Developing Linear Algebra Libraries for Supercomputers

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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.