Solving rank-deficient separable nonlinear equations (Q881481)

The paper is concerned with solving systems of nonlinear equations having a special form and called separable system. Such equations arise in many applications [see \textit{G. H. Golub} and \textit{V. Pereyra}, Inverse Probl. 19, No.~2, R1--R26 (2003; Zbl 1022.65014)]. For solving separable systems the authors propose a method which is a variant of the projection method. This new method combines bordering with reduction technique. Under suitable conditions the Jacobian matrix of the reduced system is nonsingular and then the Newton's method can be applied. The method requires only one LU factorization in each iterative step. The conclusions of the analysis are formulated into an algorithm for solving separable systems. Two numerical examples are discussed.