Structured matrices and tensors


Ng, Michael, Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.


The Third International Conference on Structured Matrices and Tensors was held from January 19 to January 22, 2010 at Hong Kong Baptist University, The Hong Kong Polytechnic University, and Chinese University of Hong Kong. It was a sequel to a similar conference held in Hong Kong (in 2002 and 2006). The conference had two major objectives: (i) to improve the dialogue and collaboration between matrix/tensor theoreticians and the computational scientists and (ii) to reduce the gap between the researchers working on the fundamentals and those working on real-life applications, with the aim in mind that emerging applications will stimulate new theoretical research and that better theoretical tools in turn can be exported back to various fields of application.

The special issue contains nine papers from invited speakers of the conference. The contributions cover different aspects in the research field of structured matrices and tensors with applications. The first five papers [1-3, 5, 6] are devoted to matrix computation, and the last four papers [7-10] are devoted to tensor computation. Noschese and Reichel [1] study generalized circulant Strang-type preconditioners for structured matrices. Chun and Park [2] design two decoupling techniques to speed-up the LLL-aided OSIC algorithm for solving clustered integer least squares problems related to structured matrices in communication. Cavoretto et al.[3] study spectral analysis and preconditioning techniques for radial basis function collocation matrices, which have almost a multilevel Toeplitz structure. Stoll and Wathen [4] propose preconditioners for the saddle point problems that arise when a primal dual active set method is used for solving optimal control problems with partial differential equations. Yin et al.[5] develop fast adaptively accelerated Arnoldi method for computing PageRank where the weights are calculated on the basis of the current residual of the approximate PageRank vector. Lee et al.[6] develop fast exponential time integration scheme based on Toeplitz structure for option pricing with jumps; the shift-and-invert Arnoldi method is employed to produce fast approximations to the computation. Savostyanov et al.[7] propose a fast algorithm based on the cross approximation of Gram matrices, for mode rank truncation of the result of a bilinear operation on three tensors given in the Tucker or canonical form. Ling et al.[8] present some bounds on the optimal value of a quadratically constrained multivariate biquadratic polynomial optimization problem via approximately solving the related bilinear semidefinite programming relaxation. Hackbusch et al.[9] study eigenvalue problems for elliptic operators in higher dimensions and, for their discretizations, admit approximations by tensor products of low rank and derive conditions providing an exponential decrease of the error with respect to the rank. Li et al.[10] develop image segmentation methods for hyperspectral space object material identification and study the segmentation with a hyperspectral image data denoising/deblurring model.

On behalf of the organizers of the conference, we would also like to thank the following sponsors of the conference for their generous support: Lee Hysan Foundation, Hong Kong Baptist University, Center for Mathematical Imaging and Vision, Hong Kong Baptist University, Institute for Computational Mathematics, Hong Kong Baptist University, The AMSS-PolyU Joint Research Institute for Engineering and Management Mathematics, The Hong Kong Polytechnic University.