Matrix Computations Draw International Group to China

June 23, 1999

Zhaojun Bai, Lothar Reichel, and Axel Ruhe

An international symposium on large-scale matrix computations was held in Dalian, a city on the northeastern coast of China, during the first week of August 1998. The meeting was organized by Zhongxiao Jia, an enthusiastic young researcher who received his degree in Bielefeld, Germany, and for the past two years has been a professor of applied mathematics at Dalian University of Science and Technology. Dalian is among the Chinese universities receiving extra research resources from the central government. Making the most of these opportunities, Zhongxiao Jia has initiated vibrant activity in computational mathematics in his department, and several of his students presented talks at the symposium. It is heartening that some Chinese students, on completing their education outside China, are returning to their native country and taking the opportunity to initiate impressive activity in research and teaching.

About 20 participants in the symposium were from outside China, and about 30 had come from cities in China other than Dalian. Some of the visitors, Chinese living abroad, were amazed to see how much their native country had changed in just a few years. Among them was Zhaojun Bai, who had a hard time finding the house where he grew up among the newly built highways and highrises.

Xiaofei Qu, director for science and technology in the Dalian government, and Gengdong Cheng, president of Dalian University of Science and Technology, spoke at the opening ceremony of the symposium. On the technical program were talks by well-established senior researchers, as well as by many young researchers and graduate students.

Many of the speakers described new iterative methods for the solution of large linear systems of equations or new analyses of known iterative methods, demonstrating that the development of iterative methods and preconditioners remains a very active area of research. Martin Gutknecht, for example, discussed the behavior of the residual vectors generated by the full orthogonalization and GMRES methods. Continuing the theme, Daniela Calvetti showed how an adaptive preconditioner can be determined during restarted GMRES iteration, Qiang Ye discussed a mixed-product Krylov subspace method for solving nonsymmetric linear systems, and Daniel Skoogh presented an adaptive-band Krylov subspace method for solving linear systems of equations with several right-hand sides. Baijiang Zhong described a new hybrid iterative method based on the GMRES algorithm, and Jianwei Cao discussed preconditioners with application to oil reservoir simulation.

A large number of talks were concerned with the computation of eigenvalues and eigenvectors of large matrices, and several speakers considered applications of large eigenvalue problems. Symposium host Zhongxiao Jia presented examples in which his refined Arnoldi algorithm gave considerably improved performance for problems that require many restarts. One of his students, Guizhi Chen, discussed the use of harmonic Ritz values in the refined Arnoldi method. Preconditioning and rational Krylov subspace, implicitly restarted Arnoldi, and Jacobi-Davidson methods were discussed by Andrew Knyazev, Axel Ruhe, Danny Sorensen, and Henk van der Vorst, respectively. As illustrated by this set of talks, the development of algorithms for the computation of a few eigenvalues of a large matrix is a vigorous area of scientific computing.

In several cases, applications of large eigenvalue problems have led to new algorithmic developments. At the symposium, Jane Cullum and Roland Freund discussed circuit simulation, Eva Lundstr�m considered signal processing, and Lothar Reichel described liquid crystal modeling; Kesheng Wu described the computation of eigenvalues of the Schr�dinger operator. As shown in these talks, interesting recent work in this area has been motivated by requirements of specific applications.

Of the numerous other topics discussed at the conference, space restrictions allow us to mention only a few: computational aspects of the efficient factorization of large sparse matrices, the subject of talks by Iain Duff, Hai-Xiang Lin, and Xiaoge Wang, and computation of the trace of the inverse of a large matrix, described by Zhaojun Bai.

In summary, the symposium provided a forum for the discussion of recent developments in large-scale matrix computations and gave researchers from China, Europe, and the U.S. the opportunity to establish a dialog and perhaps to undertake collaborative research projects.

The symposium was supported by several Chinese agencies, including the Ministry of Education, the National Natural Science Foundation, the K.C. Wang Education Foundation--Hong Kong, the State Key Project "Scientific and Engineering Computing," the Association of Dalian Science and Technology, and the Dalian University of Science and Technology.

Zhaojun Bai is an associate professor of mathematics at the University of Kentucky, Lothar Reichel is a professor of mathematics at Kent State University, and Axel Ruhe is a professor of mathematics at Chalmers Technical University, Sweden.

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