Divide-and-Conquer Methods for Functions of Matrices with Banded or Hierarchical Low-Rank Structure
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Publication:5028556
DOI10.1137/21M1432594zbMath1482.65071arXiv2107.04337OpenAlexW3181528158MaRDI QIDQ5028556
Alice Cortinovis, Daniel Kressner, Stefano Massei
Publication date: 10 February 2022
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.04337
Krylov subspace methodmatrix functionbanded matrixhierarchically semiseparable matrixdivide-and-conquer algorithm
Computational methods for sparse matrices (65F50) Numerical computation of matrix exponential and similar matrix functions (65F60)
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Cites Work
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- Computing the exponential of large block-triangular block-Toeplitz matrices encountered in fluid queues
- Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices
- Decay bounds for the numerical quasiseparable preservation in matrix functions
- Rational Krylov sequence methods for eigenvalue computation
- Decay bounds and \(O(n)\) algorithms for approximating functions of sparse matrices
- Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems
- Approximation of exp(-x) by rational functions with concentrated negative poles
- Bounds for the entries of matrix functions with applications to preconditioning
- \(\mathcal H\)-matrix approximation for the operator exponential with applications
- Estimating the trace of the matrix inverse by interpolating from the diagonal of an approximate inverse
- On the exponential of semi-infinite quasi-Toeplitz matrices
- Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices
- Decay properties for functions of matrices over \(C^\ast\)-algebras
- An estimator for the diagonal of a matrix
- On the finite section method for computing exponentials of doubly-infinite skew-Hermitian matrices
- Approximating Spectral Densities of Large Matrices
- Near-Optimal Perfectly Matched Layers for Indefinite Helmholtz Problems
- Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
- Decay Bounds for Functions of Hermitian Matrices with Banded or Kronecker Structure
- Hierarchical Matrices: Algorithms and Analysis
- The university of Florida sparse matrix collection
- A restarted Lanczos approximation to functions of a symmetric matrix
- Network Properties Revealed through Matrix Functions
- Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential
- Fast algorithms for hierarchically semiseparable matrices
- Fast Computation of the Matrix Exponential for a Toeplitz Matrix
- Decay Rates for Inverses of Band Matrices
- Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
- A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
- Low-Rank Updates and a Divide-And-Conquer Method for Linear Matrix Equations
- On the Stability of Network Indices Defined by Means of Matrix Functions
- Decay Properties of Spectral Projectors with Applications to Electronic Structure
- A probing method for computing the diagonal of a matrix inverse
- Low-Rank Updates of Matrix Functions II: Rational Krylov Methods
- hm-toolbox: MATLAB Software for HODLR and HSS Matrices
- The Block Rational Arnoldi Method
- Fast Solvers for Two-Dimensional Fractional Diffusion Equations Using Rank Structured Matrices
- A Fast $ULV$ Decomposition Solver for Hierarchically Semiseparable Representations
- The Numerical Range is a $(1+\sqrt{2})$-Spectral Set
- Fast Computation of Spectral Projectors of Banded Matrices
- Low-Rank Updates of Matrix Functions
- Functions of Matrices
- Massively parallel sparse matrix function calculations with NTPoly