Deflated shifted block Krylov subspace methods for Hermitian positive definite matrices / von Sebastian Birk. Wuppertal, 2015
Inhalt
- Introduction
- Iterative Methods
- Matrix Functions
- Definition and Properties
- Jordan Canonical Form Definition
- Polynomial Interpolation Definition
- Cauchy Integral Definition
- Properties
- The Matrix Sign Function
- Approximating f(A)
- Approximating f(A)b
- Applications
- Lattice Quantum Chromodynamics
- The Wilson-Dirac Operator
- Hadron Spectroscopy
- The Overlap Operator
- The Rational Hybrid Monte Carlo Algorithm
- Inverse Problems
- Krylov Subspace Methods for Shifted Systems
- Shifted CG
- Recurrences for the Unshifted System
- Recurrences for the Shifted System
- A Feasible Stopping Criterion
- The Shifted CG Algorithm
- Convergence of Shifted CG
- Restarted Shifted CG
- Krylov Subspace Methods for Multiple RHS
- Krylov Subspace Methods for Shifted Block Systems
- Deflated Block Lanczos Processes
- Deflated Block Krylov Subspaces
- Two-Sided Deflated Block Lanczos-Type Process
- Deflated Block Lanczos-Type Process
- Block-Featured Deflated Lanczos-Type Process
- DSBlockCG
- A Deflated Block CG Method
- Stopping Criterion for the Deflated Block CG Method
- The Deflated Shifted Block CG Method
- The DSBlockCG Algorithm
- BFDSCG
- A Block-Featured Deflated CG Method
- Stopping Criterion
- Deflation in the Block-Featured Deflated CG Method
- The Block-Featured Deflated Shifted CG Method
- The BFDSCG Algorithm
- Shifted BCGrQ
- Numerical Results
- Implementation Details and Test Problems
- Lanczos-Type Processes Tests
- Comparison of Methods for Solving Shifted Block Systems
- Lattice QCD - Prerequisites
- Lattice QCD - Methods
- Lattice QCD - Results
- Image Deconvolution - Prerequisites
- Image Deconvolution - Methods
- Image Deconvolution - Results
- Comparison of Methods for Solving Block Systems
- Conclusion for the Numerical Results
- Conclusion and Outlook
- List of Figures
- List of Tables
- List of Algorithms
- Index
- Bibliography