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A simplified rational representation for positive-dimensional polynomial systems and SHEPWM equations solving

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Abstract

The paper is concerned with the improvement of the rational representation theory for solving positive-dimensional polynomial systems. The authors simplify the expression of rational representation set proposed by Tan and Zhang (2010), obtain the simplified rational representation with less rational representation sets, and hence reduce the complexity for representing the variety of a positive-dimensional ideal. As an application, the authors compute a “nearly” parametric solution for the SHEPWM problem with a fixed number of switching angles.

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Authors and Affiliations

  1. School of Mathematics, Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education), Jilin University, Changchun, 130012, China

    Baoxin Shang & Shugong Zhang

  2. College of Science, Northeast Electric Power University, Jilin, 132012, China

    Baoxin Shang

  3. College of Science, Northeast Forestry University, Harbin, 150040, China

    Chang Tan

  4. School of Mathematics, Liaoning University, Shenyang, 110036, China

    Peng Xia

Authors
  1. Baoxin Shang
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  2. Shugong Zhang
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  3. Chang Tan
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  4. Peng Xia
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Corresponding author

Correspondence to Shugong Zhang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11671169 and partially by Scientific Research Fund of Liaoning Provincial Education Department under Grant No. L2014008.

This paper was recommended for publication by Editor LI Hongbo.

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Shang, B., Zhang, S., Tan, C. et al. A simplified rational representation for positive-dimensional polynomial systems and SHEPWM equations solving. J Syst Sci Complex 30, 1470–1482 (2017). https://doi.org/10.1007/s11424-017-6324-0

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  • DOI: https://doi.org/10.1007/s11424-017-6324-0

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