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Steve F. McCormick

Bio: Steve F. McCormick is an academic researcher from University of Colorado Boulder. The author has contributed to research in topics: Multigrid method & Solver. The author has an hindex of 9, co-authored 17 publications receiving 1805 citations.

Papers
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Book ChapterDOI
01 Jan 2007
TL;DR: The algorithm presented here combines the robustness of element interpolation, the ease of coarsening by element agglomeration, and the simplicity of defining coarse dofs through the spectral approach, and does yield a reasonable solver for the problems described.
Abstract: The purpose of this note is to describe an algorithm resulting from the uniting of two ideas introduced and applied elsewhere. For many problems, AMG has always been difficult due to complexities whose natures are difficult to discern from the entries of matrix A alone. Element-based interpolation has been shown to be an effective method for some of these problems, but it requires access to the element matrices on all levels. One way to obtain these has been to perform element agglomeration to form coarse elements, but in complicated situations defining the coarse degrees of freedom (dofs) is not easy. The spectral approach to coarse dof selection is very attractive due to its elegance and simplicity. The algorithm presented here combines the robustness of element interpolation, the ease of coarsening by element agglomeration, and the simplicity of defining coarse dofs through the spectral approach. As demonstrated in the numerical results, the method does yield a reasonable solver for the problems described. It can, however, be an expensive method due to the number and cost of the local, small dense linear algebra problems; making it a generally competitive method remains an area for further research.

26 citations

Book ChapterDOI
01 Jan 2007
TL;DR: This paper aims to demonstrate the efforts towards in-situ applicability of EMMARM, as to provide real-time information about the response of the immune system to EMTs.
Abstract: 1 Department of Applied Mathematics, University of Colorado at Boulder, Email: brannick@newton.colorado.edu, mbrezina@math.cudenver.edu, maclachl@colorado.edu, tmanteuf@colorado.edu, stevem@colorado.edu, jruge@colorado.edu 2 Department of Mathematical Sciences, Ball State University, Email: ilivshits@bsu.edu 3 Department of Applied Physics and Applied Mathematics, Columbia University, Email: david.keyes@columbia.edu 4 Department of Mathematics, The Pennsylvania State University, Email: ludmil@psu.edu 5 SCI Institute, University of Utah, Email: livne@sci.utah.edu

15 citations


Cited by
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Proceedings ArticleDOI
27 Jun 2016
TL;DR: In this article, the authors proposed a residual learning framework to ease the training of networks that are substantially deeper than those used previously, which won the 1st place on the ILSVRC 2015 classification task.
Abstract: Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers—8× deeper than VGG nets [40] but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions1, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

123,388 citations

Journal ArticleDOI
TL;DR: The guided filter is a novel explicit image filter derived from a local linear model that can be used as an edge-preserving smoothing operator like the popular bilateral filter, but it has better behaviors near edges.
Abstract: In this paper, we propose a novel explicit image filter called guided filter. Derived from a local linear model, the guided filter computes the filtering output by considering the content of a guidance image, which can be the input image itself or another different image. The guided filter can be used as an edge-preserving smoothing operator like the popular bilateral filter [1], but it has better behaviors near edges. The guided filter is also a more generic concept beyond smoothing: It can transfer the structures of the guidance image to the filtering output, enabling new filtering applications like dehazing and guided feathering. Moreover, the guided filter naturally has a fast and nonapproximate linear time algorithm, regardless of the kernel size and the intensity range. Currently, it is one of the fastest edge-preserving filters. Experiments show that the guided filter is both effective and efficient in a great variety of computer vision and computer graphics applications, including edge-aware smoothing, detail enhancement, HDR compression, image matting/feathering, dehazing, joint upsampling, etc.

4,730 citations

Journal ArticleDOI
TL;DR: This report describes, summarize, and analyzes the latest research in mapping general‐purpose computation to graphics hardware.
Abstract: The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware a compelling platform for computationally demanding tasks in a wide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping general-purpose computation to graphics hardware. We begin with the technical motivations that underlie general-purpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping general-purpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in general-purpose application development on graphics hardware. This survey should be of particular interest to researchers who are interested in using the latest GPGPU applications in their systems of interest.

1,998 citations

Proceedings Article
01 Jan 2005
TL;DR: The techniques used in mapping general-purpose computation to graphics hardware will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques.
Abstract: The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware a compelling platform for computationally demanding tasks in a wide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping general-purpose computation to graphics hardware. We begin with the technical motivations that underlie general-purpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping general-purpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in general-purpose application development on graphics hardware. This survey should be of particular interest to researchers who are interested in using the latest GPGPU applications in their systems of interest.

1,728 citations

Journal ArticleDOI
TL;DR: It is shown that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations.
Abstract: We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve an accuracy of O(e) is reduced from O(e-3) to O(e-2 (log e)2). The analysis is supported by numerical results showing significant computational savings.

1,619 citations