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About this paper
Grace Younes, Alban Quadrat, Fabrice Rouillier
The paper by Younes, Quadrat, and Rouillier systematically analyzes symbolic computation methods for calculating the L∞-norm of linear time-invariant systems. It demonstrates how these methods provide exact solutions and certified accuracy, offering an alternative to numerical approaches, particularly for parameterized and ill-conditioned problems.
Key insights
- Symbolic methods provide certified accuracy and exact solutions, addressing limitations of numerical methods like floating-point precision, convergence issues, and sensitivity to initial conditions.
- Symbolic computation uniquely excels in analyzing parameterized systems by simultaneously exploring the entire parameter space, which is challenging for numerical approaches.
- Despite higher computational complexity, symbolic methods offer guaranteed termination and are particularly advantageous for high-precision requirements or ill-conditioned problems where numerical methods struggle.
Summary by alphaXiv.
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