(Description of Seminar II)
Sep. 8, 1997
On last wednesday, Sep. 3, Dr. Marcin Paprzycki gave us a lecture about Comparisons of Gaussian Elimination Algorithms on a Cray Y-MP. Dr. Marcin Paprzycki is a professor of Computer Science in University of Southern Mississppi. He is also a scientist in Scientific Computing.
Dr. Paprzycki presents the results of various implementations of Gaussian elimination on full matrices on a single processor Cray Y-MP. He shows that the difference between the best versions of level 2 BLAS (Basic Linear Algebra Subprograms) and level 3 BLAS (blocked) implementations is almost negligible, when the manufacture supplied BLAS kernels are used. He suggests that to improve the performance of blocked Gaussian elimination it is possible to utilize Strassen's matrix multiplication algorithm.
First Dr. Paprzycki introduce the soluction of a system of linear equations: Ax = b, where A is an N*N real dense matrix, using Gaussian elimination with partial picoting. Then He discusses the purpose of BLAS. The BLAS standard was designed with two goals in mind: first, to allow portability of codes between differentmachine, and second, to assure the best available quality of performance on a given system. After that He compares the performance of different versions of Gaussian elimination on a single processor Cray Y-MP using manufacturer provided BLAS kernels.