Inverse Problems for Electrical Networks

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World Scientific, 2000 - Mathematics - 184 pages
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This book is a very timely exposition of part of an important subject which goes under the general name of “inverse problems”. The analogous problem for continuous media has been very much studied, with a great deal of difficult mathematics involved, especially partial differential equations. Some of the researchers working on the inverse conductivity problem for continuous media (the problem of recovering the conductivity inside from measurements on the outside) have taken an interest in the authors' analysis of this similar problem for resistor networks.The authors' treatment of inverse problems for electrical networks is at a fairly elementary level. It is accessible to advanced undergraduates, and mathematics students at the graduate level. The topics are of interest to mathematicians working on inverse problems, and possibly to electrical engineers. A few techniques from other areas of mathematics have been brought together in the treatment. It is this amalgamation of such topics as graph theory, medial graphs and matrix algebra, as well as the analogy to inverse problems for partial differential equations, that makes the book both original and interesting.
 

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Contents

Introduction
1
Circular Planar Graphs
11
Resistor Networks
27
Harmonic Functions
59
Characterization I
83
Adjoining Edges
99
Characterization II
109
Medial Graphs
121
Recovering a Graph
149
Layered Networks
173
References
181
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University of Washington, Seattle

University of Washington, Seattle

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