Network problems, 𝑀-functions and uniformly monotone networks

Porsching, T. A.

doi:10.1090/qam/449911

Network problems, $M$-functions and uniformly monotone networks

Author: T. A. Porsching
Journal: Quart. Appl. Math. 34 (1976), 47-57
MSC: Primary 94A20
DOI: https://doi.org/10.1090/qam/449911
MathSciNet review: 449911
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Abstract: Four classes of network problems—conductive, resistive, conductive boundary value, and resistive boundary value—are considered in this paper. In each case solution of the network problem is tantamount to determining a zero of a nonlinear system of equations. Under certain monotonicity assumptions, it is shown that the nonlinear Gauss-Seidel iterative procedure is globably convergent when applied to these systems.

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