Last Wednesday, Dr. Paprzycki gave us a seminar on computational mathematics--Comparisons of Gaussian Elimination Algorithms on a Cray Y-MP.

Dr. Paprzycki began his topic with the linear equation: Ax = b, where A is NxN real dense matrix. In order to solve this linear equation, one method is discussed. This method is Guassian Elimination.

Then the concept BLAS(Basic Linear Algebra Subprograms) is introduced. The BLAS standard was designed with two goals in mind:

• To allow portability of codes between different machines.
  To assure the best available quanlity of performance on a given system.
  

Moreover, three levels of BLASs were discussed. They are level 1 BLAS, level 2 BLAS, and level 3 BLAS.

Dr. Paprzycki emphasized three possible column oriented variants of Gaussian elimination--dot version, GAXPY version, and SAXPY version. In order to describe these version clearly, the Partitioning graphs of each variant is given and discussed in details. Dr. Paprzycki also showed how the algorithm works based on each version of patitioning strategy.

At last, the statistical data were given based on different block size for every Gaussian Elimination partitioning stratergy. It is shown that when the manufacturer supplied BLAS kernels are used, the difference between the best versions of level 2 and level 3 BLAS implementations is almost negligible.