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Solving Separable Nonlinear Equations with Jacobians of Rank Deficiency One

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Computational and Information Science (CIS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3314))

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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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Western Washington University, Bellingham, WA, 98225-9063, USA

    Yun-Qiu Shen & Tjalling J. Ypma

Authors
  1. Yun-Qiu Shen
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  2. Tjalling J. Ypma
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Editor information

Editors and Affiliations

  1. School of Electronic Science and Technology, Anhui University, Hefei, Anhui, China

    Jun Zhang

  2. College of Science, Donghua University, 1882 Yan’an Xilu Road, 20051, Shanghai, China

    Ji-Huan He

  3. BASICS, Department of Computer Science and Engineering, Shanghai Jiao Tong University, 200030, Shanghai, China

    Yuxi Fu

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© 2004 Springer-Verlag Berlin Heidelberg

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Shen, YQ., Ypma, T.J. (2004). Solving Separable Nonlinear Equations with Jacobians of Rank Deficiency One. In: Zhang, J., He, JH., Fu, Y. (eds) Computational and Information Science. CIS 2004. Lecture Notes in Computer Science, vol 3314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30497-5_16

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  • DOI: https://doi.org/10.1007/978-3-540-30497-5_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24127-0

  • Online ISBN: 978-3-540-30497-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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