Overlapping vs partitioning in block-iteration methods: Application in large-scale system theory

Abstract The concept of overlapping decomposition in splitting theory is introduced. Matrix splitting, Hamiltonian operator splitting and Riccati operator splitting are successively considered for the case of block-overlapping and are compared with classical corresponding splitting methods based on block-partitioning. Numerical simulations are given. Overlapping decomposition is shown to succeed where classical partitioning decomposition fails.

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