Solving rank-deficient separable nonlinear equations

Separable nonlinear equations have the form A(y)z+b(y)=0 where the matrix A(y) and the vector b(y) are continuously differentiable functions of y∈Rn. Such equations can be reduced to solving a smaller system of nonlinear equations in y alone. We develop a bordering and reduction technique that extends previous work in this area to the case where A(y) is (potentially highly) rank deficient at the solution y∗. Newton's method applied to solve the resulting system for y is quadratically convergent and requires only one LU factorization per iteration. Implementation details and numerical examples are provided.