Solving rank-deficient separable nonlinear equations

Authors:
Yun-Qiu Shen;Tjalling J. Ypma
Affiliations:
Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063, USA;Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063, USA
Venue:
Applied Numerical Mathematics
Year:
2007

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Abstract

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@?R^n. 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.