Estimation of Condition Number of Quasi-static Darwin Model

Shingo Hiruma; Takeshi Mifune; Tetsuji Matsuo

doi:10.1109/TMAG.2024.3464113

Estimation of Condition Number of Quasi-static Darwin Model

Computational Engineering, Finance, and Science 2026-08-04 v1

Authors: Shingo Hiruma , Takeshi Mifune , Tetsuji Matsuo

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Abstract

This study discusses the estimation of the condition number of the quasi-static Darwin model, which is shown to be a nearly singular system of equations with a large kernel derived from the gauge invariance of full Maxwell's equations. Inequality evaluations for a minimum nonzero singular value, maximum singular value, and condition number for a nearly singular system of equations and its augmented system are provided. This discussion reveals the nearly singular nature of the Darwin model and proves the effectiveness of the augmented system method for solving the Darwin model.

Keywords

condition number quasi-static Darwin model nearly singular system gauge invariance Maxwell's equations augmented system

Cite

@article{arxiv.2608.03380,
  title  = {Estimation of Condition Number of Quasi-static Darwin Model},
  author = {Shingo Hiruma and Takeshi Mifune and Tetsuji Matsuo},
  journal= {arXiv preprint arXiv:2608.03380},
  year   = {2026}
}