✦ LIBER ✦

On the global stabilization of locally convergent algorithms

✍ Scribed by E. Polak

Publisher: Elsevier Science
Year: 1976
Tongue: English
Weight: 476 KB
Volume: 12
Category: Article
ISSN: 0005-1098
DOI: 10.1016/0005-1098(76)90053-4

No coin nor oath required. For personal study only.

✦ Synopsis

It is possible to summarize the schemes, used in the past to stabilize algorithms, in the form of algorithm models. These models serve as patterns for subsequent applications.

Summm'y--There are a number of algorithms in the literature which both theoretically and empirically are known to be only locally convergent. These include such well known algorithms as secant, Newton, quasi-Newton and primal--dual algorithms. Locally, these algorithms tend to be highly efficient. Consequently, it is very desirable to find ways of extending, or modifying, these algorithms, so that they become globally convergent while retaining their attractive local properties. This paper describes a set of techniques which have recently emerged for stabilizing such algorithms and illustrates their application by means of a number of examples.

📜 SIMILAR VOLUMES

On the Convergence of an Algorithm of Jo

On the Convergence of an Algorithm of Jones

✍ Dr. E. A. Catchpole 📂 Article 📅 1981 🏛 John Wiley and Sons 🌐 English ⚖ 261 KB 👁 1 views

Stability Implies Convergence of Cascade

Stability Implies Convergence of Cascade Algorithms in Sobolev Space

✍ Di-Rong Chen; Xiaobo Zheng 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 113 KB

This article proves that the stability of the shifts of a refinable function vector ensures the convergence of the corresponding cascade algorithm in Sobolev space to which the refinable function vector belongs. An example of Hermite interpolants is presented to illustrate the result.  2002 Elsevie

Effects of Asynchronism on the Convergen

Effects of Asynchronism on the Convergence Rate of Iterative Algorithms

✍ Aydin Üresin; Michel Dubois 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 392 KB

In multiprocessor systems, iterative algorithms can be implemented synchronously or asynchronously. Unfortunately, few guidelines exist to make a choice. In this paper, we compare the execution times of an asynchronous iterative algorithm and of its synchronous counterpart. Synchronization overhead

THE STABILITY AND CONVERGENCE CHARACTERI

THE STABILITY AND CONVERGENCE CHARACTERISTICS OF THE DELAYED-X LMS ALGORITHM IN ANC SYSTEMS

✍ G. Chen; T. Sone; N. Saito; M. Abe; S. Makino 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 256 KB

The Delayed-x LMS algorithm is a simplified version of the Filtered-x LMS algorithm, in which the model C of the secondary path C from the adaptive filter output to the error sensor is represented by a pure delay of k samples (the delayed model D) in order to reduce system complexity. However, the s

Local-global analysis on localized non-l

Local-global analysis on localized non-linear shells of revolution

✍ Harintho, H. ;Gould, P. L. 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 435 KB 👁 2 views

Further results on almost sure convergen

Further results on almost sure convergence of the stochastic gradient algorithm

✍ Miloje S. Radenkovic 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 151 KB 👁 2 views

In this paper, we consider the rate of convergence of the parameter estimation error and the cost function for the stochastic gradient-type algorithm. The problem is solved in the case of the minimum-variance stochastic adaptive control. It is proven that the cost function has the rate of convergenc