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谱图理论,线性求解器及其应用

Spectral Graph Theory, Linear Solvers and Applications
课程网址: http://videolectures.net/mlss09us_miller_sgtlsa/  
主讲教师: Gary L Miller
开课单位: 卡内基梅隆大学
开课时间: 2009-07-30
课程语种: 英语
中文简介:
我们讨论了用于求解对称对角占优线性系统的组合方法的发展。在过去的十五年中,计算机科学界在SDD系统的快速求解器方面取得了实质性进展。对于一般SDD系统,上限为$ 0(m \ log ^ k n)$,对于某些常量$ k $,其中$ m $是非零项的数量,由于Spielman和Teng。较新的方法,组合多重网格,对于平面情况具有线性时间保证,并且在实践中工作得很好。使用这些新解算器的关键是减少SDD系统解决方案的问题。我们提出了一些减少,包括几个来自图像处理。
课程简介: We discuss the development of combinatorial methods for solving symmetric diagonally dominate linear systems. Over the last fifteen years the computer science community has made substantial progress in fast solvers for SDD systems. For general SDD systems the upper bound is $0(m \log^k n)$ for some constant $k$, where $m$ is the number of non-zero entries, due to Spielman and Teng. Newer methods, combinatorial multigrid, have linear time guarantee for the planar case and work very well in practice. Critical to the use of these new solvers has been the reduction of problems to the solution of SDD systems. We present some of these reductions, including several from image processing.
关 键 词: 计算学习理论; 图像处理; SDD系统
课程来源: 视频讲座网
最后编审: 2020-06-08:吴雨秋(课程编辑志愿者)
阅读次数: 50