Deflation as a Method of Variance Reduction for Estimating the Trace of a Matrix Inverse

DOI10.1137/16M1066361zbMath1365.65111arXiv1603.05988MaRDI QIDQ5738167

Andreas Stathopoulos, Kostas Orginos, Arjun Singh Gambhir

Publication date: 31 May 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.05988

zbMATH Keywords

convergenceMonte Carlodeflationsingular valuesvariance reductionlattice quantum chromodynamicsrandom unitary matriceslarge, sparse matrixHutchinsontrace of matrix inverse

Mathematics Subject Classification ID

Related Items (9)

Improved Variants of the Hutch++ Algorithm for Trace Estimation ⋮ A Multilevel Approach to Variance Reduction in the Stochastic Estimation of the Trace of a Matrix ⋮ Probing for the Trace Estimation of a Permuted Matrix Inverse Corresponding to a Lattice Displacement ⋮ Krylov-Aware Stochastic Trace Estimation ⋮ XT<scp>race</scp>: Making the Most of Every Sample in Stochastic Trace Estimation ⋮ Disconnected loop subtraction methods in lattice QCD ⋮ Nuclear matrix elements from lattice QCD for electroweak and beyond-standard-model processes ⋮ A Golub--Kahan Davidson Method for Accurately Computing a Few Singular Triplets of Large Sparse Matrices ⋮ Multigrid deflation for lattice QCD

Uses Software

• PRIMME
• SparseMatrix

Cites Work

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• PRIMME
• How many entries of a typical orthogonal matrix can be approximated by independent normals?
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• An estimator for the diagonal of a matrix
• Hierarchical Probing for Estimating the Trace of the Matrix Inverse on Toroidal Lattices
• The university of Florida sparse matrix collection
• Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
• Computing and Deflating Eigenvalues While Solving Multiple Right-Hand Side Linear Systems with an Application to Quantum Chromodynamics
• Domain-Decomposition-Type Methods for Computing the Diagonal of a Matrix Inverse
• Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides
• A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines

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