Computation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methods
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Publication:6153360
DOI10.1007/s00211-023-01368-6arXiv2212.09642MaRDI QIDQ6153360
Igor Simunec, Michele Benzi, Michele Rinelli
Publication date: 19 March 2024
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2212.09642
Matrix exponential and similar functions of matrices (15A16) Numerical computation of matrix exponential and similar matrix functions (65F60)
Cites Work
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- Quantum dynamical entropy and an algorithm by Gene Golub
- The Laplacian of a graph as a density matrix: a basic combinatorial approach to separability of mixed states
- Acyclic and \(k\)-distance coloring of the grid
- Bounds for the entries of matrix functions with applications to preconditioning
- Non-Toeplitz decay bounds for inverses of Hermitian positive definite tridiagonal matrices
- Rational Krylov methods for fractional diffusion problems on graphs
- Refined decay bounds on the entries of spectral projectors associated with sparse Hermitian matrices
- Fast computation of von Neumann entropy for large-scale graphs via quadratic approximations
- Randomized matrix-free trace and log-determinant estimators
- Tridiagonalization of a symmetric band matrix
- On interpolation by rational functions
- Rational Krylov for Stieltjes matrix functions: convergence and pole selection
- Rational Gauss quadrature rules for the approximation of matrix functionals involving Stieltjes functions
- On randomized trace estimates for indefinite matrices with an application to determinants
- Estimating the trace of matrix functions with application to complex networks
- Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
- Decay Bounds for Functions of Hermitian Matrices with Banded or Kronecker Structure
- Localization in Matrix Computations: Theory and Applications
- The university of Florida sparse matrix collection
- Error Estimates and Evaluation of Matrix Functions via the Faber Transform
- Analysis of Probing Techniques for Sparse Approximation and Trace Estimation of Decaying Matrix Functions
- A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines
- Block algorithms for reordering standard and generalized Schur forms
- Decay Rates for Inverses of Band Matrices
- Bounds for the decay of the entries in inverses and Cauchy–Stieltjes functions of certain sparse, normal matrices
- Graph Colorings
- Decay Properties of Spectral Projectors with Applications to Electronic Structure
- Improved Variants of the Hutch++ Algorithm for Trace Estimation
- The Short-Term Rational Lanczos Method and Applications
- Computing the entropy of a large matrix
- Generalized Rational Krylov Decompositions with an Application to Rational Approximation
- Parallelization of the Rational Arnoldi Algorithm
- Functions of Matrices
- Geometry of Quantum States
- Rational Gauss Quadrature
- Krylov-Aware Stochastic Trace Estimation
