Showing papers on "Convergence (routing) published in 1977"
TL;DR: A new global convergence theorem for noncontinuous iteration algorithms is developed that converges, with successive updates of the routing tables, to the minimum average delay over all routing assignments.
Abstract: An algorithm is defined for establishing routing tables in the individual nodes of a data network. The routing table at a node i specifies, for each other node j , what fraction of the traffic destined for node j should leave node i on each of the links emanating from node i . The algorithm is applied independently at each node and successively updates the routing table at that node based on information communicated between adjacent nodes about the marginal delay to each destination. For stationary input traffic statistics, the average delay per message through the network converges, with successive updates of the routing tables, to the minimum average delay over all routing assignments. The algorithm has the additional property that the traffic to each destination is guaranteed to be loop free at each iteration of the algorithm. In addition, a new global convergence theorem for noncontinuous iteration algorithms is developed.
676 citations
TL;DR: The convergence with probability one of a recently suggested recursive identification method by Landau is investigated and the positive realness of a certain transfer function is shown to play a crucial role, both for the proof of convergence and for convergence itself.
Abstract: The convergence with probability one of a recently suggested recursive identification method by Landau is investigated. The positive realness of a certain transfer function is shown to play a crucial role, both for the proof of convergence and for convergence itself. A completely analogous analysis can be performed also for the extended least squares method and for the self-tuning regulator of Astrom and Wittenmark. Explicit conditions for convergence of all these schemes are given. A more general structure is also discussed, as well as relations to other recursive algorithms.
413 citations
01 Jan 1977
TL;DR: In this paper, fast recursive estimation techniques, originally introduced by Morf and Ljung, can be adapted to the equalizer adjustment problem, resulting in the same fast convergence as the conventional Kalman implementation, but with far fewer operations per iteration (proportional to the number of equalizer taps, rather than the square of the number).
Abstract: Very rapid initial convergence of the equalizer tap coefficients is a requirement of many data communication systems which employ adaptive equalizers to minimize intersymbol interference. As shown in recent papers by Godard, and by Gitlin and Magee, a recursive least squares estimation algorithm, which is a special case of the Kalman estimation algorithm, is applicable to the estimation of the optimal (minimum MSE) set of tap coefficients. It was furthermore shown to yield much faster equalizer convergence than that achieved by the simple estimated gradient algorithm, especially for severely distorted channels. We show how certain "fast recursive estimation" techniques, originally introduced by Morf and Ljung, can be adapted to the equalizer adjustment problem, resulting in the same fast convergence as the conventional Kalman implementation, but with far fewer operations per iteration (proportional to the number of equalizer taps, rather than the square of the number of equalizer taps). These fast algorithms, applicable to both linear and decision feedback equalizers, exploit a certain shift-invariance property of successive equalizer contents. The rapid convergence properties of the "fast Kalman" adaptation algorithm are confirmed by simulation.
242 citations
01 Jan 1977
TL;DR: Convergence proofs in mixed finite element methods show that building the operator Tlh can be done through an interpolation operator, and some properties of discrete operators invohed in the approximation are characterized.
Abstract: — This paper deals with convergence proofs in mixed finite element methods. After recalling abstract conditions ofBrezzi, one shows that these conditions are, in some cases, equivalent to the possibility of building an uniformly continuous operator Yih from V into Vh. Moreover some properties of discrete operators invohed in the approximation are characterized'. Two examples show that building the operator Tlh can be done through an interpolation operator. A third example présents a case which is still out of reach of present techniques.
225 citations
01 Jan 1977
178 citations
TL;DR: The Topology Information Protocol that was implemented on the MERIT Computer Network is presented and explained; this protocol is quite general and could be implemented on any computer network.
Abstract: In order for the nodes of a distributed computer network to communicate, each node must have information about the network's topology. Since nodes and links sometimes crash, a scheme is needed to update this information. One of the major constraints on such a topology information scheme is that it may not involve a central controller. The Topology Information Protocol that was implemented on the MERIT Computer Network is presented and explained; this protocol is quite general and could be implemented on any computer network. It is based on Baran's “Hot Potato Heuristic Routing Doctrine.” A correctness proof of this Topology Information Protocol is also presented.
125 citations
TL;DR: In this article, a theoretical study of Stott's fast decoupled load flow (DLF) is presented, where convergence conditions for the DLF are obtained by using the data of the network parameters and the calculation from the first iteration.
Abstract: A theoretical study of Stott's fast decoupled load flow (DLF) is presented. Convergence conditions for the DLF are obtained. The conditions can be checked by using the data of the network parameters and the calculation from the first iteration. The dependence of the conditions on the line R/X ratio, scheduled power injections, etc. is explained. At each iteration an error estimate of the computed value to the true solution is given. The convergence conditions also guarantee the existence and the uniqueness of load flow solution in a specified region of interest.
117 citations
TL;DR: A comparison is made of several self-orthogonalizing adjustment algorithms for linear tapped delay line equalizers that accelerate the rate of convergence of the equalizer tap weights to those which minimize the output mean-squared error of a data transmission system.
