Developing Accuracy Assured High Performance Numerical Libraries for Eigenproblems
Abstract
Eigenproblem is one of essential numerical problems for several numerical simulations. Its accuracy, however, is not well-assured in many conventional numerical computations. Basic Linear Algebra Subprograms (BLAS) is a frequently used to perform linear algebra computations. Ensuring the accuracy of the computational results of BLAS operations is a still crucial problem now. Even in solving linear equations using LAPACK is also a typical example, because LAPACK is rich in BLAS operations, especially matrix-matrix multiplication (MMM) operations for solving linear equations.
With respect to this background, we focus on the following three topics:
(1) Developing an accuracy assured numerical libraries for eigenproblems;
(2) Development of high-performance implementation and auto-tuning (AT) technology for the developed accuracy assured numerical libraries;
(3) Discussing an extension for non-liner problems based on obtained knowledge of accuracy assured algorithms.