Lecture 11 - Lecture 11 Solving equations BMEn 2401...

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11/23/2010 1 Lecture 11: Solving equations BMEn 2401 Programming for Biomedical Engineers Rich Beck November 23, 2010 1 Today’s Lecture Linear equations Nonlinear equations Ordinary differential equations Partial differential equations BONUS: Polynomial regression Curve fitting of data points polyval polyfit
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11/23/2010 2 Solving linear equations A simple case: ax = b a, b are known scalars and x is the unknown scalar) x = b/a 3 Solving linear equations If we have a system of linear equations, a 11 x 1 + a 12 x 2 + a 13 x 3 = b 1 a 21 x 1 + a 22 x 2 + a 23 x 3 = b 2 a 33 x 1 + a 32 x 2 + a 33 x 3 = b 3 Ax = b , A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 , x = x 1 x 2 x 3 , b = b 1 b 2 b 3 4 we can express it in matrix format:
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11/23/2010 3 Solving linear equations Previously, we learned: Ax = b A -1 Ax = A -1 b Ix = A -1 b x = A -1 b While this method is mathematically correct, we almost never use it when solving linear equations. 5 Solving linear equations What are the options? Direct methods Gauss elimination Iterative methods Gauss-Seidel MATLAB \ and / operators 6 For more on linear eqns in MATLAB: http://www.mathworks.com/moler/lu.pdf
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11/23/2010 4 Solving linear equations MATLAB \ and / operators are used to calculate the solution to linear systems. MATLAB checks the coefficient matrix and finds the
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Lecture 11 - Lecture 11 Solving equations BMEn 2401...

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