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求是前沿讲座

Intrinsic complexity and its scaling law: from approximation of random vectors and random fields to high frequency waves

报告人：Hongkai Zhao教授

University of California, Irvine

时间:  2018年8月13日（星期一）下午3:00开始

地点: 浙江大学玉泉校区逸夫工商管理楼200-9

摘要：

We characterize the intrinsic complexity of a set in a metric space by the least dimension of a linear space that can approximate the set to a given tolerance. This is dual to the characterization using Kolmogorov n-width, the distance from the set to the best n-dimensional linear space. We start with approximate embedding of a set of random vectors (principal component analysis a.k.a. singular value decomposition), then study the approximation of random fields and high frequency waves. We provide lower bounds and upper bounds for the intrinsic complexity and its explicit asymptotic scaling laws in terms of the total number of random vectors, the correlation length for random fields, and the wave length for high frequency waves respectively.