Avoiding zero pivots in the modified nodal approach

The modified nodal approach has been widely used for formulating network equations. Although this approach is quite general, zero-diagonal elements may exist in the network matrix. When sparse matrix techniques with diagonal pivoting are used to solve these equations, extreme care should be taken so as not to choose a zero-valued pivot. In this paper it is shown that under certain conditions all previously published methods have the potential of generating zero-diagonal pivots, regardless of element values in the network. A simple partitioning and ordering strategy is then presented which guarantees that no zero-valued pivots will be generated for any choice of diagonal pivots. The method has been implemented and well tested and various illustrative examples are included.