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March 15, 2024Open Access

Structural Preprocessing Method for Nonlinear Differential-Algebraic Equations Using Linear Symbolic Matrices

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Authors

TOTaihei OkiHokkaido University of EducationYSYu-Jin SongYonsei University

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Implication

Theoretical study demonstrates fast regularization in nonlinear differential-algebraic equations, highlighting scalable preprocessing for large-scale dynamical systems.

Key Points

  • A novel regularization method successfully resolves singular system Jacobian matrices in differential-algebraic equations while globally preserving their original solution sets.
  • Theoretical framework approximates the system Jacobian using rank-1 coefficient mixed matrices, providing a combinatorial algorithm to find a singularity certificate rapidly.
  • Numerical experiments confirm this combinatorial formulation executes efficiently on large-scale differential-algebraic equations, enabling practical structural preprocessing.

Cite This Study

Oki et al. (2024) studied this question.

synapsesocial.com/papers/68e73ed6b6db6435876b8755https://doi.org/10.48550/arxiv.2403.10260
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