Last friday, Dr Paprzycki gave us high performance seminar on high performance eigensolver for complex symmetric matrices.

At first, Dr paprzycki presented a practical application---chamical reaction modelling. Using reduction method, this problem can be transformed to the eigenvalue solving problem. Then he list some typical solving methods and results about real/complex, hermitian and symmetric matrices.

For the nonsymmetric, complex general matrices, the efficiency of reducing to upper heisenburg matrix is O(n^3), and the efficiency of finding eigenvalue is O(n^3). For the real symmetric, complex hermitian matrices, the efficiency of reducing to a tridiagonal matrix is O(n^2), and the efficiency of finding eigenvalue is O(n^2).

He then present a new algorithm which is a direct and efficient eigensolver for complex symmetric matrices. The new algorithm with other algorithms are compared on several different computers. A lot of results of comparing are presented.

The comparing includes: (1) in different super-computers, (2) with different models, (3) with different algorithms, (4) with different parameters.

At last, Dr Paprzycki show that the new algorithm is best for single computer system. The most important thing learning from this seminar is the researching methods rather than the knowledge itself.

Last Update: 1/23/98
Web Author: Zizhong Wang
The report is for Dr Paprzycki@ marcin.paprzycki@ibspan.waw.pl or@ Home Page