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Showing papers on "Convergence (routing) published in 1990"


Proceedings ArticleDOI
05 Dec 1990
TL;DR: In this article, the convergence of a wide class of approximation schemes to the viscosity solution of fully nonlinear second-order elliptic or parabolic, possibly degenerate, partial differential equations is studied.
Abstract: The convergence of a wide class of approximation schemes to the viscosity solution of fully nonlinear second-order elliptic or parabolic, possibly degenerate, partial differential equations is studied It is proved that any monotone, stable, and consistent scheme converges (to the correct solution), provided that there exists a comparison principle for the limiting equation Several examples are given where the result applies >

532 citations


Journal ArticleDOI
TL;DR: In this article, general conditions and a new formulation for proving the convergence of Adomian's method for the numerical resolution of nonlinear functional equations depending on one or several variables are proposed.

254 citations


Journal ArticleDOI
TL;DR: An alternative to multigrid relaxation that is much easier to implement and more generally applicable is presented and the relationship of this approach to other multiresolution relaxation and representation schemes is discussed.
Abstract: An alternative to multigrid relaxation that is much easier to implement and more generally applicable is presented. Conjugate gradient descent is used in conjunction with a hierarchical (multiresolution) set of basis functions. The resultant algorithm uses a pyramid to smooth the residual vector before the direction is computed. Simulation results showing the speed of convergence and its dependence on the choice of interpolator, the number of smoothing levels, and other factors are presented. The relationship of this approach to other multiresolution relaxation and representation schemes is also discussed. >

192 citations


Journal ArticleDOI
TL;DR: In this paper, a hybrid method combining the output-least-squares and the equation error method is proposed for the estimation of parameters in elliptic partial differential equations, which is realized by an augmented Lagrangian formulation, and convergence and rate of convergence proofs are provided.
Abstract: In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.

168 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a new method of producing optimizing sequences for highly symmetric functionals with good convergence properties built in, and apply the method in different settings to give elementary proofs of some classical inequalities such as the Hardy-Littlewood-Sobolev and the logarithmic Sobolev inequality.

160 citations


Journal ArticleDOI
TL;DR: This work proves consistency, stability and convergence of the point vortex approximation to the 2-D incompressible Euler equations with smooth solutions to be stable in l p norm for all time.
Abstract: We prove consistency, stability and convergence of the point vortex approximation to the 2-D incompressible Euler equations with smooth solutions. We first show that the discretization error is second-order accurate. Then we show that the method is stable in l p norm. Consequently the method converge in l p norm for all time. The convergence is also illustrated by a numerical experiment

151 citations


Journal ArticleDOI
TL;DR: In this article, an approximation scheme for the nonlinear minimum-time problem with compact target is presented, derived from a discrete dynamic programming principle and the main convergence result is obtained by applying techniques related to discontinuous viscosity solutions for Hamilton-Jacobi equations.
Abstract: This paper presents an approximation scheme for the nonlinear minimum time problem with compact target. The scheme is derived from a discrete dynamic programming principle and the main convergence result is obtained by applying techniques related to discontinuous viscosity solutions for Hamilton–Jacobi equations. The convergence is proved under general controllability assumptions on both the continuous-time and the discrete-time systems. An explicit sufficient condition on the system and the target ensuring the desired controllability is given. This condition is shown to be necessary and sufficient for the Lipschitz continuity of the minimum time function if the target is smooth. An extension to the case of a point-shaped target is given.

129 citations



Journal ArticleDOI
TL;DR: In this article, the stability, convergence, asymptotic optimality, and self-tuning properties of stochastic adaptive control schemes based on least-squares estimates of the unknown parameters are examined.
Abstract: The stability, convergence, asymptotic optimality, and self-tuning properties of stochastic adaptive control schemes based on least-squares estimates of the unknown parameters are examined. It is assumed that the additive noise is i.i.d. and Gaussian, and that the true system is of minimum phase. The Bayesian embedding technique is used to show that the recursive least-squares parameter estimates converge in general. The normal equations of least squares are used to establish that all stable control law designs used in a certainty-equivalent (i.e. indirect) procedure generally yield a stable adaptive control system. Four results are given to characterize the limiting behavior precisely. A certainty-equivalent self-tuning regulator is shown to yield strongly consistent parameter estimates when the delay is strictly greater than one, even without any excitation in the reference trajectory. >

111 citations


Journal ArticleDOI
TL;DR: The main conclusions are that DF is simply convergent, but not exponentially convergent and the exponential convergence can be achieved by means of a suitable modification of DF.

