DocumentCode :
765623
Title :
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
Link To Document :
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