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Volume 39, Issue 4
Iterative ILU Preconditioners for Linear Systems and Eigenproblems

Daniele Boffi, Zhongjie Lu & Luca F. Pavarino

DOI: 10.4208/jcm.2009-m2020-0138

J. Comp. Math., 39 (2021), pp. 633-654.

Published online: 2021-06

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  • Abstract

Iterative ILU factorizations are constructed, analyzed and applied as preconditioners to solve both linear systems and eigenproblems. The computational kernels of these novel Iterative ILU factorizations are sparse matrix-matrix multiplications, which are easy and efficient to implement on both serial and parallel computer architectures and can take full advantage of existing matrix-matrix multiplication codes. We also introduce level-based and threshold-based algorithms in order to enhance the accuracy of the proposed Iterative ILU factorizations. The results of several numerical experiments illustrate the efficiency of the proposed preconditioners to solve both linear systems and eigenvalue problems.

  • Keywords

Iterative ILU factorization, Matrix-matrix multiplication, Fill-in, Eigenvalue problem, Parallel preconditioner.

  • AMS Subject Headings

65F08, 65F15, 15A23

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

daniele.boffi@kaust.edu.sa (Daniele Boffi)

zhjlu@ustc.edu.cn (Zhongjie Lu)

luca.pavarino@unipv.it (Luca F. Pavarino)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-633, author = {Boffi , DanieleLu , Zhongjie and Pavarino , Luca F.}, title = {Iterative ILU Preconditioners for Linear Systems and Eigenproblems}, journal = {Journal of Computational Mathematics}, year = {2021}, volume = {39}, number = {4}, pages = {633--654}, abstract = {

Iterative ILU factorizations are constructed, analyzed and applied as preconditioners to solve both linear systems and eigenproblems. The computational kernels of these novel Iterative ILU factorizations are sparse matrix-matrix multiplications, which are easy and efficient to implement on both serial and parallel computer architectures and can take full advantage of existing matrix-matrix multiplication codes. We also introduce level-based and threshold-based algorithms in order to enhance the accuracy of the proposed Iterative ILU factorizations. The results of several numerical experiments illustrate the efficiency of the proposed preconditioners to solve both linear systems and eigenvalue problems.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009-m2020-0138}, url = {http://global-sci.org/intro/article_detail/jcm/19262.html} }
TY - JOUR T1 - Iterative ILU Preconditioners for Linear Systems and Eigenproblems AU - Boffi , Daniele AU - Lu , Zhongjie AU - Pavarino , Luca F. JO - Journal of Computational Mathematics VL - 4 SP - 633 EP - 654 PY - 2021 DA - 2021/06 SN - 39 DO - http://doi.org/10.4208/jcm.2009-m2020-0138 UR - https://global-sci.org/intro/article_detail/jcm/19262.html KW - Iterative ILU factorization, Matrix-matrix multiplication, Fill-in, Eigenvalue problem, Parallel preconditioner. AB -

Iterative ILU factorizations are constructed, analyzed and applied as preconditioners to solve both linear systems and eigenproblems. The computational kernels of these novel Iterative ILU factorizations are sparse matrix-matrix multiplications, which are easy and efficient to implement on both serial and parallel computer architectures and can take full advantage of existing matrix-matrix multiplication codes. We also introduce level-based and threshold-based algorithms in order to enhance the accuracy of the proposed Iterative ILU factorizations. The results of several numerical experiments illustrate the efficiency of the proposed preconditioners to solve both linear systems and eigenvalue problems.

Daniele Boffi, Zhongjie Lu & Luca F. Pavarino. (2021). Iterative ILU Preconditioners for Linear Systems and Eigenproblems. Journal of Computational Mathematics. 39 (4). 633-654. doi:10.4208/jcm.2009-m2020-0138
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