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- W2912781535 abstract "Generating sparsity patterns for effective block-Jacobi preconditioners is a challenging and computationally expensive task, in particular for problems with unknown origin. In this paper we design a convolutional neural network (CNN) to detect natural block structures in matrix sparsity patterns. For test matrices where a natural block structure is complemented with a random distribution of nonzeros (noise), we show that a trained network succeeds in identifying strongly connected components with more than 95% prediction accuracy, and the resulting block-Jacobi preconditioner effectively accelerating an iterative GMRES solver. Segmenting a matrix into diagonal tiles of size 128x128, for each tile the sparsity pattern of an effective block-Jacobi preconditioner can be generated in less than a millisecond when using a production-line GPU." @default.
- W2912781535 created "2019-02-21" @default.
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- W2912781535 date "2018-11-01" @default.
- W2912781535 modified "2023-10-14" @default.
- W2912781535 title "Machine Learning-Aided Numerical Linear Algebra: Convolutional Neural Networks for the Efficient Preconditioner Generation" @default.
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- W2912781535 doi "https://doi.org/10.1109/scala.2018.00010" @default.
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