lect_10 - Lecture 10 Numerical Marine Hydrodynamics 2.29...

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Unformatted text preview: Lecture 10 Numerical Marine Hydrodynamics 2.29 Introduction to Numerical Analysis for Engineers Minimization Problems Least Square Approximation – Normal Equation – Parameter Estimation – Curve fitting Optimization Methods – Simulated Annealing • Traveling salesman problem – Genetic Algorithms • • • Minimization Problems Data Modeling – Curve Fitting Linear Model Non-linear Model Minimimize Overall Error Objective: Find c that minimizes error 2.29 Numerical Marine Hydrodynamics Lecture 10 Lecture 10 Numerical Marine Hydrodynamics 2.29 Least Square Approximation n model parameters m measurements n unknowns m > n m measurements m n Linear Measurement Model Overdetermined System Least Square Solution Minimize Residual Norm Lecture 10 Numerical Marine Hydrodynamics 2.29 Least Square Approximation Theorem Proof q.e.d Normal Equation ) A Symmetric n x n matrix. Non- singular if columns of A are linearly independent E B C D A F Normal Equation Points D, E, and F at sea level. Find altitude of inland points A, B, and C. A=[ [1 0 0 -1 0 -1]' [0 1 0 1 -1 0]' [0 0 1 0 1 1]'] b=[1 2 3 1 2 1]'; C=A'*A c=A'*b % Least square solution Residual Vector z=inv(C)*c lstsq.m % Residual r=b-A*z rn=sqrt(r'*r) 2.29 Numerical Marine Hydrodynamics Lecture 10 Least Square Approximation Parameter estimation Example Island Survey Measured Altitude Differences % Quadratic data model...
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.29 taught by Professor Henrikschmidt during the Spring '07 term at MIT.

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lect_10 - Lecture 10 Numerical Marine Hydrodynamics 2.29...

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