final stage to obtain improved estimates of the controlled arma process it is shown that the estimate is globally p consistent i e that the estimate converges a s as the number of data tends to infinity to a vector which in turn converges to the true parameter vector as the degree p of the ar model tends to infinity

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

identification and adaptive control of change point arx models via rao blackwellized particle filters by proper choice of proposal distributions for importance sampling and of resampling schemes for sequentially updating the importance weights we address the problem of on line identification and adaptive control of autoregressive models with exogenous inputs arx models with markov parameter jumps particle filters that can be implemented online via parallel recursions are developed by making use of explicit formulas of the posterior means of the time varying parameters theoretical analysis and simulation studies show improvements of this approach over conventional methods

preconditioning chebyshev spectral collocation by finite difference operators in 1979 orszag proposed a finite difference preconditioning of the chebyshev collocation discretization of the poisson equation in 1984 haldenwang labrosse abboudi and deville gave analytic formulae for the eigenvalues of this preconditioned operator in the one dimensional case experimental results over many years have shown the effectiveness of this procedure and appropriate bounds on the eigenvalues in two dimensions however there have been no mathematical proofs describing the behavior of the eigenvalues in two or more dimensions in this work we consider the generalized field of values u hat a nu u l nu where hat a n is the matrix of the chebyshev collocation scheme and l n is the matrix of the finite difference operator for the case of the chebyshev collocation of the helmoltz operator au delta u au a ge 0 preconditioned by the finite difference operator associated with the helmholtz operator bu delta u bu b ge 0 we prove that there are two constants 0 0 and u hat a nu u l nu le lambda 1 these results extend to higher dimensions and to bounds on l n 1 hat a n 1 w and hat a n 1 l n 1 w in the general case where au delta u a 1u x a 2u y au