Showing papers on "Convergence (routing) published in 1979"
TL;DR: An optimal convergence condition for Newton iteration in a Banach space is established and which stronger condition must be imposed to also assure good complexity.
Abstract: : An optimal convergence condition for Newton iteration in a Banach space is established. There exist problems for which the iteration converges but the complexity is unbounded. It is shown which stronger condition must be imposed to also assure good complexity.
118 citations
TL;DR: In this paper, the identification of constant unknown parameters of a linear system is studied, and a membership set for this vector is constructed such that any vector in this set is consistent with the measurements and noise specifications.
Abstract: In this paper the identification of constant unknown parameters of a linear system is studied. Rather than finding an estimate of the parameters vector, a membership set for this vector is constructed such that any vector in this set is consistent with the measurements and noise specifications. The usual statistical specification of the noise is replaced here by energy constraints. Convergence of the membership set to a single point (the "true" vector) is studied. The convergence results are related to the convergence of the identification algorithm in the probability sense.
110 citations
01 Jan 1979
81 citations
TL;DR: Schubert's method for solving sparse nonlinear equations is an extension of Broyden's method The zero-nonzero structure defined by the sparse Jacobian is preserved by updating the approximate Jacobian row by row as discussed by the authors.
Abstract: Schubert’s method for solving sparse nonlinear equations is an extension of Broyden’s method The zero-nonzero structure defined by the sparse Jacobian is preserved by updating the approximate Jacobian row by row An estimate is presented which permits the extension of the convergence results for Broyden’s method to Schubert’s method The analysis for local and q-superlinear convergence given here includes, as a special case, results in a recent paper by B Lam; this generalization seems theoretically and computationally more satisfying A Kantorovich analysis paralleling one for Broyden’s method is given This leads to a convergence result for linear equations that includes another result by Lam A result by More and Trangenstein is extended to show that a modified Schubert’s method applied to linear equations is globally and q-superlinearly convergent
80 citations
TL;DR: In this article, the nonlinear transformations to accelerate the convergence of sequences due to Levin are considered and bounds on the errors are derived, and convergence theorems for oscillatory and some monotone sequences are proved.
Abstract: The nonlinear transformations to accelerate the convergence of sequences due to Levin are considered and bounds on the errors are derived. Convergence theorems for oscillatory and some monotone sequences are proved.
72 citations
TL;DR: A theorem giving necessary and sufficient conditions for the optimum for the central optimization problem of the lower bound method of reduced density matrix theory is developed.
69 citations
TL;DR: In this article, various short cut procedures for estimation of parameters in mathematical models given in the form of differential equations are compared with each other as well as with the maximum likelihood (ML) approach.
53 citations
TL;DR: In this paper, the authors present an approach for rearrangements of functions and convergence in orlicz spaces, which is based on the concept of convergence in the space of functions.
Abstract: (1979). Rearrangements of functions and convergence in orlicz spaces. Applicable Analysis: Vol. 9, No. 1, pp. 23-27.
47 citations
TL;DR: Two of the updating methods for the multipliers in augmented Lagrangians are shown to be linearly convergent locally, while a third method has superlinear convergence locally.
Abstract: The convergence properties of different updating methods for the multipliers in augmented Lagrangians are considered. It is assumed that the updating of the multipliers takes place after each line search of a quasi-Newton method. Two of the updating methods are shown to be linearly convergent locally, while a third method has superlinear convergence locally. Modifications of the algorithms to ensure global convergence are considered. The results of a computational comparison with other methods are presented.
45 citations
TL;DR: In this article, a new iterative method for solving nonlinear equations is presented which is shown to converge locally withR-order of convergence $$1 + \sqrt 2 $$ at least under suitable differentiability assumptions.
Abstract: A new iterative method for solving nonlinear equations is presented which is shown to converge locally withR-order of convergence $$1 + \sqrt 2 $$ at least under suitable differentiability assumptions. The method needs as many function evaluations per step as the classical Newton method.
43 citations
TL;DR: In this article, a survey of convergence analysis and convergence properties of recursive identification methods for dynamical, stochastic systems is presented, where two classes of recursive estimators are recognized: recursive prediction error methods and pseudo linear regressions.
TL;DR: Two examples are presented to show that variable metric methods may cycle between two points instead of converging to the required solution.
Abstract: Although variable metric methods for constrained minimization generally give good numerical results, many of their convergence properties are still open. In this note two examples are presented to show that variable metric methods may cycle between two points instead of converging to the required solution.
