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Article
Solving Rank-deficient Separable Nonlinear Equations
Applied Numerical Mathematics (2007)
  • Tjalling Ypma, Western Washington University
  • Yun-Qiu Shen
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∈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.
Keywords
  • Separable nonlinear equations,
  • Nonlinear variables,
  • Rank-deficient matrices,
  • Bordered matrix,
  • Newton's method,
  • Quadratic convergence,
  • LU factorization
Disciplines
Publication Date
May, 2007
Publisher Statement
Copyright © 2006 IMACS. Published by Elsevier B.V. doi:10.1016/j.apnum.2006.07.025
Citation Information
Tjalling Ypma and Yun-Qiu Shen. "Solving Rank-deficient Separable Nonlinear Equations" Applied Numerical Mathematics Vol. 57 Iss. 5-7 Special Issue for the International Conference on Scientific Computing (2007)
Available at: http://works.bepress.com/tjalling_ypma/3/