Stable Computation of Generalized Matrix Functions via Polynomial Interpolation

DOI10.1137/18M1191786zbMath1409.65030MaRDI QIDQ3119538

Michele Benzi, Anthony P. Austin, Vassilis Kalantzis, Jared Lee Aurentz

Publication date: 12 March 2019

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Chebyshev polynomialsgraph theoryClenshaw's algorithmgeneralized matrix functions

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Matrix exponential and similar functions of matrices (15A16) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items

Computation of generalized matrix functions with rational Krylov methods ⋮ Generalized tensor function via the tensor singular value decomposition based on the T-product ⋮ Continuity, differentiability and semismoothness of generalized tensor functions ⋮ Matrix functions in network analysis ⋮ Limited‐memory polynomial methods for large‐scale matrix functions ⋮ Faster stochastic trace estimation with a Chebyshev product identity ⋮ Some matrix properties preserved by generalized matrix functions ⋮ Mittag--Leffler Functions and their Applications in Network Science

Uses Software

• SparseMatrix
• mctoolbox
• Chebfun
• na26
• mftoolbox
• Cucheb

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bounding the spectrum of large Hermitian matrices
• Mapping directed networks
• Restarted block Lanczos bidiagonalization methods
• Computation of functions of Hamiltonian and skew-symmetric matrices
• Cucheb: a GPU implementation of the filtered Lanczos procedure
• Backward stability of Clenshaw's algorithm
• Ranking hubs and authorities using matrix functions
• Semigroup methods for evolution equations on networks
• A new status index derived from sociometric analysis
• Operator-Lipschitz estimates for the singular value functional calculus
• Edge Modification Criteria for Enhancing the Communicability of Digraphs
• The university of Florida sparse matrix collection
• A Filtered Lanczos Procedure for Extreme and Interior Eigenvalue Problems
• Computation of Generalized Matrix Functions
• On generalized matrix functions
• Low-Rank Matrix Approximation Using the Lanczos Bidiagonalization Process with Applications
• A New Frequency Estimation Method for Equally and Unequally Spaced Data
• Accuracy and Stability of Numerical Algorithms
• A Formula for the Fréchet Derivative of a Generalized Matrix Function
• Functions of Matrices
• Computation of the Exponential of Large Sparse Skew-Symmetric Matrices
• Two polynomial methods of calculating functions of symmetric matrices