Linear Algebra
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Addendum: Hit-And-Run CG Algorithm, Maximum Volume Ellipsoid Method, Chebyshev Center Method, Analytic Center Cutting-Plane Method, Extensions (Of Cutting-Plane Methods), Dropping Constraints, Epigraph Cutting-Plane Method, PWL Lower Bound On Convex Function, Lower Bound, Analytic Center Cutting-Plane Method, ACCPM Algorithm, Constructing Cutting-Planes, Computing The Analytic Center, Infeasible Start Newton Method Algorithm, Properties...more
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After discussing the statistical basis of the law of mass action, the lecture turns to developing a framework for understanding reaction rates. A potential energy surface that associates energy with polyatomic geometry can be realized physically for a linear, triatomic system, but it is more practical to use collective energies for starting material, transition state, and product, together with Eyring theory, to predict rates....more
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Newton's Method (Cont.), Newton Step At Infeasible Points, Solving KKT Systems, Equality Constrained Analytic Centering, Complexity Per Iteration Of Three Methods Is Identical, Network Flow Optimization, Analytic Center Of Linear Matrix Inequality, Interior-Point Methods, Logarithmic Barrier
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Guest Lecturer: Krasimir Kolarov, Trajectory Generation - Basic Problem, Cartesian Planning, Cubic Polynomial, Finding Via Point Velocities, Linear Interpolation, Higher Order Polynomials, Trajectory Planning with Obstacles
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Jordan Canonical Form, Generalized Modes, Cayley-Hamilton Theorem, Proof Of C-H Theorem, Linear Dynamical Systems With Inputs & Outputs, Block Diagram, Transfer Matrix, Impulse Matrix, Step Matrix
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Continue On Experiment Design, Geometric Problems, Minimum Volume Ellipsoid Around A Set, Maximum Volume Inscribed Ellipsoid, Efficiency Of Ellipsoidal Approximations, Centering, Analytic Center Of A Set Of Inequalities, Linear Discrimination
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Using the method of undetermined coefficients to solve nonhomogeneous linear differential equations.
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Creating a Generic Swap Function for Data Types of Arbitrary Size, Void* Type for Generic Pointers, Implementation of Swap Function Using memcpy, Client Interface to Generic Swap Function, Pros and Cons of C Generics vs. C++ Generics, Errors Resulting from Improper Use of C Generic Swap Function that Compile, Swapping Pointers, Pitfalls when Swapping Pointers Using Generics, Implementing a Generic Linear Search, Implementing a Generic...more
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Methods (Truncated Newton Method), Convergence Versus Iterations, Convergence Versus Cumulative CG Steps, Truncated PCG Newton Method, Truncated Newton Interior-Point Methods, Network Rate Control, Dual Rate Control Problem, Primal-Dual Search Direction (BV Section 11.7), Truncated Netwon Primal-Dual Algorithm, Primal And Dual Objective Evolution, Relative Duality Gap Evolution, Relative Duality Gap Evolution (N = 10^6), L_1-Norm Methods...more
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Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories
MIT / Mathematics
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Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues
MIT / Mathematics
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