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Verified error bounds for singular solutions of nonlinear systems

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Abstract

We discuss the verification for isolated singular solutions and non-isolated singular solutions with maximum rank deficiency of general nonlinear systems which have all the relevant partial derivatives. Using the border system technique, we present a deflation algorithm to compute verified error bound for such a singular solution of the given system or for a solution of a slight perturbed system, where the solution of the slight perturbed system is near the above singular solution of the given system. By adding certain components of the solution of certain linear system, our algorithm decreases the dimension of the deflation system in each step. Numerical experiments show the performance of our algorithm.

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Authors and Affiliations

  1. School of Science, Changchun University of Science and Technology, Changchun, 130022, China

    Zhe Li

  2. Automated Reasoning and Cognition Key Laboratory of Chongqing, Chongqing, 400741, China

    Zhe Li

  3. College of Mathematics and Statistics, Beihua University, Jilin, 132013, China

    Haifeng Sang

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  1. Zhe Li
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  2. Haifeng Sang
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Li, Z., Sang, H. Verified error bounds for singular solutions of nonlinear systems. Numer Algor 70, 309–331 (2015). https://doi.org/10.1007/s11075-014-9948-3

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  • DOI: https://doi.org/10.1007/s11075-014-9948-3

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