Decomposition of systems of nonlinear algebraic equations

A new method for decomposing irreducible subsets, in the solution of systems of nonlinear algebraic equations, is presented. This method consists of two steps: (1) elimination of the nonlinearity from some of the equations by replacing nonlinear expressions by new variables; and (2) formulation of a problem of smaller dimension by tearing the linear subset of equations. It is shown that these modifications do not change considerably the convergence rate of the Newton‐Raphson and Broyden's methods while reducing the problem's dimension. Computer time reduction up to 80% is demonstrated in the examples solved. An algorithm for elimination of nonlinear expressions, which uses Boolean matrices instead of formula manipulation, is also presented.