Variable dimension algorithms for solving resistive circuits

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Abstract
Variable dimension algorithms are a recent class of globally convergent algorithms for solving sets of non‐linear equations. This paper introduces a simple circuit‐theoretical interpretation of the underlying idea and describes its advantages as compared to the globally convergent methods better known in circuit theory, such as the generalized Katzenelson algorithm. the convergence criterion is also stated in topological terms, and these conditions turn out to coincide with very general sufficient conditions for existence of solutions. the approach taken here can therefore be seen as a constructive way to prove solvability of resistive circuits. the paper also discusses how to implement the algorithm in an efficient and practical way.

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