报告人: Arieh Iserles教授 （剑桥大学）

报告题目: Tridiagonal, skew-symmetric differentiation matrices

报告摘要：Using spectral methods for time-dependent problems, there is significant advantage in choosing an orthogonal system with a skew-symmetric differentiation matrix. Further advantage follows if this matrix is also tridiagonal: examples are the Fourier basis and the basis of Hermite functions. In this talk we explore this question further, demonstrate a procedure to generate differentiation matrices which are both skew-symmetric and tridiagonal — but not necessarily consistent with orthogonality — and prove a no-go theorem: suppose that the orthogonal system is $\{G(x)p_n(x)\}_{n\geq0}$, where $G$ is meromorphic and nonzero, while each $p_n$ is an $n$th-degree polynomial. Then the only such system which yields a tridiagonal skew-symmetric matrix is that of Hermite functions. We also introduce a general mechanism to generate orthogonal systems of this kind.

报告人简介：Arieh Iserles教授是国际著名数值分析学家、剑桥大学终身教授、国际著名期刊《Acta Numerica》,《IMA Journal of Numerical Analysis》的主编，以及国际著名计算数学期刊《Numerische Mathematik》, 《Advances in Computational Mathematics》,《Foundations of Computational Mathematics》的编委，在高振荡数值分析、微分方程的数值解法、几何数值积分、逼近论等领域的研究和创新方面做出了卓越的贡献。

报告时间: 2017年12月16日（星期六）下午2:00-3:00

报告地点: 科技楼南楼702室