ITR/ACS: Collaborative Research - Linbox: A Generic Library for Seminumeric Black Box Linear Algebra

ITR/ACS：合作研究 - Linbox：半数值黑盒线性代数通用库

• 批准号: 0113463
• 负责人: Austin Lobo
• 金额: $ 2.99万
• 依托单位: Washington College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-15 至 2005-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0113463&HistoricalAwards=false
• 关键词: ITR; ACS; Collaborative; Research; Linbox

The LinBox group of twelve researchers in three countries (USA, France, Canada) proposes research in the design of efficient algorithms for linear algebra, in their implementation in a software library, and in how to interface the library to widely-used scientific computing software. Algorithms will be implemented, and new algorithms designed, for the black box representation of matrices---hence the name LinBox---over entry domains that are either symbolic, that is, exact, or floating point, that is, inexact. The library is generically programmed as C++ template classes with abstract underlying arithmetics; they can be compiled with a variety of fast libraries for the basic field, floating point, and polynomial operations. A server/client interface seamlessly attaches the library to the common general purpose symbolic systems Maple and Mathematica and to the numeric system MatLab. Parallel execution of the implemented algorithms is facilitated. Black box matrices are stored as functions (as linear operators in effect): the matrix is a procedure that takes an arbitrary vector as input and efficiently computes the matrix-times-vector product. Black box linear algebra generalizes sparsity. The LinBox library will contain algorithms for solving singular and non-singular systems of linear equations whose coefficient matrix is given in black box representation. Furthermore, it is proposed to develop fast methods for the rank and the minimal and characteristic polynomial of a black box matrix. Finally, LinBox will contain methods for linear Diophantine problems with black box matrices, such as computing an integral solution to a linear system with integer entries and computing the Smith normal form of an integer matrix.

LinBox 小组由来自三个国家（美国、法国、加拿大）的 12 名研究人员组成，提议研究线性代数的有效算法设计、在软件库中的实现以及如何将库与广泛使用的科学计算软件连接起来。将在符号（即精确）或浮点（即不精确）的入口域上实现矩阵的黑盒表示（因此得名 LinBox）的算法，并设计新的算法。该库通常被编程为具有抽象底层算术的 C++ 模板类；它们可以使用各种快速库进行编译，用于基本域、浮点和多项式运算。服务器/客户端接口将该库无缝连接到通用通用符号系统 Maple 和 Mathematica 以及数字系统 MatLab。促进了所实现的算法的并行执行。 黑盒矩阵存储为函数（实际上是线性运算符）：矩阵是一个以任意向量作为输入并有效计算矩阵乘向量乘积的过程。黑盒线性代数概括了稀疏性。 LinBox 库将包含用于求解奇异和非奇异线性方程组的算法，其系数矩阵以黑盒表示形式给出。此外，建议开发黑盒矩阵的秩以及最小特征多项式的快速方法。最后，LinBox 将包含处理黑盒矩阵线性丢番图问题的方法，例如计算具有整数项的线性系统的积分解以及计算整数矩阵的史密斯范式。