Dr. Paprzycki presented a talk centered on the test results from performance measurements of a new algorithm for the complex symmetric eigenproblem. Many numerical methods for studying chemical reaction problems require the computation of the eigenvalues of very large complex symmetric matrices. Dr. Paprzycki pointed out that most modern state of the art software libraries, such as LAPACK, provide routines for computing the eigenvalues of complex Hermitian and general matrices but lack support for the complex symmetric matrices. The researcher can use other approaches to achieve the computations but for large matrices (order 5000 or more) this becomes extremely time consuming.

 The platforms used in his test were:

• DEC Alpha server
• SGI Power Challenge 8000
• Cray J-916

 Bar-On and Ryaboy formulated the new algorithm code from a proposed algorithm. LAPACK routines used to produce test results for the current method.

Dr. Paprzycki first presented details on the standard method for computing the eigenvalues of general complex matrices followed by a description of the Hermitian eigensolver. He then presented the results from the comparison of the general and Hermitian eigensolvers on the Cray. Next, he presented detail information on the new algorithm and its performance results from the Cray. This was followed with comparisons of all the algorithms on the super scalar machines.

 The results of the test were quite interesting. He showed the performance of the general algorithm on the three machines and we were able to observe that the Cray computer was significantly faster on the Reductions step even though its theoretical peak performance is the second lowest. The SGI, which is RISC based, theoretically should have been twice as fast but was twice as slow in the QR step. In general the Cray results showed the new algorithm to be an improvement over the old method. The performance results on the superscalar were sometimes worst than the old method. But, overall, the new algorithm was superior. This study indicates that further research will be needed. Some areas include enhancing the performance of the Reduction process on the super scalar machines and the tridiagonal QR process on the Cray. The numerical stability of the proposed algorithm also needs further investigation along with implementing an efficient parallel version of the algorithm.