Abstract: A comparison is made of several self-orthogonalizing adjustment algorithms for linear tapped delay line equalizers. These adaptive algorithms accelerate the rate of convergence of the equalizer tap weights to those which minimize the output mean-squared error of a data transmission system. Accelerated convergence of the estimated gradient algorithm is effected by premultiplying the correction term in the algorithm by a matrix which is an estimate of the inverse of the channel correlation matrix. The various algorithms differ in the manner in which this estimate is sequentially computed. Depending on the degree of complexity available, the equalizer convergence time may be reduced more than an order of magnitude from that required by the simple gradient algorithm.
106 citations
75 citations
TL;DR: In this paper, the convergence properties of long-range interactions in a periodic polar system are considered and an efficient method for their evaluation is proposed, applied to a Monte-Carlo simulation of water at 1 g cm-3 and a nominal temperature of 300 K, using the ST2 potential of Rahman and Stillinger.
Abstract: The convergence properties of long-range interactions in a periodic polar system are considered and an efficient method for their evaluation proposed. This method is applied to a Monte-Carlo simulation of water at 1 g cm-3 and a nominal temperature of 300 K, using the ST2 potential of Rahman and Stillinger.
72 citations
TL;DR: Conditions are given under which any product of matrices from this set converges to a constant stochastic matrix and it is shown that the convergence is exponentially fast.
TL;DR: In this article, a new correction factor (η) for reaction rate has been defined, analogous to θ for correcting molal flow rates in the multi-θ method of convergence.
Abstract: A new correction factor (η) for reaction rate has been defined. It is analogous to θ for correcting molal flow rates in the multi-θ method of convergence. Then a new calculation method with two such kinds of the independent variables as θ and η has been developed for solving reacting distillation problems at the steady state and at the unsteady state. Convergence is obtained without difficulty in the case where vapor liquid equilibrium ratios may be formulated as a function of temperature only. However, in the case of calculations based on experimental data in the esterification systems, the values of Δη and Δη resulted from the Newton Raphson''s method have some time a large number. Therefore the correction method for these by use of arctangent function has been proposed in order to avoid divergence. This new calculation method is called "Multi θ-η method of convergence".
TL;DR: In this paper, weak convergence results and concepts in the theory of weak convergence of a sequence of probability measures are applied to convergence problems for a variety of recursive adaptive (stochastic approximation-like) methods.
Abstract: Results and concepts in the theory of weak convergence of a sequence of probability measures are applied to convergence problems for a variety of recursive adaptive (stochastic approximation-like) methods. Similar techniques have had wide applicability in areas of operations research and in some other areas in stochastic control. It is quite likely that they will play a much more important role in control theory than they do at present, since they allow relatively simple and natural proofs for many types of convergence and approximation problems. Part of the aim of the paper is tutorial: to introduce the ideas and to show how they might be applied. Also, many of the results are new, and they can all be generalized in many directions.
TL;DR: In this article, for sums of independent and identically distributed random vectors, the authors investigated the convergence to normality of the expectation of bounded and certain unbounded Borel measurable functions, and nonuniform convergence rates.
Abstract: Speeds of convergence to normality for sums of independent and identically distributed random vectors in $\mathbb{R}^k, k \geqq 1$, are investigated using the method of operators. Results obtained improve and extend existing results on speeds of convergence for the expectations of both bounded and certain unbounded Borel measurable functions, and nonuniform convergence rates.
TL;DR: In this paper, the convergence rate of the Marcinkiewicz-zygmund strong law for stationary mixing sequences was shown to be Ω(r$)-approximation, and the finiteness of moments of the largest excess of boundary crossings for such sequences was proved.
Abstract: In this paper we prove a theorem on the convergence rate in the Marcinkiewicz-Zygmund strong law for stationary mixing sequences. Our result gives the $r$-quick strong law and the finiteness of moments of the largest excess of boundary crossings for such sequences.
01 Jan 1977
TL;DR: In this paper, the convergence properties of rational approximation schemes in several variables were studied, defined by interpolation conditions generalizing those that define Pade approximants in one variable.
Abstract: We study the convergence properties of certain rational approximation schemes in several variables. These schemes are defined by interpolation conditions generalizing those that define Pade approximants in one variable.
01 Mar 1977
TL;DR: In this article, a modification of Broyden's method for finding a zero of n nonlinear equations in n unknowns when analytic derivatives are not available is introduced, and the method retains the local Q-superlinear convergence and has the additional property that if any or all of the equations are linear, it locates a zero in n+1 or fewer iterations.
Abstract: We introduce a modification of Broyden's method for finding a zero of n nonlinear equations in n unknowns when analytic derivatives are not available. The method retains the local Q-superlinear convergence of Broyden's method and has the additional property that if any or all of the equations are linear, it locates a zero of these equations in n+1 or fewer iterations. Limited computational experience suggests that our modification often improves upon Broyden's method.
