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Mathematical Sciences > Operations Research > Advanced Mathematical Software
Research in Advanced Mathematical Software

Our groups are currently focusing on three main areas:

The first is high performance computational kernels on serial, shared-memory parallel and message-passing parallel hardware platforms. These are basic scientific algorithmic building blocks such as matrix multiply or fast fourier transforms. Our aim is to provide novel implementations which produce the fastest possible code for IBM computers. We have supported the IBM Product Engineering and Scientific Subroutine Library (ESSL) for more than ten years. We also provide fast implementations of math intrinsic functions for the popular (free) AIX Mathematical Acceleration SubSystem (MASS).

The second activity involves advanced Optimization software for solving linear, integer, and non-linear programming problems. Our aim is to produce software that can solve the most challenging problems which IBM customers (or our sister group the Optimization Center) need solved. To do this, we may also have to develop new optimization algorithms. The results of this research are then transferred to the IBM product Optimization Solutions and Library (OSL). Current areas of research include simplex and barrier methods for parallel computers, non-linear software and software to make optimization easier to use.

The third area of research in this group touches several aspects of direct solution of sparse linear systems and includes developing novel ordering algorithms and fast serial and parallel algorithms for factoring sparse matrices. This research to date has resulted in Watson Sparse Matrix Package (WSMP), a high-performance, robust, and easy to use software package for solving large sparse symmetric systems of linear equations.

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