Analysis of stochastic Lanczos quadrature for spectrum approximation
Abstract
The cumulative empirical spectral measure (CESM) \Phi[\mathbf{A}] : \mathbb{R} \to [0,1]of a n\times nsymmetric matrix \mathbf{A}is defined as the fraction of eigenvalues of \mathbf{A}less than a given threshold, i.e., \Phi[\mathbf{A}](x) := \sum_{i=1}^{n} \frac{1}{n} {\large\unicode{x1D7D9}}[ \lambda_i[\mathbf{A}]\leq x] Spectral sums \operatorname{tr}(f[\mathbf{A}])can be computed as the Riemann--Stieltjes integral of f..
Paper Details
Title
Analysis of stochastic Lanczos quadrature for spectrum approximation
Published Date
May 13, 2021
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