Limited-memory polynomial methods for large-scale matrix functions
arXiv:2002.01682 · doi:10.1002/gamm.202000019
Abstract
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of a large-scale matrix function on a vector. Emphasis is put on polynomial methods, whose memory requirements are known or prescribed a priori. Methods based on explicit polynomial approximation or interpolation, as well as restarted Arnoldi methods, are treated in detail. An overview of existing software is also given, as well as a discussion of challenging open problems.
arXiv comment25 pages, 2 figures, 4 algorithms
References in corpus (9)
- The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
- GSPBOX: A toolbox for signal processing on graphs
- Numerical Methods for the QCD Overlap Operator: I. Sign-Function and Error Bounds
- The Leja method revisited: backward error analysis for the matrix exponential
- High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations
- Weak convergence of Galerkin approximations for fractional elliptic stochastic PDEs with spatial white noise
- Clustering Signed Networks with the Geometric Mean of Laplacians
- Lattice QCD: concepts, techniques and some results
- A New Algorithm for Computing the Actions of Trigonometric and Hyperbolic Matrix Functions