ALGORITHMS: Collaborative Research: New Contributions to the Theory and Practice of Programming Linear Algebra Libraries

虽然许多见解很容易证明密集线性代数运算，有纳塔尔的扩展，影响稀疏直接方法。拟议项目的目标是对所有这些见解采取统一的方法，努力将线性代数库的软件架构建立在坚实的科学基础上。 我们将进行一个为期一年的试点项目，将证明：（1）系统的方法可以用来获得高效率的核心专门密集线性代数运算中遇到的稀疏直接方法;（2）抽象程序接口，已被证明允许高-密集线性代数运算的性能实现将被扩展到应用于被视为分层矩阵的稀疏矩阵;（3）我们将为稀疏矩阵作为层次矩阵的数学描述奠定基础，我们相信这将允许推导方法扩展到层次矩阵上的运算。

While many of the insights are readily demonstrated for dense linear algebra operations, there are natal extensions that impact sparse direct methods. It is the goal of the proposed project to pursue a unified approach to all of these insights in an effort to put software architectures of linear algebra libraries for this domain of operations on a solid scientific footing. We will undertake a one year pilot project that will demonstrate the following: (1) The systematic approach can be used to derive highly efficient kernels for specialized dense linear algebra operations that are encountered in sparse direct methods; (2) The abstract program interface that has been demonstrated to allow high-performance implementation of dense linear algebra operations will be extended to apply to sparse matrices that are viewed as hierarchical matrices; (3) We will lay the foundation for a mathematical description of sparse matrices as hierarchical matrices which we believe will allow the derivation methods to be extended to operations on hierarchical matrices.