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Event(s) on January 2010
- Thursday, 7th January, 2010
Title: Linear Algebra Algorithms as Dynamical Systems: Orthogonal Polynomials, Moments, Measure Deformation, Dynamical System, and SVD Algorithm Speaker: Prof. Moody CHU Ten-Chao, Department of Mathematics, North Carolina State University, USA Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Iterates generated from discrete dynamical systems such as the QR algorithm and the SVD algorithm are time-1 samples of solutions to the Toda lattice and the Lotka-Volterra equation, respectively. In this talk we present some recent discoveries that connect diverse topics such as soliton theory, integrable systems, continuous fractions, tau functions, orthogonal polynomials, Sylvester identity, moments, and Hankel determinants together. Of particular interest are the three facts that 1. Each of the Toda lattice and the Lotka-Volterra equation governs the evolution of a certain class of orthogonal polynomials whose orthogonality is determined by a specific time-dependent measure. 2. Since the measure deformation is explicitly known, moments can be calculated which, when properly assembled, lead to the abstract but literal conclusion that the iterates of the QR algorithm and the SVD algorithm can be expressed in closed-form! 3. Hankel determinantal solutions are too complicated to be useful. However, a “smart” integrability-preserving discretization of the Lotka-Volterra equation can yield a new SVD algorithm - Friday, 15th January, 2010
Title: ICM Colloquium: IDR --- A Brief Introduction Speaker: Prof. Martin H. Gutknecht, ETH Zurich, Switzerland Time/Place: 16:30 - 17:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: The Induced Dimension Reduction (IDR) method is a Krylov space method for solving linear systems that was first developed by Sonneveld around 1979 and documented on three and a half pages of a 1980 proceedings paper by Wesseling and Sonneveld. Soon after IDR, Sonneveld introduced his widely applied Conjugate Gradient Squared (CGS) algorithm. Then, in 1990, van der Vorst suggested Bi-CGSTAB, which he claimed to improve both those methods. Bi-CGSTAB has become a method of choice for nonsymmetric linear systems, and it has been generalized in various ways in the hope of further improving its reliability and speed. Among these generalizations there is the ML(k)BiCGSTAB method of Yeung and Chan, which in the framework of block Lanczos methods can be understood as a variation of Bi-CGSTAB with right-hand side block size 1 and left-hand side block size k. In 2007 Sonneveld and van Gijzen reconsidered IDR and generalized it to IDR(s), claiming that IDR is equally fast but preferable to Bi-CGSTAB, and that IDR(s) may be much faster than IDR(1) approx IDR. It turned out that IDR(s) is closely related to BiCGSTAB if s = 1 and to ML(s)BiCGSTAB if s > 1. In 2008, a new, particularly ingenious and elegant variant of IDR(s) has been proposed by the same authors. In this talk we first try to explain the basic, seemingly quite general IDR approach, which differs completely from traditional approaches to Krylov space methods. Then we compare the basic properties of the above mentioned methods and discuss some of their connections. - Tuesday, 26th January, 2010
Title: Continuous methods in optimization for linear programming Speaker: Mr. SUN Liming, MATH Dept, Hong Kong Baptist University, Hong Kong Time/Place: 14:30 - 15:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In this report, we propose two continuous methods for linear programming. The first one, the continuous path-following method can be viewed as the continuous realization of some existing interior point methods. The second one, projective dynamic system is based on variational inequality method for linear programming. The continuous trajectories resulting from these continuous methods are the solutions of ordinary differential equations. The existence and convergence properties of these solutions are analyzed and discussed in details. - Wednesday, 27th January, 2010
Title: An Efficient Algorithm for a Two-ingredients Flow with Stiff Source Speaker: Prof. LI Ruo, School of Mathematical Sciences, Peking University, China Time/Place: 14:30 - 15:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: We developed an efficient algorithm to solve an engineering problem with two ingredients in the flow and extreme stiff source term. The convection terms in the flow equations are solved by the "standard" method. The stiff source term is clearly erased by a sequence of very special techniques based on ideas from mathematical and physical side.