演講公告

新聞標題：　( 2010-03-30 )

• 演講主題：Linear Algebra Algorithms as Dynamical Systems: Orthogonal Polynomials, Moments, Measure Deformation, Dynamical Systems, and SVD Algorithm

• 主講人：朱天照 教授（北卡州立大學數學系）

• 演講日期：99年3月30日(星期二)<br> 下午3:10 –4:00

• 演講地點：(光復校區)科學一館223室

• 茶會時間：當天下午1:30科學一館205室

• 摘要內容：
  

  Abstract: 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, functions, orthogonal polynomials, Sylvester identity, moments, and Hankel determinants together. Of particular interest are the three facts that
  (a) 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.
  (b) 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!
  (c) Hankel determinantal solutions are too complicated to be useful. However, a “smart” integrabilitypreserving discretization of the Lotka-Volterra equation can yield a new SVD algorithm.

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