Efficient Algorithms and System Interface for Scientific Computation

用于科学计算的高效算法和系统接口

• 批准号: 9503650
• 负责人: Paul Wang
• 金额: $ 11.99万
• 依托单位: Kent State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-09-01 至 1999-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9503650&HistoricalAwards=false
• 关键词: Efficient; Algorithms; System; Interface; Scientific

This project focuses on three related areas: (1) No-missing-term p-adic lifting --- Establishing a faster algorithm for recovering final results in multivariate polynomial operations such as GCD (Greatest Common Divisor) and factoring. The lifting method is most effective when the polynomials involved are sparse, containing just a few of all possible terms. (2) Function Evaluation Optimization and Applications --- Speeding up the repeated evaluation of functions in closed- form formulas through the application of recurrence relations. Nested recurrences called ``chain of recurrences'' will be derived by symbolic computation and applied to increase the evaluation speed of formulas at regular intervals. Application in interactive graphical visualization will be made. (3) Interfacing Distributed Scientific Systems --- Seeking to establish an efficient and standardized protocol to connect different autonomous systems for scientific computation. Such a protocol is necessary to build distributed ``problem solving environments''. By exploiting sparseness and solving systems of linear equations, the p-adic lifting procedure of item (1) will be investigated. Feasibility will be studied. Algorithms will be specified, implemented and applied. For area (2), automatic generation of chain of recurrences (CR) for functions of one or more variables will be implemented, and tested for speed and effectiveness. The numeric properties of CRs will be studied. The technique will be applied to speed up interactive graphical visualization of mathematical functions. For area (3), an efficient and protocol(called MP) will be designed. Libraries in C will support the protocol.

本项目主要关注三个相关领域：（1）无缺失项p-adic提升-建立一个更快的 多元多项式最终结果的恢复算法 最大公因子（Greatest Common Divisor，GCD）和因子分解。的提升方法 当所涉及的多项式稀疏时是最有效的， 只包含所有可能项中的几个。 (2)函数求值优化及应用-利用递推关系式加快封闭式公式中函数的重复求值。 嵌套 被称为“递归链”的递归将由符号 计算和应用，以提高评估速度， 每隔一段时间就有公式。 在交互式应用中 将进行图形可视化。 (3)分布式科学系统接口-寻求 建立一个有效和标准化的协议， 不同的自治系统进行科学计算。 这样的协议对于构建分布式“问题”是必要的 解决环境问题”。 通过利用稀疏性和求解线性系统， 方程，项目（1）的p-adic提升过程将是 研究了 将研究可行性。将指定算法， 实施和应用。 对于区域（2），自动生成 将实现一个或多个变量的函数的递归（CR）， 测试速度和效率。 CR的数字属性为 研究了 该技术将用于加速交互式图形 数学函数的可视化 对于区域（3），一个有效且 协议（称为MP）。 C中的库将 支持协议。