Approximating Spectral Sums of Large-Scale Matrices using Stochastic Chebyshev Approximations
From MaRDI portal
Publication:5350223
DOI10.1137/16M1078148zbMath1372.65126arXiv1606.00942OpenAlexW2750001921MaRDI QIDQ5350223
Dmitry M. Malioutov, Jinwoo Shin, Insu Han, Haim Avron
Publication date: 28 August 2017
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1606.00942
algorithmspectral functionSchatten \(p\)-normEstrada indexChebyshev approximationmatrix computationnumerical expampleslog-determinantHutchinson's methodtrace of matrix functions
Determinants, permanents, traces, other special matrix functions (15A15) Numerical computation of matrix exponential and similar matrix functions (65F60)
Related Items
Spectrum Approximation Beyond Fast Matrix Multiplication: Algorithms and Hardness, A randomized algorithm for approximating the log determinant of a symmetric positive definite matrix, On randomized trace estimates for indefinite matrices with an application to determinants, Monte Carlo estimators for the Schatten \(p\)-norm of symmetric positive semidefinite matrices, A Multilevel Approach to Variance Reduction in the Stochastic Estimation of the Trace of a Matrix, Fast Estimation of $tr(f(A))$ via Stochastic Lanczos Quadrature, Krylov-Aware Stochastic Trace Estimation, Linear-Cost Covariance Functions for Gaussian Random Fields, Solving trust region subproblems using Riemannian optimization, Conditional gradient method for double-convex fractional programming matrix problems, A general scheme for log-determinant computation of matrices via stochastic polynomial approximation, Faster stochastic trace estimation with a Chebyshev product identity, Multiplicative perturbation bounds for multivariate multiple linear regression in Schatten \(p\)-norms, Randomized block Krylov subspace methods for trace and log-determinant estimators, A multilevel approach to stochastic trace estimation, Unnamed Item
Uses Software
Cites Work
- Smooth function topological structure descriptors based on graph-spectra
- Error bounds for approximation in Chebyshev points
- Improved bounds on sample size for implicit matrix trace estimators
- Parameter estimation in high dimensional Gaussian distributions
- Bounds for norms of the matrix inverse and the smallest singular value
- Chebyshev approximation of log-determinants of spatial weight matrices
- Random matrices: The distribution of the smallest singular values
- Estimating the trace of the matrix inverse by interpolating from the diagonal of an approximate inverse
- Accelerating data uncertainty quantification by solving linear systems with multiple right-hand sides
- An estimator for the diagonal of a matrix
- Estimating the Estrada index
- Inverse Littlewood-Offord theorems and the condition number of random discrete matrices
- A randomized algorithm for approximating the log determinant of a symmetric positive definite matrix
- Stochastic approximation of score functions for Gaussian processes
- Some large-scale matrix computation problems
- How Accurately Should I Compute Implicit Matrix-Vector Products When Applying the Hutchinson Trace Estimator?
- Hierarchical Probing for Estimating the Trace of the Matrix Inverse on Toroidal Lattices
- Efficient estimation of eigenvalue counts in an interval
- The university of Florida sparse matrix collection
- Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
- Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem
- Approximate implementation of the logarithm of the matrix determinant in Gaussian process regression
- Computing an Eigenvector with Inverse Iteration
- Log-determinant relaxation for approximate inference in discrete Markov random fields
- Barycentric Lagrange Interpolation
- Gaussian Markov Random Fields
- Functions of Matrices
- A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
