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Direct Multi-Grid Methods for Linear Systems With Harmonic Aliasing Patterns

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1 Author(s)
Navarrete Michelini, P. ; Dept. of Electr. Eng., Univ. de Chile, Santiago, Chile

Multi-level numerical methods that obtain the exact solution of a linear system are presented. The methods are devised by combining ideas from the full multi-grid algorithm and perfect reconstruction filters. The problem is stated as whether a direct solver is possible in a full multi-grid scheme by avoiding smoothing iterations and using different coarse grids at each step. The coarse grids must form a partition of the fine grid and thus establishes a strong connection with domain decomposition methods. An important analogy is established between the conditions for direct solution in multi-grid solvers and perfect reconstruction in filter banks. Furthermore, simple solutions of these conditions for direct multi-grid solvers are found by using mirror filters. As a result, different configurations of direct multi-grid solvers are obtained and studied.

Published in:

Signal Processing, IEEE Transactions on  (Volume:58 ,  Issue: 10 )

Date of Publication:

Oct. 2010

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