104 citations


Journal ArticleDOI
TL;DR: In this article, an operator splitting method is applied to the time integration of the Zakai equation, which decomposes the numerical integration into a stochastic step and a deterministic one, both of them much simpler to handle than the original problem.
Abstract: The objective of this article is to apply an operator splitting method to the time integration of Zakai equation. Using this approach one can decompose the numerical integration into a stochastic step and a deterministic one, both of them much simpler to handle than the original problem. A strong convergence theorem is given, in the spirit of existing results for deterministic problems.

Journal ArticleDOI
TL;DR: In this paper, the convergence of a mixed method continuous-time scheme for the hyperbolic problem is reduced to a question of convergence of the associated elliptic problem and stability conditions are derived for a conditionally stable explicit scheme.
Abstract: This paper treats mixed methods for second order hyperbolic equations. The convergence of a mixed method continuous-time scheme for the hyperbolic problem is reduced to a question of convergence of the associated elliptic problem. Stability conditions are also derived for a conditionally stable explicit scheme. Numerical experiments are presented that verify the theoretical rates of convergence and compare two of the discrete schemes discussed.

Journal ArticleDOI
TL;DR: In this article, it is demonstrated that convergence of the classical Rayleigh-Ritz method can be improved by introducing a new class of admissible functions, called quasi-comparison functions.
Abstract: It is demonstrated in this paper that convergence of the classical Rayleigh-Ritz method can be vastly improved by introducing a new class of admissible functions, called quasi-comparison functions

Journal ArticleDOI
TL;DR: A multigrid algorithm is described that can be used to obtain the finite element solution of linear elastic solid mechanics problems and is applied to some two dimensional problems to evaluate its strengths and weaknesses.
Abstract: A multigrid algorithm is described that can be used to obtain the finite element solution of linear elastic solid mechanics problems. The method is applied to some two dimensional problems to evaluate its strengths and weaknesses. Extensive studies are made to determine the convergence behaviour of the method. In general, this depends on many factors: the number of degrees-of-freedom in the discretization, characteristics of the algorithm, Poisson's ratio when it is close to 0·5, the amount of bending deformation in the problem under consideration, and the degree of non-uniformity in the mesh. Only certain values of the multigrid parameters allow a converged solution to be obtained with a computational effort proportional to the number of degrees-of-freedom. These values include the optimum ones, i.e. those that lead to convergence with the least computational effort. The constant of proportionality is only independent of the number of degrees-of-freedom and still depends on the other factors listed above.

Journal ArticleDOI
TL;DR: Finite convergence of the algorithm equipped with some simple convergence tests has been proved and using the stronger convergence tests finite exact convergence is shown in the first cases.
Abstract: Cross decomposition is a recent method for mixed integer programming problems, exploiting simultaneously both the primal and the dual structure of the problem, thus combining the advantages of Dantzig—Wolfe decomposition and Benders decomposition. Finite convergence of the algorithm equipped with some simple convergence tests has been proved. Stronger convergence tests have been proposed, but not shown to yield finite convergence. In this paper cross decomposition is generalized and applied to linear programming problems, mixed integer programming problems and nonlinear programming problems (with and without linear parts). Using the stronger convergence tests finite exact convergence is shown in the first cases. Unbounded cases are discussed and also included in the convergence tests. The behaviour of the algorithm when parts of the constraint matrix are zero is also discussed. The cross decomposition procedure is generalized (by using generalized Benders decomposition) in order to enable the solution of nonlinear programming problems.

Journal ArticleDOI
TL;DR: The estimation of a multiple-input single-output discrete Hammerstein system that contains a nonlinear memoryless subsystem followed by a dynamic linear subsystem is studied, and the distribution-free pointwise and global convergence of the estimate is demonstrated.
Abstract: The estimation of a multiple-input single-output discrete Hammerstein system is studied. Such a system contains a nonlinear memoryless subsystem followed by a dynamic linear subsystem. The impulse response of the dynamic linear subsystem is obtained by the correlation method. The main results concern the estimation of the nonlinear memoryless subsystem. No conditions are imposed on the functional form of the nonlinear subsystem, and the nonlinearity is recovered using the kernel regression estimate. The distribution-free pointwise and global convergence of the estimate is demonstrated-that is, no conditions are imposed on the input distribution, and convergence is proven for virtually all nonlinearities. The rates of pointwise as well as global convergence are obtained for all input distributions and for Lipschitz type nonlinearities. >

