PPT-Random Matrix Approach to Linear Control Systems

Charlotte Kiang May 16 2012 About me My name is Charlotte Kiang and I am a junior at Wellesley College majoring in math and computer science with a focus on engineering applications What I hope to accomplish today. New York Chichester Brisbane Toronto brPage 3br Copyright 0 1972 by Jom Wiley Sons Inc All rights reserved Published simultaneously in Canada Reproduclion or translation of any part of this work beyond that permitted by Sections 107 or 108 of the Richard Peng. M.I.T.. Joint work with . Dehua. Cheng, Yu Cheng, Yan Liu and . Shanghua. . Teng. (U.S.C.). Outline. Gaussian sampling, linear systems, matrix-roots. Sparse factorizations of . L. p. College Algebra. Section 8.2: . Matrix Notation and Gaussian Elimination. Objectives. Linear systems, matrices, and augmented matrices.. Gaussian elimination and row echelon form.. Gauss-Jordan elimination and reduced row echelon form.. legacy. AI systems. Tyukin. I. Y.. Jointly with A.N. . Gorban. , K. . Sofeikov. , R. Burton, I. . Romamenko. . The World of BIG Legacy AI Systems. AI systems that are already created and form crucial parts of existing solutions/service. Richard Peng. M.I.T.. Joint work with . Dehua. Cheng, Yu Cheng, Yan Liu and . Shanghua. . Teng. (U.S.C.). Outline. Gaussian sampling, linear systems, matrix-roots. Sparse factorizations of . L. 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. June 12, 2017. Benjamin Skikos. Outline. Information & Square Root Filters. Square Root SAM. Batch Approach. Variable ordering and structure of SLAM. Incremental Approach 1. Bayes Tree. Incremental Approach 2. DETERMINANT. a “determinant” is a certain . kind of . function that associates a real number with a square . matrix. We will . obtain a formula for the inverse of an invertible matrix as well as . 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 . Algebra 2. Chapter 3. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. Chapter 3.8. Square Matrix. Although a matrix may have any number of rows and columns, . square matrices. have properties that we can use to solve systems of equations. A square matrix is one of the form . Richard Peng. Georgia Tech. OUtline. (Structured) Linear Systems. Iterative and Direct Methods. (. Graph) . Sparsification. Sparsified. Squaring. Speeding up Gaussian Elimination. Graph Laplacians. 1. Richard Peng. Georgia Tech. OUtline. (Structured) Linear Systems. Iterative and Direct Methods. (. Graph) . Sparsification. Sparsified. Squaring. Speeding up Gaussian Elimination. Graph Laplacians. 1. ME 343 Control Systems Fall 2009Solution of State Space Equation426We consider the linear time-invariant systemAnd we solve to obtainSolution by the Laplace TransformWe Laplace transform the state equ