Kernel polynomial approximations for densities of states and spectral functions
Journal of Computational Physics
Lower bounds on the maximum cross correlation of signals (Corresp.)
IEEE Transactions on Information Theory
Low cost high performance uncertainty quantification
Proceedings of the 2nd Workshop on High Performance Computational Finance
Journal of the ACM (JACM)
Analysis and Computation of Compatible Least-Squares Methods for div-curl Equations
SIAM Journal on Numerical Analysis
Primal-dual coding to probe light transport
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Randomized Algorithms for Matrices and Data
Foundations and Trends® in Machine Learning
Low-cost data uncertainty quantification
Concurrency and Computation: Practice & Experience
Fast approximation of matrix coherence and statistical leverage
The Journal of Machine Learning Research
Parameter estimation in high dimensional Gaussian distributions
Statistics and Computing
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A number of applications require to compute an approximation of the diagonal of a matrix when this matrix is not explicitly available but matrix-vector products with it are easy to evaluate. In some cases, it is the trace of the matrix rather than the diagonal that is needed. This paper describes methods for estimating diagonals and traces of matrices in these situations. The goal is to obtain a good estimate of the diagonal by applying only a small number of matrix-vector products, using selected vectors. We begin by considering the use of random test vectors and then explore special vectors obtained from Hadamard matrices. The methods are tested in the context of computational materials science to estimate the diagonal of the density matrix which holds the charge densities. Numerical experiments indicate that the diagonal estimator may offer an alternative method that in some cases can greatly reduce computational costs in electronic structures calculations.