A Hankel norm for quadrature rules solving random linear dynamical systems

详细信息    查看全文

• 作者：Roland Pulch ^{roland.pulch@uni-greifswald.de}
• 关键词：Linear dynamical system ; Random variables ; Quadrature rule ; Polynomial chaos expansion ; Hankel norm ; Uncertainty quantification
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：316
• 期：Complete
• 页码：307-318
• 全文大小：517 K
• 卷排序：316

文摘

In linear time-invariant dynamical systems, random variables are included to quantify uncertainties. The solution can be expanded into a series with predetermined orthogonal basis functions, which depend on the random variables. We define a norm of Hankel-type associated to a truncated series. A quadrature rule or a sampling method yields approximations of the unknown time-dependent coefficient functions in the truncated series. We arrange a Hankel norm for the quadrature technique in this context. Assuming a convergent sequence of quadrature rules, we show that the Hankel norms of the quadrature methods converge to the Hankel norm of the truncated series. Hence a numerical method is obtained to calculate the Hankel norm of the truncated series approximately. Results of numerical computations confirm the convergence property in a test example.