PPT-Accelerated Sparse Linear Algebra: Emerging Challenges and Capabilities for Numerical

Michael A Heroux Director of Software Technology Exascale Computing Project Senior Scientist Sandia National Laboratories Numerical algorithms for highperformance computational science London UK. e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations Volkan . Cevher. volkan.cevher@epfl.ch. Laboratory. for Information . . and Inference Systems - . LIONS. . http://lions.epfl.ch. Linear Dimensionality Reduction. Compressive sensing. non-adaptive measurements. Least Absolute Shrinkage via . The . CLASH. Operator. Volkan. Cevher. Laboratory. for Information . . and Inference Systems – . LIONS / EPFL. http://lions.epfl.ch . . & . Idiap. Research Institute. Aswin C Sankaranarayanan. Rice University. Richard G. . Baraniuk. Andrew E. Waters. Background subtraction in surveillance videos. s. tatic camera with foreground objects. r. ank 1 . background. s. parse. &. Miriam . Leeser. Dana Brooks. mel@coe.neu.edu brooks@ece.neu.edu. 1. This . work . is supported by: . NSF . CenSSIS. - The Center for Subsurface Sensing and Imaging. Sparse Beamforming. Volkan. . cevher. Joint work with: . baran. . gözcü. , . afsaneh. . asaei. outline. 2. Array . a. cquisition model. Spatial linear prediction. Minimum variance distortion-less response (MVDR). Richard Peng. M.I.T.. Joint work with Dan Spielman (Yale). Efficient Parallel Solvers for SDD Linear Systems. Richard Peng. M.I.T.. Work in progress with . Dehua. Cheng (USC),. Yu Cheng (USC), . Yintat. Weihong Deng (. 邓伟洪. ). Beijing Univ. Post. & Telecom.(. 北京邮电大学. ) . 2. Characteristics of Face Pattern. The facial shapes are too similar, sometimes identical ! (~100% face detection rate, kinship verification). . Jeremy Watt and . Aggelos. . Katsaggelos. Northwestern University. Department of EECS. Part 2: Quick and dirty optimization techniques. Big picture – a story of 2’s. 2 excellent greedy algorithms: . ITEC 7445: EMERGING TECHNOLOGY. NOVEMBER 12, 2012. Accelerated Math. Provided by Renaissance Learning.. A software tool that is used to customize assignments and monitor progress in mathematics.. Creates individualized goals and assignments.. :. Application to Compressed Sensing and . Other Inverse . Problems. M´ario. A. T. . Figueiredo. Robert . D. . Nowak. Stephen . J. Wright. Background. Previous Algorithms. Interior-point method. . Applications. Lecture 5. : Sparse optimization. Zhu Han. University of Houston. Thanks Dr. . Shaohua. Qin’s efforts on slides. 1. Outline (chapter 4). Sparse optimization models. Classic solvers and omitted solvers (BSUM and ADMM). John R. Gilbert (. gilbert@cs.ucsb.edu. ). www.cs.ucsb.edu/~gilbert/. cs219. Systems of linear equations:. . Ax = . b. Eigenvalues and eigenvectors:. Aw = . λw. Systems of linear equations: Ax = b. Xin Qian. BNL. 1. Introduction. Linear Algebra (LA) has a very long history:. First appears in “The Nine Chapters on the Mathematical Art” . Systematically i. ntroduced by Rene Descartes. Application of LA is very broad:.