Design and Analysis of Algorithms for Structured Nonlinear Problems

现代科学在很大程度上依赖于计算机模拟的情况下，根据理论模型的行为。如果模拟在“测试”阶段的表现符合预期，那么对模型理论的信心就会得到加强。如果模拟能够预测真实世界的行为，特别是如果它令人惊讶（或者如果无法预料，可能会付出生命或金钱的代价），那么它们就具有社会效益，而不仅仅是学术意义。 但是在计算机上进行这样的模拟通常涉及到求解潜在的大量非线性方程。要做到足够可靠和有效，以便能够在真实的时间内做出预测，这可能是非常具有挑战性的（取决于主题领域）。该项目旨在产生新的算法，使这些解决方案更可靠，更有效。

Modern science relies very heavily on computer simulation of scenarios that behave according to theoretical models. If the simulations perform as expected in the “testing” phase, then confidence in the theory underlying the model is bolstered. If the simulations manage to predict real-world behavior, especially if it is surprising (or might potentially cost lives or money if unanticipated) then they are of social benefit, not just academic importance.  But carrying out such simulations on a computer often involves solving a potentially large number of nonlinear equations. Doing so reliably and efficiently enough that predictions can be made in real time can be (depending on the subject area) extremely challenging. This project aims at producing new algorithms to make such solutions both more reliable and more efficient.