In this paper we study convergence estimates for a multigrid algorithm with smoothers of successive subspace correction (ssc) type, applied to symmetric elliptic PDEs under no regularity assumptions on the solution of...
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In this paper we study convergence estimates for a multigrid algorithm with smoothers of successive subspace correction (ssc) type, applied to symmetric elliptic PDEs under no regularity assumptions on the solution of the problem. The proposed analysis provides three main contributions to the existing theory. The first novel contribution of this study is a convergence bound that depends on the number of multigrid smoothing iterations. This result is obtained under no regularity assumptions on the solution of the problem. A similar result has been shown in the literature for the cases of full regularity and partial regularity assumptions. Second, our theory applies to local refinement applications with arbitrary level hanging nodes. More specifically, for the smoothing algorithm we provide subspace decompositions that are suitable for applications where the multigrid spaces are defined on finite element grids with arbitrary level hanging nodes. Third, global smoothing is employed on the entire multigrid space with hanging nodes. When hanging nodes are present, existing multigrid strategies advise to carry out the smoothing procedure only on a subspace of the multigrid space that does not contain hanging nodes. However, with such an approach, if the number of smoothing iterations is increased, convergence can improve only up to a saturation value. Global smoothing guarantees an arbitrary improvement in the convergence when the number of smoothing iterations is increased. Numerical results are also included to support our theoretical findings. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.
Clustering for hyperspectral images (HSIs) is a very challenging task because HSIs usually have large spectral variability, high dimensionality, and complex structures. The main issue of this study is to develop an im...
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Clustering for hyperspectral images (HSIs) is a very challenging task because HSIs usually have large spectral variability, high dimensionality, and complex structures. The main issue of this study is to develop an improved sparse subspace clustering (ssc) method for HSIs. As an extension of spectral clustering, ssc algorithm has achieved great success;however, the direct self-representation dictionary which is created by raw samples has poor representation power and also the widely used dictionary learning (DL) such as K-Singular Value Decomposition (K-SVD) faces with the problems of high computational complexity. In this study, the authors propose a novel HSI clustering method based on sparse DL and anchored regression. The proposed method follows three stages: (i) sparse DL;(ii) anchored subspace construction and regression;and (iii) representation-based spectral clustering. Specifically, we adopt a fast sparse DL method under a double sparsity constrained optimising model to capture the intrinsic HSIs. To establish a compact subspace for collaborative representation, we present an anchored subspace construction method by using atoms clustering and grouping methods. Owing to the anchored subspace, we can fast compute the representation coefficients with a predefined projection matrix. Experimental results demonstrate that the proposed method achieves the best performance for the HSIs clustering.
The ssc local dimming algorithm, originally developed for direct-lit LCD using a local optimization approach, has been modified and extended. A global optimization approach was used to cover the wide light spread over...
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The ssc local dimming algorithm, originally developed for direct-lit LCD using a local optimization approach, has been modified and extended. A global optimization approach was used to cover the wide light spread over the display due to the edge-lit. The existing six LED-strings of a commercial available edge-lit TV are controlled by our own driver circuit, while the PWM values for each LED are delivered by the ssc algorithm. The display parameters were measured and used in the ssc processing. An average power saving of up to 51% of the TV power consumption standard video has been achieved, while the visual quality is proven and the brightness is nearly the same as that of the original undimmed TV. with a higher number of LED strings a power saving significantly higher than 50% is to be expected.
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