Newton‐Type Decomposition Methods for Equations Arising in Network Analysis

Abstract

Abstract This paper presents two‐ and multilevel Newton‐type decomposition methods for the iterative solution of large nonlinear systems of equations which arise with a special block‐wise sparsity pattern e.g. in electric circuit analysis. The structure of the systems is widely utilized by the proposed algorithms, which only require soling linear subsystems of the sizes of the diagonal blocks. The methods developed are shown to be locally superlinearly convergent.