Exploratory Experimentation and Computation in the Mathematical Sciences: Theory and Practice

数学科学中的探索性实验和计算：理论与实践

• 批准号: DP140101417
• 负责人: Prof Richard Brent
• 金额: $ 28.99万
• 依托单位: The University of Newcastle
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-05-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140101417
• 关键词: Exploratory; Experimentation; Computation; Mathematical; Sciences

Seemingly disparate mathematical research projects rely on subtle experimental mathematics methods, and have unveiled weaknesses in current computer algebra systems and symbolic-numeric-graphic tools. The project attacks issues of efficiency, effectiveness, reliability, and certifiability in high-precision mathematical and scientific computation. This will be done by developing enhanced tools for advanced computation of special functions driven by pursuit of challenging research problems. The focus is on tractable components that arose in prior research on effective high-precision algorithms for multiple integrals, such as arise throughout mathematical physics, number theory and elsewhere.

看似完全不同的数学研究项目依赖于微妙的实验数学方法，并暴露了当前计算机代数系统和符号-数字-图形工具的弱点。该项目解决了高精度数学和科学计算中的效率、有效性、可靠性和可证实性问题。这将通过为特殊功能的高级计算开发增强的工具来实现，这些工具是由追求具有挑战性的研究问题驱动的。重点是在先前关于多重积分的有效高精度算法的研究中出现的易处理的组件，例如在整个数学物理、数论和其他方面出现的组件。