## Matrix analysis and parallel computing |

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### Contents

Preface | 1 |

Efficient Implementation of Multigrid Preconditioned Conjugate Gradient | 13 |

Parallel Computation for Parametric Study | 14 |

16 other sections not shown

### Common terms and phrases

algorithm Analysis and Parallel applied approximation arithmetic banyan network Bi-CG Bi-CGSTAB bound broadcasting calculation CG method coefficient matrix columns composite step condition number conjugate gradient method convergence rate decomposition defined denote diagonal discretization eddy current edge element efficient eigenvalues evaluate Figure filter factors finite element finite precision Gauss-Seidel Gauss-Seidel method Gaussian Elimination grid levels ICCG ill-posed problems implementation iterative methods iterative solvers Jacobi Jacobi method Keio University Krylov subspace latency linear equations linear systems loop LSQR memory modules MFlops MGCG method multigrid method network topologies nonsymmetric nonzero norm number of iterations number of processors operations orthogonal packets Parallel Computing parallel prefix parameter PBSF performance polynomial positive definite preconditioned preconditioner PU's relative error residual Ritz values serial shared memory SIAM singular values solution solving sparse sparse matrix SSS-MIN subspace symmetric TBSF technique Theorem tridiagonal matrix update variable workstation