Developing Linear Algebra Libraries for Supercomputers

主要研究者建议设计和实施 线性代数库，适用于当前广泛使用的 超级计算机 该库旨在提供一套统一的 子程序来解决最常见的线性代数问题 并在一系列架构上高效运行。 这 图书馆，将通过计算机网络免费访问， 不仅可以简化代码开发， 在不同架构的机器之间， 效率，而且还将提供评估工具， 超级计算机性能 图书馆将以 众所周知的和广泛使用的LINPACK和EISPACK包， 线性方程求解，特征值问题，线性最小 正方形。 LINPACK和EISPACK提供了一个重要的 在串行机器上进行科学计算的基础设施，但 它们不是为了利用大量的并行和 矢量架构现在变得可用。 我们建议 重写算法，调用少量 扩展的基本线性代数子程序， 实现诸如矩阵乘法的基本操作， rank-k矩阵更新和求解三角系统。 这些 可以针对每个架构优化操作，但 基本的数值算法将是相同的， 机械.

The Principal Investigator proposes to design and implement linear algebra library for a wide range of currently used supercomputers. The library is intended to provide a uniform set of subroutines to solve the most common linear algebra problems and to run efficiently on a range of architectures. This library, which will be freely accessible via computer network, not only will ease code development, make codes more portable among machines of different architectures, and increase efficiency, but also will provide tools for evaluating supercomputer performance. The library will be based on the well-known and widely used LINPACK and EISPACK packages for linear equation solving, eigenvalue problems, and linear least squares. LINPACK and EISPACK have provided an important infrastructure for scientific computing on serial machines, but they are not designed to exploit the profusion of parallel and vector architectures now becoming available. We propose to rewrite the algorithms in terms of calls to a small number of Extended Basic Linear Algebra Subroutines each of which implements a basic operation such as matrix multiplication, rank-k matrix updates, and solving triangular systems. These operations can be optimized for each architecture, but the underlying numerical algorithms will be the same for all machines.