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Our experiments not only confirm the known behavior of these methods, but also demonstrate their previously undocumented properties (e.g., RCP's transient overshoot under abrupt traffic load changes and JetMax's low utilization in the presence mice flows).
Often, the statistical properties and the behavior of these methods need to be assessed and tested by simulation.
In order to understand the behavior of these methods, it is interesting to perform a review about some words statistical concepts.
Due to this lack of theoretical guarantees and the stochastic behavior of these methods, one must resort to empirical tuning and performance assessments.
To better understand the behavior of these methods in a known situation, we conducted a series of simulation studies with parameters derived from the motivating example.
Observing the convergence behavior of these methods on a simple solid mechanics test and on cardiac models, we highlight the fact that the LM and penalty methods, although often used equivalently in cardiac mechanics, may present significant variations in results.
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However, the numerical behaviors of these methods can differ drastically in practice, and no systematic analysis and comparison have been reported previously for these methods.
All this is useful for correctly, deeply and completely understanding the application scopes, theoretical properties and numerical behaviors of these methods, and is also helpful in designing new methods for solving systems of linear equations.
Quite a lot is known about the behavior of these numerical methods when applied to specific linear problems, but in the case of non-linear problems relatively little research has been performed due to complexities inherent in the non-linear systems.
We also compared the behavior of these three methods in two cases of nonequilibrium demography: Bottleneck expansion and exponential decline.
The experiments were designed with emphasis on the evaluation of the "scaffold-hopping" behavior of the methods.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com