PPT-Sketching as a Tool for Numerical Linear Algebra

All Lectures 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. Calculus Mean value theorems Theorems of integral calculus Evaluation of definite and improper integrals Partial Derivatives Maxima and minima Multiple integrals Fourier series Vector identities Directional derivatives Line Surface and Volume integ N is the process noise or disturbance at time are IID with 0 is independent of with 0 Linear Quadratic Stochastic Control 52 brPage 3br Control policies statefeedback control 0 N called the control policy at time roughly speaking we choo 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 Hermitian skewHermitian and unitary matriceseigenvalues and eigenvectors diagonalisation of matrices CayleyHamilton Theorem Calculus Functions of single variable limit continuity and differentiability Mean value theorems Indeterminate forms and LHos (what is that?). What . is linear algebra? Functions and equations that arise in the "real world" often involve many tens or hundreds or thousands of variables, and one can only deal with such things by being much more organized than one typically is when treating equations and functions of a single variable. Linear algebra is essentially a ". Purposes of Sketching. Think through a design. Convey your ideas. Uses lines and symbols to describe a design. Common Uses of Sketching . Brainstorm. Communicate. Document Measurements. Advantages of Sketching. Anne Watson. Winchester 2014. Big issues (for today). Algebra. Division. What is algebra?. What are the pre-algebraic and algebraic experiences appropriate for primary children?. ACME comments. Expectations of algebraic thinking could be based on reasoning about relations between quantities, such as patterns, structure, equivalence, . Explain the importance of sketching in the engineering design process. Make simple sketches of basic shapes such as lines, circles, and ellipses. Use 3-D coordinate systems, particularly right-handed systems. Design and Modeling. Common Uses of Sketching . Brainstorm. Communicate. Document. Advantages of Hand Sketching. Convenient. Inexpensive. Sketching Techniques. Lines. Vertical Line. Horizontal Line. Test Design. Performance Level Indicators. Algebra 1 . Keystones. Eligible Content – Test Design – Performance Level Indicators. Ms. Clarkson. Ms. . Hetrick. Ms. Sirio. Eligible Content. Eligible . . SYFTET. Göteborgs universitet ska skapa en modern, lättanvänd och . effektiv webbmiljö med fokus på användarnas förväntningar.. 1. ETT UNIVERSITET – EN GEMENSAM WEBB. Innehåll som är intressant för de prioriterade målgrupperna samlas på ett ställe till exempel:. Michael A. Heroux. Director of Software Technology, Exascale Computing Project. Senior Scientist, Sandia National Laboratories. Numerical algorithms for . highperformance. computational science. London, UK. 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. 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:.