A convergence improvement of the BSAIC preconditioner by deflation

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概要

• 論文の詳細を見る

• We have proposed a block sparse approximate inverse with cutoff (BSAIC) preconditioner for relatively dense matrices. The BSAIC preconditioner is effective for semi-sparse matrices which have relatively large number of nonzero elements. This method reduces the computational cost for generating the preconditioning matrix, and overcomes the performance bottlenecks of SAI using the blocked version of Frobenius norm minimization and the drop-threshold schemes (cutoff) for semi-sparse matrices. However, a larger parameter of cutoff leads to a less effective preconditioning matrix with a large number of iterations. We analyze this convergence deterioration in terms of eigenvalues, and describe a deflation-type method which improves the convergence.

• The Japan Society for Industrial and Applied Mathematicsの論文

著者

• Tadano Hiroto

  Graduate School of Systems and Information Engineering, University of Tsukuba

• Sakurai Tetsuya

  Graduate School of Systems and Information Engineering, University of Tsukuba

• Yamazaki Ikuro

  Graduate School of Systems and Information Engineering, University of Tsukuba

• Teranishi Keita

  Cray, Inc.

関連論文

• A quadrature-based eigensolver with a Krylov subspace method for shifted linear systems for Hermitian eigenproblems in lattice QCD
• Parallel stochastic estimation method of eigenvalue distribution
• A block sparse approximate inverse with cutoff preconditioner for semi-sparse linear systems derived from Molecular Orbital calculations
• A convergence improvement of the BSAIC preconditioner by deflation

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