01 Jan 1977
TL;DR: A method for accelerating the convergence of the algorithm based on the Frank and Wolfe linear approximation method for the convex cost multicommodity flow problem known as the "equilibrium traffic assignment problem" in transportation networks and the "optimal routing of packet switched messages" in communication networks is presented.
Abstract: A method is presented for accelerating the convergence of the algorithm based on the Frank and Wolfe linear approximation method for the convex cost multicommodity flow problem known as the "equilibrium traffic assignment problem" in transportation networks and as the "optimal routing of packet switched messages" in communication networks. The acceleration of the convergence of this algorithm is achieved with a nontrivial adaptation of Wolfe's suggestion of an "away" step in the linear approximation method and a variant of this adaptation based on restriction.
01 Dec 1977
TL;DR: In this article, the Frank and Wolfe linear approximation method for the convex cost multicommodity flow problem known as the equilibrium traffic assignment problem in transportation networks and as the optimal routing of packet switched messages in communication networks is presented.
Abstract: We present a method for accelerating the convergence of the algorithm based on the Frank and Wolfe linear approximation method for the convex cost multicommodity flow problem known as the "equilibrium traffic assignment problem" in transportation networks and as the "optimal routing of packet switched messages" in communication networks. The acceleration of the convergence of this algorithm is achieved with a non trivial adaptation of Wolfe's suggestion of an "away" step in the linear approximation method and a variant of this adaptation based on restriction.
TL;DR: Two prototype identifiable structures are presented which make possible the identification via an equation-error model reference adaptive system of linear plants with rational transfer function matrices.
TL;DR: In this article, sufficient conditions for the convergence of methods for the numerical integration of a system of ordinary differential equations, possibly stiff, are presented, and the asymptotic error formula for such a solution is developed.
Abstract: Sufficient conditions for the convergence of methods for the numerical integration of a system of ordinary differential equations, possibly stiff, are presented. The asymptotic error formula for such a solution is developed. The existence of more stringent conditions for convergence of multi-derivative formulas over first derivative formulas is noted. A class of computationally A-stable formulas is presented, with notes on implementing a set of them in a variable stepsize, variable order method. Tests on one such implementation show the capabilities of such methods on stiff problems.
TL;DR: The development of an interpolative or approximation algorithm for use in conjunction with a more accurate K value generator to reduce the cost in computer time for process simulation.
01 Jan 1977
TL;DR: The Reduced Hessian method, which is inherently a second order method, has been applied to the optimal load flow problem and results in highly reliable convergence and excellent accuracy.
01 Jan 1977
TL;DR: In this article, a truncation function is introduced which converts integration over a sphere to integration over the cell, and the properties of the spherical harmonic series are investigated for the Green function which appears in the integration.
Abstract: The solution of Poisson's equation is an essential step in the formulation of self-consistent calculations. An efficient method of solution is presented for a system of arbitrary geometry. The charge density and potential within a cell of arbitrary shape are expanded in spherical harmonic series. A truncation function is introduced which converts integration over a sphere to integration over the cell. Tables of this function for common cell shapes are presented. The properties of the spherical harmonic series are investigated for the Green function which appears in the integration. Its convergence is much slower than has previously been assumed. An optimum approximate treatment is proposed.
TL;DR: It becomes clear that passing the patch test is not a necessary condition for convergence and that the simple patch test will be sufficient for accuracy and not merely for convergence analysis.
TL;DR: In this paper, an iterative method for solving the matrix equation XA+AY=F is discussed, and algorithms and techniques for accelerating convergence are outlined; the method compares favourably with existing techniques.
Abstract: An iterative method for solving the matrix equationXA+AY=F is discussed Algorithms and techniques for accelerating convergence are outlined. The method compares favourably with existing techniques.
TL;DR: The paper treats general convergence conditions for a class of algorithms for finding the minima of a function f(x) when f( x) is of unknown (or partly unknown) form, and when only noise corrupted observations can be taken.
TL;DR: In this article, a relaxation method for finding the local extrema in non-linear programming is described, and the convergence rate of the continuous and discrete versions of the relaxation method is investigated.
Abstract: A RELAXATION method is described for finding the local extrema in the general problem of non-linear programming. The convergence is proved, the convergence rate of the continuous and discrete versions of the method is investigated, and an extension to the case of finding saddle-points is given. The results of numerical computations are quoted.
01 Dec 1977
TL;DR: A first order algorithm for optimal control is used to solve optimal trajectories associated with aircraft applications including pursuit-evasion problems, and a convergence control technique is described in which a set of convergence control parameters is introduced.
Abstract: A first order algorithm for optimal control is used to solve optimal trajectories associated with aircraft applications including pursuit-evasion problems. To overcome the stability problems which occur in the algorithm, a convergence control technique is described in which a set of convergence control parameters is introduced. The effect of these parameters and how to choose them are discussed and demonstrated on optimal climb and pursuit-evasion problems. A fixed terminal time is assumed, although this is not a requirement. Numerical results are presented which illustrate the features of the algorithm, especially the ability to select different optimal solutions in the case of a nonunique solution.