Algorithms for computer algebra applied to industrial modelling

应用于工业建模的计算机代数算法

• 批准号: 6868-2011
• 负责人: Jeffrey, David
• 金额: $ 2.4万
• 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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568494
• 关键词: Algorithms; computer; algebra; applied; industrial

In science, engineering and in industrial modelling, computers can be used both for numeric and symbolic calculations. Symbolic calculation is often called computer algebra, and the Maple program, developed in Waterloo, is one of several systems widely used for such calculations. In this proposal, new or improved algorithms will be developed which will allow computer algebra systems, specifically Maple, to solve mathematical problems more effectively. The research will emphasize mathematical problems known to arise in industry, but more general problems will also be addressed. The first set of problems concern "large-expression management". One of the important differences between symbolic computing and numerical computing is the way computer memory is handled. For some important problems, symbolic computations generate equations that would take very many pages to print if someone chose to try. Not only are the equations too large for a person to comprehend, but even the computer cannot continue to work with them, and all progress slows to a halt. By implementing new data structures and algorithms, these problems can be alleviated. Another set of problems concerns the analysis of the equations of typical industrial models when they include switching behaviour. Handling the discontinuous behaviour in a general algorithmic way requires software development and mathematical development. Other topics of more general mathematical interest include algorithms for solving nonlinear matrix equations, and further investigations of the properties of the Lambert W function.

在科学、工程和工业建模中，计算机可用于数值和符号计算。符号计算通常称为计算机代数，在滑铁卢开发的 Maple 程序是广泛用于此类计算的几个系统之一。 在该提案中，将开发新的或改进的算法，使计算机代数系统（特别是 Maple）能够更有效地解决数学问题。该研究将强调工业中已知的数学问题，但也将解决更普遍的问题。 第一组问题涉及“大表达管理”。符号计算和数值计算之间的重要区别之一是计算机内存的处理方式。对于一些重要的问题，符号计算生成的方程如果有人选择尝试的话将需要很多页才能打印。这些方程不仅太大，让人无法理解，而且连计算机也无法继续处理它们，所有的进展都会减慢到停止。 通过实施新的数据结构和算法，可以缓解这些问题。 另一组问题涉及对包含开关行为的典型工业模型的方程进行分析。以通用算法方式处理不连续行为需要软件开发和数学开发。 其他更普遍的数学兴趣主题包括求解非线性矩阵方程的算法，以及对 Lambert W 函数属性的进一步研究。