Bounds for the entries of matrix functions with applications to preconditioning

From MaRDI portal
Publication:1307237

DOI10.1023/A:1022362401426zbMath0934.65054MaRDI QIDQ1307237

Michele Benzi, Gene H. Golub

Publication date: 1 December 1999

Published in: BIT (Search for Journal in Brave)




Related Items

Refined decay bounds on the entries of spectral projectors associated with sparse Hermitian matricesBlock diagonal dominance of matrices revisited: bounds for the norms of inverses and eigenvalue inclusion setsUpdating and Downdating Techniques for Optimizing Network CommunicabilitySolvers for $\mathcal{O} (N)$ Electronic Structure in the Strong Scaling LimitDecay bounds for Bernstein functions of Hermitian matrices with applications to the fractional graph LaplacianQuantum states on harmonic latticesSolving multi-linear systems with \(\mathcal {M}\)-tensorsSparse solution of the Lyapunov equation for large-scale interconnected systemsPredicting Triadic Closure in Networks Using Communicability Distance FunctionsDecay Bounds for Functions of Hermitian Matrices with Banded or Kronecker StructureError Bounds for the Krylov Subspace Methods for Computations of Matrix ExponentialsThe Short-Term Rational Lanczos Method and ApplicationsA Preconditioned MINRES Method for Optimal Control of Wave Equations and its Asymptotic Spectral Distribution TheoryParameter estimation in high dimensional Gaussian distributionsLocalization of matrix factorizationsRanking hubs and authorities using matrix functionsInexact rational Krylov Subspace methods for approximating the action of functions of matricesComputation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methodsMassively parallel sparse matrix function calculations with NTPolyA block Toeplitz preconditioner for all-at-once systems from linear wave equationsA sine transform based preconditioned MINRES method for all-at-once systems from constant and variable-coefficient evolutionary PDEsVertex-frequency analysis on graphsNumerical Structure of the Hessian of the Lagrange Dual Function for a Class of Convex ProblemsLocalization in Matrix Computations: Theory and ApplicationsLow-Rank Updates of Matrix FunctionsLocalized spectrum slicingOn the finite section method for computing exponentials of doubly-infinite skew-Hermitian matricesOn the decay of the inverse of matrices that are sum of Kronecker productsExploring the “Middle Earth” of network spectra via a Gaussian matrix functionSparsity preserving optimal control of discretized PDE systemsSpatially Dependent Polya Tree Modeling for Survival DataNon-Toeplitz decay bounds for inverses of Hermitian positive definite tridiagonal matricesDecay properties for functions of matrices over \(C^\ast\)-algebrasEntrywise relative perturbation bounds for exponentials of essentially non-negative matricesA probing method for computing the diagonal of a matrix inverseMonotone convex sequences and Cholesky decomposition of symmetric Toeplitz matricesInexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matricesNew updates of incomplete LU factorizations and applications to large nonlinear systemsQuadrature rule-based bounds for functions of adjacency matricesOn the inverses of general tridiagonal matricesSome uses of the field of values in numerical analysisModified iterations for data-sparse solution of linear systemsColloquium: Area laws for the entanglement entropyAnalysis of Probing Techniques for Sparse Approximation and Trace Estimation of Decaying Matrix FunctionsComputing the reciprocal of a \(\phi\)-function by rational approximationComputing exponentials of essentially non-negative matrices entrywise to high relative accuracyMaking almost commuting matrices commuteAn exact formulation of the time-ordered exponential using path-sumsHigh-Performance Computation of the Exponential of a Large Sparse MatrixDivide-and-Conquer Methods for Functions of Matrices with Banded or Hierarchical Low-Rank Structure