Solving separable nonlinear equations with jacobians of rank deficiency one

Authors:
Yun-Qiu Shen;Tjalling J. Ypma
Affiliations:
Department of Mathematics, Western Washington University, Bellingham, WA;Department of Mathematics, Western Washington University, Bellingham, WA
Venue:
CIS'04 Proceedings of the First international conference on Computational and Information Science
Year:
2004

Citing 3
Cited 1

Solving nonlinear systems of equations with only one nonlinear variable

Journal of Computational and Applied Mathematics
Fundamentals of matrix computations

Fundamentals of matrix computations
The differentiation of pseudoinverses and nonlinear least squares problems whose variables separate.

The differentiation of pseudoinverses and nonlinear least squares problems whose variables separate.

Solving rank-deficient separable nonlinear equations

Applied Numerical Mathematics

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Abstract

Nonlinear systems of equations of the separable form A(y)z + b(y) = 0, with only one nonlinear variable y∈ℝ, can be reduced to a single nonlinear equation in y. We develop a technique for the case in which A(y) has rank deficiency one. The method requires only one LU factorization per iteration and is quadratically convergent. Numerical examples and applications are provided.