Monte Carlo estimators for the Schatten \(p\)-norm of symmetric positive semidefinite matrices

DOI10.1553/etna_vol55s213zbMath1487.65046arXiv2005.10174OpenAlexW3026754706MaRDI QIDQ2672173

Alen Alexanderian, Ethan Dudley, Arvind K. Saibaba

Publication date: 8 June 2022

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.10174

zbMATH Keywords

Chebyshev polynomialsSchatten \(p\)-normoptimal experimental designMonte Carlo estimator

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Monte Carlo methods (65C05) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (1)

Randomized Low-Rank Approximation of Monotone Matrix Functions

Uses Software

• SuiteSparse
• SparseMatrix

Cites Work

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• Improved bounds on sample size for implicit matrix trace estimators
• Approximation of monomials by lower degree polynomials
• Spectrum estimation from samples
• Probability essentials.
• Inequalities for variances of some functions of random variables
• Numerical Methods for Large Eigenvalue Problems
• Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
• Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations
• Randomization and Reweighted $\ell_1$-Minimization for A-Optimal Design of Linear Inverse Problems
• Fast Estimation of $tr(f(A))$ via Stochastic Lanczos Quadrature
• High-Dimensional Probability
• Inverse Problem Theory and Methods for Model Parameter Estimation
• Efficient D-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems
• Rational approximation of 𝐱ⁿ
• Spectrum Approximation Beyond Fast Matrix Multiplication: Algorithms and Hardness
• On Approximating Matrix Norms in Data Streams
• Approximating Spectral Sums of Large-Scale Matrices using Stochastic Chebyshev Approximations
• On Sketching Matrix Norms and the Top Singular Vector
• A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion
• Is Gauss Quadrature Better than Clenshaw–Curtis?
• Functions of Matrices
• A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines

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