Title :
Direct Multi-Grid Methods for Linear Systems With Harmonic Aliasing Patterns
Author :
Michelini, Pablo Navarrete
Author_Institution :
Dept. of Electr. Eng., Univ. de Chile, Santiago, Chile
Abstract :
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.
Keywords :
channel bank filters; iterative methods; signal reconstruction; smoothing methods; coarse grids; direct multi-grid solvers; domain decomposition; filter banks; harmonic aliasing patterns; linear systems; mirror filters; perfect reconstruction filters; smoothing iterations; Copper; Equations; Filter bank; Iterative methods; Jacobian matrices; Linear systems; Partitioning algorithms; Permission; Power harmonic filters; Smoothing methods; Aliasing; direct solver; domain decomposition; multigrid; perfect reconstruction filter;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2010.2053363