Correspondence

Keywords

1 INTRODUCTION  
Organization of the survey  
Notation  

2 ITERATIVE PROJECTION METHODS – KRYLOV SUBSPACE METHODS  
The non-Hermitian Lanczos process  

3 SUBSPACE AUGMENTATION AND THE STRATEGY OF DEFLATION  
Deflation  
Multigrid and domain decomposition  
Bordering methods  
Polynomial preconditioning  

4 SUBSPACE RECYCLING  
When is an augmented method subspace recycling?  
Augmentation based on ideas of deflation  
Analysis  
Alternative approaches  

5 PRACTICAL REALIZATIONS OF THE RECYCLING FRAMEWORK  
Full basis storage methods  
Short-recurrence-based methods  

6 WHAT TO RECYCLE  
Approximate singular vector augmentation  
Optimal truncation  
Proper Orthogonal Decomposition (POD)-type strategies  

7 EXPLOITING OPERATOR STRUCTURE AND MULTIPLE RIGHT-HAND SIDES  
Scalar shifted matrices  
Difficulties combining recycling with shifted system solvers  
Effective recycling strategies for shifted systems  
Sequences of shifted systems with shift independent RHS  
Inner-outer recycling  
Updating across shifted systems  
A family of matrices  
Double shifts, single RHS  
Other methods  
General parameterized families with continuous parameter dependence  

8 USES IN PRACTICAL APPLICATIONS  
Large Scale Software Libraries  

9 OUTLOOK AND FUTURE WORK