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On locating the zeros and poles of a meromorphic function. (English) Zbl 1490.65090

Summary: On the basis of the generalized argument principle, here we develop a numerical scheme for locating zeros and poles of a meromorphic function. A subdivision-transformation-calculation scheme is proposed to ensure the algorithm stability. A novel feature of this algorithm is the ability to estimate the error level automatically. Numerical examples are also presented, with an emphasis on potential applications to plasma physics.

MSC:

65H05 Numerical computation of solutions to single equations
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)

Software:

minpack; SciPy; ZEAL; NLEVP
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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