Titlebook: Matrix-Based Multigrid; Theory and Applicati Yair Shapira Book 20031st edition Springer Science+Business Media New York 2003 algebra.algori

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The Automug Methodt stencil on uniform grids. The AutoMUG method can be viewed as an extension of the Cyclic Reduction method. The advantage of AutoMUG is not only in its inexpensive implementation for this kind of problem, but also in the opportunity to learn from it about suitable implementation of other matrix-bas

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Applications in Image Processingorm, rectangular grids because images are often stored in 2-d uniform arrays of pixels. We introduce algorithms for denoising noisy grayscale (noncolor) as well as color images. These algorithms are based on nonlinear elliptic PDEs. These PDEs are linearized by the fixed point iteration, and the lin

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The Black-Box Multigrid MethodDEs. This method is a matrix-based multigrid method that is suitable for uniform, rectangular grids and coefficient matrices with 9-point stencil. We also show how the method should be modified for a most difficult problem arising from the finite-volume discretization of a diffusion problem with dis

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Conclusionslliptic PDEs that are discretized on uniform, rectangular grids, such as applications in image processing, should probably be solved by the multigrid methods in Part II, which can be implemented by efficient data structures such as arrays of numbers. On the other hand, PDEs that are discretized on l