研究目的
To present a flexible and effective algorithm for finding complex roots and poles in a wide class of analytic functions within any arbitrarily shaped search region, improving computational efficiency and accuracy.
研究成果
The proposed algorithm is effective for finding complex roots and poles in a wide class of analytic functions within any arbitrarily shaped search region. It is shown to be up to three orders of magnitude faster and requires significantly fewer function evaluations compared to alternative techniques. The method's reliability and efficiency are confirmed through numerical tests.
研究不足
The algorithm's effectiveness depends on the initial mesh step ?r being sufficiently small to ensure proper discretization. There is no clear recipe for a priori estimation of the initial sampling for an arbitrary function, which may require user experimentation.
1：Experimental Design and Method Selection:
The algorithm involves sampling a function at the nodes of a regular mesh and analyzing the function phase to identify candidate regions for roots/poles. A discretized Cauchy’s argument principle is then used for verification. A self-adaptive mesh can be applied to improve accuracy.
2：Sample Selection and Data Sources:
The method can be applied to any analytic function, including those with singularities or branch cuts, in any arbitrarily shaped search region.
3：List of Experimental Equipment and Materials:
The algorithm was implemented in the MATLAB environment, and tests were performed using an Intel(R) Core i7-2600K CPU 3.40-GHz, 16-GB RAM computer.
4：40-GHz, 16-GB RAM computer.
Experimental Procedures and Operational Workflow:
4. Experimental Procedures and Operational Workflow: The process includes sampling the function, analyzing phase changes to identify candidate regions, verifying roots/poles using a discretized Cauchy’s argument principle, and optionally applying a self-adaptive mesh for refinement.
5：Data Analysis Methods:
The accuracy and computational efficiency of the method are compared with alternative techniques through numerical tests.
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