Filter banks allowing perfect reconstruction
Signal Processing
Direct methods for sparse matrices
Direct methods for sparse matrices
Multirate systems and filter banks
Multirate systems and filter banks
Rigorous quantitative analysis of multigrid, I: constant coefficients two-level cycle with L2-norm
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Wavelets and subband coding
A multigrid tutorial (2nd ed.)
A multigrid tutorial (2nd ed.)
Multigrid
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Mobility models based on correlated random walks
Mobility '08 Proceedings of the International Conference on Mobile Technology, Applications, and Systems
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
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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.