The interface probing technique in domain decomposition
SIAM Journal on Matrix Analysis and Applications
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Approximate sparsity patterns for the inverse of a matrix and preconditioning
IMACS'97 Proceedings on the on Iterative methods and preconditioners
A comparative study of sparse approximate inverse preconditioners
IMACS'97 Proceedings on the on Iterative methods and preconditioners
Sparse Approximate Inverses and Target Matrices
SIAM Journal on Scientific Computing
An MPI Implementation of the SPAI Preconditioner on the T3E
International Journal of High Performance Computing Applications
International Journal of High Performance Computing Applications
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Frobenius norm minimization and probing for preconditioning
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Iterative image restoration using approximate inverse preconditioning
IEEE Transactions on Image Processing
Banded target matrices and recursive FSAI for parallel preconditioning
Numerical Algorithms
On scalability behaviour of Monte Carlo sparse approximate inverse for matrix computations
ScalA '13 Proceedings of the Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems
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We present an efficient implementation of the Modified SParse Approximate Inverse (MSPAI) preconditioner. MSPAI generalizes the class of preconditioners based on Frobenius norm minimizations, the class of modified preconditioners such as MILU, as well as interface probing techniques in domain decomposition: it adds probing constraints to the basic SPAI formulation, and one can thus optimize the preconditioner relative to certain subspaces. We demonstrate MSPAI's qualities for iterative regularization problems arising from image deblurring. Such applications demand for a fast and parallel preconditioner realization. We present such an implementation introducing two new optimization techniques: First, we avoid redundant calculations using a dictionary. Second, our implementation reduces the runtime spent on the most demanding numerical parts as the code switches to sparse QR decomposition methods wherever profitable. The optimized code runs in parallel with a dynamic load balancing.