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. Calculus Functions of single variable Limit con tinuity and differentiability Mean value theorems Evaluation of definite and improper integrals Partial derivatives Total derivative Maxima and minima Gradient Divergence and Curl Vector identities Di Such matrices has several attractive properties they support algorithms with low computational complexity and make it easy to perform in cremental updates to signals We discuss applications to several areas including compressive sensing data stream Calculus Functions of single variable Limit continuity and differentiability Mean value theorems Evaluation of definite and improper integrals Partial derivatives Total derivative Maxima and minima Gradient Divergence and Cu rl Vector identities Di for Linear Algebra and Beyond. Jim . Demmel. EECS & Math Departments. UC Berkeley. 2. Why avoid communication? (1/3). Algorithms have two costs (measured in time or energy):. Arithmetic (FLOPS). Communication: moving data between . Recovery. . (. Using . Sparse. . Matrices). Piotr. . Indyk. MIT. Heavy Hitters. Also called frequent elements and elephants. Define. HH. p. φ. . (. x. ) = { . i. : |x. i. | ≥ . φ. ||. x||. p. Lectures 1-2. David Woodruff. IBM Almaden. Massive data sets. Examples. Internet traffic logs. Financial data. etc.. Algorithms. Want nearly linear time or less . Usually at the cost of a randomized approximation. Contents. Problem Statement. Motivation. Types . of . Algorithms. Sparse . Matrices. Methods to solve Sparse Matrices. Problem Statement. Problem Statement. The . solution . of . the linear system is the values of the unknown vector . 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). Alexander G. Ororbia II. The Pennsylvania State University. IST 597: Foundations of Deep Learning. About this chapter. Not a comprehensive survey of all of linear algebra. Focused on the subset most relevant to deep learning. Object Recognition. Murad Megjhani. MATH : 6397. 1. Agenda. Sparse Coding. Dictionary Learning. Problem Formulation (Kernel). Results and Discussions. 2. Motivation. Given a 16x16(or . nxn. ) image . 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. Ms. Abelson & Ms. Treece. Acc. Algebra 1/Geometry A. Accelerated moves at a faster pace – level of rigor is much higher . Covers 9 units instead of 6 - (covers 3 units of geometry). Students should be very self motivated, organized, excel at time management, should not be afraid to ask for help, and advocate for themselves.. and . Vector Calculus . and . Calculus of several Variables. Details of the Course M - 107. Math - 107 . Vectors and Matrices (3+0) credit-hours.. 1438– 1439 . H. 2. Dr.Khawaja. Zafar . Elahi. Jim . Demmel. EECS & Math Departments. UC Berkeley. Why avoid communication? . Communication = moving data. Between level of memory hierarchy. Between processors over a network. Running time of an algorithm is sum of 3 terms:.