Triangular Decomposition Methods for Solving Reducible Nonlinear Systems of Equations

@article{Dennis1994TriangularDM,
title={Triangular Decomposition Methods for Solving Reducible Nonlinear Systems of Equations},
author={John E. Dennis and Jos{\'e} Mario Mart{\'i}nez and Xiaodong Zhang},
journal={SIAM Journal on Optimization},
year={1994},
volume={4},
pages={358-382}
}

Abstract. This paper generalizes to the nonlinear case a standard way to solve general sparse systems of linear equations. In particular, Duff [J. Inst. Math. Appl., 19 (1977), pp. 339-342] has suggested that row and column interchanges be applied to permute the coefficient matrix of a linear system into block lower triangular form., The linear system then can be solved by using the associated block Gauss-Seidel or forward block substitution scheme. This is the approach taken in the Harwell… CONTINUE READING