Journal ArticleDOI
TL;DR: In this paper, the convergence properties of a fairly general class of adaptive recursive least-squares algorithms are studied under the assumption that the data generation mechanism is deterministic and time invariant.
Abstract: The convergence properties of a fairly general class of adaptive recursive least-squares algorithms are studied under the assumption that the data generation mechanism is deterministic and time invariant. First, the (open-loop) identification case is considered. By a suitable notion of excitation subspace, the convergence analysis of the identification algorithm is carried out with no persistent excitation hypothesis, i.e. it is proven that the projection of the parameter error on the excitation subspace tends to zero, while the orthogonal component of the error remains bounded. The convergence of an adaptive control scheme based on the minimum variance control law is then dealt with. It is shown that under the standard minimum-phase assumption, the tracking error converges to zero whenever the reference signal is bounded. Furthermore, the control variable turns out to be bounded. >

Journal ArticleDOI
TL;DR: A parametrized class of algorithms, which includes stochastic relaxation (Gibbs sampler), is proposed and its convergence properties are established, where a suitable choice for the parameter improves the rate of convergence with respect to stochastics relaxation for special classes of covariance matrices.
Abstract: In this paper, we are concerned with the simulation of Gaussian random fields by means of iterative stochastic algorithms, which are compared in terms of rate of convergence. A parametrized class of algorithms, which includes stochastic relaxation (Gibbs sampler), is proposed and its convergence properties are established. A suitable choice for the parameter improves the rate of convergence with respect to stochastic relaxation for special classes of covariance matrices. Some examples and numerical experiments are given.

PatentDOI
TL;DR: In this article, a method for reducing the convergence time of an active acoustic attenuation system upon start-up or upon a given sensed parameter change is presented. But the method is limited to the case where the weights of the adaptive filter model coefficient weight vector are started at or changed to values which are closer to the converged value than the initial or present non-converged value.
Abstract: A method is provided for reducing convergence time of an active acoustic attenuation system upon start-up or upon a given sensed parameter change. The weights of the adaptive filter model coefficient weight vector are started at or changed to values which are closer to the converged value than the initial or present nonconverged value is to the converged value. The filter model converges in a shorter time as the weights change and are updated from their starting or changed value to the converged value.

Journal ArticleDOI
TL;DR: A parallel method for the transient stability simulation of power systems is presented, using the trapezoidal rule and a parallel Block-Newton relaxation technique to solve the overall set of algebraic equations concurrently on all the time steps.
Abstract: A parallel method for the transient stability simulation of power systems is presented. The trapezoidal rule is used to discretize the set of algebraic-differential equations which describes the transient stability problem. A parallel Block-Newton relaxation technique is used to solve the overall set of algebraic equations concurrently on all the time steps. The parallelism in space of the problem is also exploited. Furthermore, the parallel-in-time formulation is used to change the time steps between iterations by a nested iteration multigrid technique, in order to enhance the convergence of the algorithm. The method has the same reliability and model-handling characteristics of typical dishonest Newton-like procedures. Test results on realistic power systems are presented to show the capability and usefulness of the suggested technique. >

Journal ArticleDOI
TL;DR: It is demonstrated that it is possible for processors to perform useful work on many time levels simultaneously and for processors assigned to “later” time levels to compute a very good initial guess for the solution based on partial solutions from previous time levels, thus reducing the time required for solution.
Abstract: Parabolic and hyperbolic differential equations are often solved numerically by time-stepping algorithms. These algorithms have been regarded as sequential in time; that is, the solution on a time level must be known before the computation of the solution at subsequent time levels can start. While this remains true in principle, it is demonstrated that it is possible for processors to perform useful work on many time levels simultaneously. Specifically, it is possible for processors assigned to “later” time levels to compute a very good initial guess for the solution based on partial solutions from previous time levels, thus reducing the time required for solution. The reduction in the solution time can be measured as parallel speedup.This algorithm is demonstrated for both linear and nonlinear problems. In addition, the convergence properties of the method based on the convergence properties of the underlying iterative method are discussed, and an accurate performance model from which the speedup and oth...

Journal ArticleDOI
TL;DR: A new mathematical state-space model for a class of nonlinear time-varying parallel iterative schemes is proposed, and it is shown that the well-known quasidominance condition on a certain aggregated matrix guarantees exponential convergence of this class of methods.

