Design and Analysis of Algorithms for Structured Nonlinear Problems

结构化非线性问题的算法设计与分析

• 批准号: RGPIN-2015-05481
• 负责人: Corless, Robert
• 金额: $ 1.75万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=634880
• 关键词: Design; Analysis; Algorithms; Structured; Nonlinear

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.

现代科学在很大程度上依赖于根据理论模型运行的情景的计算机模拟。如果模拟在“测试”阶段表现出预期的效果，那么人们对该模型背后的理论的信心就会增强。如果这些模拟能够预测真实世界的行为，特别是如果它令人惊讶(或者如果出乎意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，而不仅仅是学术上的重要性。但在计算机上进行这样的模拟往往涉及求解潜在的大量非线性方程。要做到足够可靠和高效，以便能够实时做出预测，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，使此类解决方案更可靠、更高效。