Decomposition
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Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix...more
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Continuation of Convex Optimization I. Topics include: Subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and...more
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Programming Methodology is the largest of the introductory programming courses and is one of the largest courses at Stanford. Topics focus on the introduction to the engineering of computer applications emphasizing modern software engineering principles: object-oriented design, decomposition, encapsulation, abstraction, and testing. Programming Methodology teaches the widely-used Java programming language along with good software...more
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Seeing Functions as Data: Specific Plot Functions, Generic Plot Function, Back to the Set, Live Coding Example: Use of Set with User Defined Data Types, Client Callback Function, Review of the Classes Seen,5 Using Nested ADTs (Abstract Data Types), Live Coding Example, Recursion, Recursive Decomposition
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Orthonormal Set Of Vectors, Geometric Interpretation, Gram-Schmidt Procedure, General Gram-Schmidt Procedure, Applications Of Gram-Schmidt Procedure, 'Full' QR Factorization, Orthogonal Decomposition Induced By A, Least-Squares
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Professor Sylvia Ceyer covers radioactive decay and its various uses in modern medicine. Second order half-life, as a second order integrated rate law, is then discussed. The lecture concludes with the overlap of kinetics and chemical equilibrium: the equilibrium constant, elementary reactions, and an example, the decomposition of ozone.
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Latent Semantic Indexing (LSI), Singular Value Decomposition (SVD) Implementation, Independent Component Analysis (ICA), The Application of ICA, Cumulative Distribution Function (CDF), ICA Algorithm, The Applications of ICA
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Gain Of A Matrix In A Direction, Singular Value Decomposition, Interpretations, Singular Value Decomposition (SVD) Applications, General Pseudo-Inverse, Pseudo-Inverse Via Regularization, Full SVD, Image Of Unit Ball Under Linear Transformation, SVD In Estimation/Inversion, Sensitivity Of Linear Equations To Data Error
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Karel and Java, Common Errors, Comments, Pre-conditions and Post-conditions, Decomposition, The DoubleBeepers Example, Importance of Good Software Engineering, The Right Decomposition, The CleanUpKarel Example
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Decomposition Applications, Rate Control Setup, Rate Control Problem, Rate Control Lagrangian, Aside: Utility Functions, Rate Control Dual, Dual Decomposition Rate Control Algorithm, Generating Feasible Flows, Convergence Of Primal And Dual Objectives, Maximum Capacity Violation, Single Commodity Network Flow Setup, Network Flow Problem, Network Flow Lagrangian, Network Flow Dual, Recovering Primal From Dual, Dual Decomposition Network...more
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Decomposition and abstraction through functions; introduction to recursion