Journal ArticleDOI
J.P.C. Blanc1
TL;DR: In this article, an iterative numerical technique for the evaluation of queue length distributions is applied to multi-queue systems with one server and cyclic service discipline with Bernoulli schedules.
Abstract: An iterative numerical technique for the evaluation of queue length distributions is applied to multi-queue systems with one server and cyclic service discipline with Bernoulli schedules. The technique is based on power-series expansions of the state probabilities as functions of the load of the system. The convergence of the series is accelerated by applying a modified form of the epsilon algorithm. Attention is paid to economic use of memory space. The technique is based on power-series expansions of the state probabilities as functions of one parameter (the traffic intensity) of the systems. The coefficients of these power series can be recursively calculated for a large class of multi-queue models. The coefficients of the power-series expansions of the moments of the queue length distributions follow directly from those of the state probabillities. In most instances a bilinear transformation ensures convergence of the power series over the whole range of traffic intensities for which the system is stable. We have introduced in Blanc (2,3) extrapolations of the coefficients of the power series in order to accelerate the convergence of the series. One of these extrapolations will be combined with the epsilon algorithm (cf. Brezinski (6), Wynn (13)) in the present paper. The advantages of the present technique are that quantities are calculated iteratively, that it is relatively easy to compute additional terms of the power series in order to increase accuracy, that algorithms for accelerating the convergence of sequences can be applied, and that, once the coefficients of the

Journal ArticleDOI
TL;DR: The task of finding a class of balanced minimal realizations is shown to be equivalent to finding limiting solutions of certain gradient flow differential equations, and convergence is rapid and numerical stability properties are attractive.


Proceedings ArticleDOI
A. Bar-Noy1, M. Gopal1
01 Aug 1990
TL;DR: This work presents a trade-off between the amount of topology information exchanged among these pieces and the efficiency of routing in the network.
Abstract: Routing a message in a network is efficient (in terms of weight of the path used to carry the message) when nodes know the full topology of the network. This may not be the case in large networks since a network may be composed of smaller autonomous pieces by design or by requirements on performance, with each piece having less than complete information about other pieces. We present a trade-off between the amount of topology information exchanged among these pieces and the efficiency of routing in the network. The large network that we study is a collection of networks connected by boundary nodes. Each boundary node knows the topology of its network and the connectivity of networks to each other. The question addressed here is how much topology information about each network should be distributed to other networks in order to achieve reasonably efficient routing.

Journal ArticleDOI
TL;DR: A steepest-descent algorithm for unconstrained problems and a feasible-direction algorithm for problems with inequality constraints are developed.
Abstract: Stochastic algorithms for optimization problems, where function evaluations are done by Monte Carlo simulations, are presented. At each iteratexi, they draw a predetermined numbern(i) of sample points from an underlying probability space; based on these sample points, they compute a feasible-descent direction, an Armijo stepsize, and the next iteratexi+1. For an appropriate optimality function σ, corresponding to an optimality condition, it is shown that, ifn(i) → ∞, then σ(xi) → 0, whereJ is a set of integers whose upper density is zero. First, convergence is shown for a general algorithm prototype: then, a steepest-descent algorithm for unconstrained problems and a feasible-direction algorithm for problems with inequality constraints are developed. A numerical example is supplied.

Journal ArticleDOI
TL;DR: A variation of the back-propagation algorithm is described, using a log-likelihood cost function, where the range of initial weights leading to proper convergence is increased, and the number of iterations required is significantly reduced.
Abstract: A variation of the back-propagation algorithm is described, using a log-likelihood cost function. Appropriate choices of learning parameters are discussed. An example is given where the range of initial weights leading to proper convergence is increased, and the number of iterations required is significantly reduced.


Journal ArticleDOI
TL;DR: In this paper, a trust-region-type, two-sided, projected quasi-Newton method was proposed, which preserves the local two-step superlinear convergence of the original algorithm and also ensures global convergence.
Abstract: In Ref. 1, Nocedal and Overton proposed a two-sided projected Hessian updating technique for equality constrained optimization problems. Although local two-step Q-superlinear rate was proved, its global convergence is not assured. In this paper, we suggest a trust-region-type, two-sided, projected quasi-Newton method, which preserves the local two-step superlinear convergence of the original algorithm and also ensures global convergence. The subproblem that we propose is as simple as the one often used when solving unconstrained optimization problems by trust-region strategies and therefore is easy to implement.