TL;DR: In this article, the authors prove a convergence theorem for an implicit iterative scheme and then apply it to an explicit one and prove that the convergence theorem holds for both implicit and explicit iterative schemes.
Abstract: We prove a convergence theorem for an implicit iterative scheme and then apply it to an explicit one.
TL;DR: In this paper, the authors used a summability method which includes both convergence and almost convergence, and obtained estimates for approximation by positive linear operators with the use of a sumability method.
TL;DR: Convergence properties are obtained as well as a Q superlinear rate of convergence of a newly developed algorithm for unconstrained optimization that takes any sparsity of the second derivative matrix into account.
Abstract: This paper is concerned with the proof of some convergence properties of a newly developed algorithm for unconstrained optimization that takes any sparsity of the second derivative matrix into account. It is shown that the considered algorithm is a member of a class of algorithms studied by Powell. Convergence properties are then obtained as well as a Q superlinear rate of convergence. Convergence of the sequence of quasi-Newton matrices to the Hessian matrix at the optimum is also shown under more restrictive assumptions.
Abstract: The well-known concept of conjugate slowly varying functions is specialized to the subclass $\Pi$ of the slowly varying functions. The concept is then used to connect convergence of certain increasing stochastic processes (suitably normalized) with convergence of their inverses.
TL;DR: In this paper, two schemes are proposed to synthesize multierror adaptive observers for nth order, linear, single-output, observable and time-invariant systems with improved convergence characteristics.
Abstract: A general description of the implicit adaptive observer [13] is presented which defines the interrelationship between the different adapfive observers that have been reported in literature. Within the framework of the general formulation, two schemes are proposed to synthesize multierror adaptive observers for nth order, linear, single-output, observable and time-invariant systems with improved convergence characteristics. The proposed schemes use only input and output measurements, are globally asymptotically stable and have an arbitrarily fast rate of exponential convergence for both the system parameters and the system state. If all system parameters are unknown, the second scheme is the minimal order observer that can afford arbitrarily fast exponential convergence. Simulation results are included.
TL;DR: This work develops several algorithms that obtain the global optimum to the indefinite quadratic programming problem, and develops exact cuts, which are locally precise representations of a reduced objective.
Abstract: We develop several algorithms that obtain the global optimum to the indefinite quadratic programming problem. A generalized Benders cut method is employed. These algorithms all possess ϵ-finite convergence. To obtain finite convergence, we develop exact cuts, which are locally precise representations of a reduced objective. A finite algorithm is then constructed. Introductory computational results are presented.
Journal Article•
TL;DR: The authors find that equilibrium methods are easy to incorporate into existing computer packages, require minimal user intervention, are stable in heavily-congested networks and avoid extreme misfits between predicted and observed flows.
Abstract: The paper is in three sections: (1) the convergence of stochastic methods. The convergence of stochastic methods of road assignment such as BURRELL or DIAL are investigated in capacity-restrained networks where the cost of travel on any link depends on the flow of that link. A convergent solution is one where the costs assumed by the route-finding algorithm are identical to those corresponding to the resulting link flows. Both all-or-nothing and dial assignments are shown to be inherently non-convergent whereas under certain, quite reasonable, conditions the hypothesis underpinning BURRELL assignment should lead to convergent solutions. However, simplications made by BURRELL in the method of solution for a large network may make the point of convergence extremely difficult, if not impossible, to find. The authors conclude that the instability of these methods, reflected by severe oscillations in flows between interations, is generally an unaboidable feature of such models. (2) Equilibrium methods. This section reviews the equilibrium methods of assignment to capacity-restraint road networks, methods which are well-known theoretically but have not been used extensively in practice. Their major advantage over heuristic techniques is that they guarantee ultimate convergence to a solution which satisfies Wardrop's first principle of equal and minimum travel costs on all routes used. The principles of equilibrium assignment and a straightforward method based on iterative loading are presented. Results obtained by applying this method to a network of Leeds give better goodness of fit statistics with observed counts than conventional methods requiring comparable cpu times. In addition, the authors find that equilibrium methods are easy to incorporate into existing computer packages, require minimal user intervention, are stable in heavily-congested networks and avoid extreme misfits between predicted and observed flows. (3) Improved equilibrium methods. Two methods of improved solutions to equilibrium assignment models are described. The first, "quantal loading", is in fact based on a technique first used in Chicago over 20 years ago in which updates of the link times or costs are carried out at regular intervals within a single assignment rather than at the end. An extension which applies the same ideas as part of a series of iterative equilibrium assignments is developed. The major advantage of quantal loading is that it greatly accelerates the rate of convergence to Wardrop equilibrium, on a network of Leeds by a factor of 5 on the first iteration and factors of 2 thereafter. The potential reductions in cpu times are therefore considerable. The second technique is based on an improved method of combining or averaging different sets of link flows, again with the objective of accelerating convergences and reducing cpu. The results are less spectacular, but do show that the
TL;DR: In this article, an iterative algorithm for nonlinear mapping of high-dimensional data is developed, where the step size of the descent algorithm is chosen to assure convergence, and Steepest descent and Coordinate descent are treated.
