Randomized matrix-free trace and log-determinant estimators
From MaRDI portal
Publication:2408935
DOI10.1007/s00211-017-0880-zzbMath1378.65094arXiv1605.04893OpenAlexW2964350355WikidataQ57424476 ScholiaQ57424476MaRDI QIDQ2408935
Ilse C. F. Ipsen, Alen Alexanderian, Arvind K. Saibaba
Publication date: 10 October 2017
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1605.04893
numerical experimentstracedeterminantrandomized algorithmsHermitian positive definite matrixsubspace iterationlarge eigenvalue gap
Bayesian inference (62F15) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of matrix norms, conditioning, scaling (65F35) Numerical computation of determinants (65F40) Random matrices (algebraic aspects) (15B52) Randomized algorithms (68W20) Orthogonalization in numerical linear algebra (65F25)
Related Items
An Offline-Online Decomposition Method for Efficient Linear Bayesian Goal-Oriented Optimal Experimental Design: Application to Optimal Sensor Placement, Randomized approaches to accelerate MCMC algorithms for Bayesian inverse problems, Stochastic Learning Approach for Binary Optimization: Application to Bayesian Optimal Design of Experiments, A randomized algorithm for approximating the log determinant of a symmetric positive definite matrix, Goal-oriented optimal design of experiments for large-scale Bayesian linear inverse problems, Improved Variants of the Hutch++ Algorithm for Trace Estimation, On randomized trace estimates for indefinite matrices with an application to determinants, Krylov-Aware Stochastic Trace Estimation, A Fast and Scalable Computational Framework for Large-Scale High-Dimensional Bayesian Optimal Experimental Design, Computation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methods, Large-scale Bayesian optimal experimental design with derivative-informed projected neural network, Randomized Low-Rank Approximation of Monotone Matrix Functions, XT<scp>race</scp>: Making the Most of Every Sample in Stochastic Trace Estimation, A general scheme for log-determinant computation of matrices via stochastic polynomial approximation, Randomization and Reweighted $\ell_1$-Minimization for A-Optimal Design of Linear Inverse Problems, Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity, Flexible GMRES for total variation regularization, Efficient D-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems, Randomized block Krylov subspace methods for trace and log-determinant estimators, Sampled Tikhonov regularization for large linear inverse problems, Stochastic sampling for deterministic structural topology optimization with many load cases: density-based and ground structure approaches, Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review, Interpolating log-determinant and trace of the powers of matrix \(\mathbf{A}+ t\mathbf{B}\)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- On Bayesian A- and D-optimal experimental designs in infinite dimensions
- Randomized estimation of spectral densities of large matrices made accurate
- A randomized algorithm for the decomposition of matrices
- Numerical methods for \(A\)-optimal designs with a sparsity constraint for ill-posed inverse problems
- Improved bounds on sample size for implicit matrix trace estimators
- Log-det approximation based on uniformly distributed seeds and its application to Gaussian process regression
- Chebyshev approximation of log-determinants of spatial weight matrices
- Schur complements and statistics
- Monte Carlo estimates of the log determinant of large sparse matrices
- Bayesian experimental design: A review
- A randomized algorithm for approximating the log determinant of a symmetric positive definite matrix
- Some large-scale matrix computation problems
- A DEIM Induced CUR Factorization
- A Matrix-free Approach for Solving the Parametric Gaussian Process Maximum Likelihood Problem
- A-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems with Regularized $\ell_0$-Sparsification
- Randomized algorithms for the low-rank approximation of matrices
- Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
- Computing $f(A)b$ via Least Squares Polynomial Approximations
- Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations
- IMPROVED ANALYSIS OF THE SUBSAMPLED RANDOMIZED HADAMARD TRANSFORM
- Randomized Algorithms for Matrices and Data
- On Talagrand's deviation inequalities for product measures
- A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines
- Numerical methods for experimental design of large-scale linear ill-posed inverse problems
- Optimal Measurement Methods for Distributed Parameter System Identification
- Smallest singular value of a random rectangular matrix
- Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy
- Accuracy and Stability of Numerical Algorithms
- A probing method for computing the diagonal of a matrix inverse
- Subspace Iteration Randomization and Singular Value Problems
- Probability and Computing
- An Introduction to Matrix Concentration Inequalities
