An efficient parallel implementation of the MSPAI preconditioner. 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.par 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.

References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Carr, Arielle; de Sturler, Eric; Gugercin, Serkan: Preconditioning parametrized linear systems (2021)
  2. Singh, Navneet Pratap; Ahuja, Kapil: Preconditioned linear solves for parametric model order reduction (2020)
  3. Alexandrov, Vassil; Davila, Diego; Esquivel-Flores, Oscar; Karaivanova, Aneta; Gurov, Todor; Atanassov, Emanouil: On Monte Carlo and quasi-Monte Carlo for matrix computations (2018)
  4. Bu, Yiming; Carpentieri, Bruno; Shen, Zhaoli; Huang, Ting-Zhu: A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems (2016)
  5. Alexandrov, Vassil; Esquivel-Flores, Oscar A.: Towards Monte Carlo preconditioning approach and hybrid Monte Carlo algorithms for matrix computations (2015)
  6. Alexandrov, V.; Esquivel-Flores, O.; Ivanovska, S.; Karaivanova, A.: On the preconditioned quasi-Monte Carlo algorithm for matrix computations (2015)
  7. González, Luis; Suárez, Antonio: Improving approximate inverses based on Frobenius norm minimization (2013)
  8. Bergamaschi, Luca; Martínez, Àngeles: Banded target matrices and recursive FSAI for parallel preconditioning (2012)
  9. Huckle, T.; Kallischko, A.; Roy, A.; Sedlacek, M.; Weinzierl, T.: An efficient parallel implementation of the MSPAI preconditioner (2010)
  10. Huckle, T.; Sedlacek, M.: Smoothing and regularization with modified sparse approximate inverses (2010)
  11. Huckle, T.; Kallischko, A.: Frobenius norm minimization and probing for preconditioning (2007)