Abstract: An iterative algorithm for nonlinear mapping of high-dimensional data is developed. The step size of the descent algorithm is chosen to assure convergence. Steepest descent and Coordinate descent are treated. The algorithm is applied to artificial and real data to demonstrate its excellent convergence properties.
01 Jan 1979
TL;DR: In this paper, the authors introduced stack convergence, which contains nearly each essential concept of generalizing topological and uniform spaces, including the notion of pre-nearness spaces, and proved that convergence contains nearness.
Abstract: Generalizing usual filter convergence, we introduce stack convergence. This convergence contains nearly each essential concept of generalizing topological and uniform spaces. In particular, the belonging category SCO includes as well the topological spaces as the prenearness spaces. Thus we have solved a problem of Herrlich (1974) and have proved: Convergence contains nearness.
TL;DR: In this article, a general Poisson limit theorems for U-statistics are studied and a general rate of convergence is obtained; this rate is improved for the special case where the Ustatistic arises from the consideration of distances between uniformly
Abstract: Poisson limit theorems for U-statistics are studied. A general rate of convergence is obtained; this rate is improved for the special case where the U-statistic arises from the consideration of distances between uniformly
TL;DR: In this article, the concept of a semi-martingale is extended to processes with index set in the plane, and sufficient conditions for a Doob-Meyer decomposition are obtained, and a maximal inequality and almost everywhere convergence theorem is given for planar Semi-Martingales in LlogL.
TL;DR: In this article, it was shown that linear convergence to a local maximum of a certain potential is possible for a large class of such problems and a simple version of such algorithms that can be obtained.
Abstract: In recent years, a group of inverse iteration type algorithms have been developed for solving nonlinear elliptic eigenvalue problems in plasma physics [4]. Although these algorithms have been very successful in practice, no satisfactory theoretical justification of convergence has been available. The present paper fills this gap and proves for a large class of such problems and a simple version of such algorithms that linear convergence to a local maximum of a certain potential is obtained.
TL;DR: In this article, the conventional dynamic flexibility matrix in series forms is re-examined and the convergence may be accelerated to a large extent by using the condensed stiffness and mass matrices of the system.
TL;DR: Here it is rigorously proven that the method is convergent, and mathematically correct procedures are described that speed up convergence and make the approximate energies approach the exact value from one side only.
TL;DR: It is shown that for 1
Abstract: The convergence properties of an algorithm for discreteL p approximation (1?p<2) that has been considered by several authors are studied. In particular, it is shown that for 1
01 Jan 1979
TL;DR: A general structure is established that allows the comparison of various conditions that are sufficient for convergence of algorithms that can be modeled as the recursive application of a point-to-set map.
Abstract: A general structure is established that allows the comparison of various conditions that are sufficient for convergence of algorithms that can be modeled as the recursive application of a point-to-set map. This structure is used to compare several earlier sufficient conditions as well as three new sets of sufficient conditions. One of the new sets of conditions is shown to be the most general in that all other sets of conditions imply this new set. This new set of conditions is also extended to the case where the point-to-set map can change from iteration to iteration.
TL;DR: The stability and convergence about the SHASTA FCT algorithm is studied, which is one of the basic schemes among many FCT techniques, though not in its original form but a slightly modified one for technical reason.
Abstract: In recent years, Boris, Book and Hain have proposed a family of finite difference methods called FCT techniques for the Cauchy problem of the continuity equation. The purpose of this paper is to study the stability and convergence about the SHASTA FCT algorithm, which is one of the basic schemes among many FCT techniques, though not in its original form but a slightly modified one for our technical reason. (Our numerical experiments indicate less distinction between the algorithm dealt with here and the original SHASTA FCT one in terms of reproduction ofsharp discontinuities.) The main results are Theorems 1 and 2 concerning the L -stability and the Ljoc-convergence, respectively.
TL;DR: An examination of the convergence and efficiency of general purpose chemical process simulators indicates that there is room for significant improvement through the use of efficient local thermodynamic approximations generated in the context of the specific problem by reference to a full thermodynamic computer package and data base.