Structure of a C++ Library for Parallel Accurate Linear Algebra

摘要

Basic matrix and vector operations are very important for the portability, efficiency, and accuracy of many numerical calculations on parallel computers. We require that they shall be as accurate as usual standard functions. In other words our matrix multiplication, e.g., is as accurate as usual real multiplication, i.e. the error is less than 1 ulp (unit last place) for every matrix component. The class library combines two hierarchies, one for the hardware of the distributed or parallel computing environment and one for different matrix and vector structures. It also provides the basic linear algebra subroutines yielding sharp enclosures or approximations with 1 ulp accuracy. It is an extendable toolkit which allows for easy porting but also enables the sophisticated user to instantiate an optimized version for a specific hardware environment.