An inequality in the theory of networks with monotone elements

Author

Sandberg, Irwin W.

Author_Institution

Dept. of Electr. & Comput. Eng., Texas Univ., Austin, TX, USA

Volume

42

Issue

3

fYear

1995

fDate

3/1/1995 12:00:00 AM

Firstpage

151

Lastpage

155

Abstract

We consider a certain inequality that arises in the study of iterative methods for solving equations in a Hilbert space, and give equivalent characterizations of the inequality. We then show that the inequality is satisfied by the members of a large class of networks of monotone (possibly dynamic) two-terminal elements. This establishes the applicability of a simple algorithm that, for a large class of monotone resistive networks, will converge to a solution of the network equations whenever a solution exists, and that will generate an unbounded sequence of iterates if no solution exists

Keywords

Hilbert spaces; equivalent circuits; iterative methods; multiterminal networks; nonlinear network analysis; Hilbert space; equivalent characterizations; iterative methods; monotone elements; network equations; nonlinear resistive networks; two-terminal elements; unbounded sequence; Differential equations; Helium; Hilbert space; Intelligent networks; Iterative algorithms; Iterative methods; Jacobian matrices; Nonlinear equations; Resistors; Voltage;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.376875

Filename

376875