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A Comparison Result for Multisplittings Based on Overlapping Blocks and its Application to Waveform Relaxation Methods

by A. Frommer and B. Pohl

(Report number 1993-05)

Abstract
We show that certain multisplitting iterative methods based on overlapping blocks yield faster convergence than corresponding non-overlapping block iterations, provided the coefficient matrix is an M-matrix. This result is then applied to compare different waveform relaxation methods for solving initial value problems. Numerical experiments on the Intel iPSC/860 hypercube are included.

Keywords: multisplittings, overlapping blocks, comparison results, M-matrices, regular splittings, waveform relaxation, initial value problems, parallel algorithms

@Techreport{FP93_30,
  author = {A. Frommer and B. Pohl},
  title = {A Comparison Result for Multisplittings Based on Overlapping Blocks and its Application to Waveform Relaxation Methods},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1993-05},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1993/1993-05.pdf },
  year = {1993}
}

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