Lecture 31 - Chapter 15 Polynomial Interpolation...

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Polynomial Interpolation Chapter 15
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Interpolation & Extrapolation Interpolation : data to be found are within the range of observed data. Extrapolation : data to be found are beyond the range of observation data. ( Not reliable *)
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Interpolation Used to estimate values between data points Difference from regression - exactly goes through data points therefore, no error at data points The most common method is the polynomial interpolation
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Interpolation vs. Regression Same data points, different curve fitting
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Superheat tables -- compressed liquid tables are similar u = u ( P,T ) , h = h ( P,T ) , etc.
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Given n data points, fit a unique (n-1) th - order polynomial through them Use polynomial interpolation to determine a ’s For consistency with MATLAB, use ( 29 1 n n 2 3 2 1 x a x a x a a x f - + + + + = ... Polynomial Interpolation n 1 n 2 n 2 1 n 1 p x p x p x p x f + + + + = - - - ) (
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Interpolating Polynomials First-order second-order third-order
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Coefficients of an Interpolating Polynomial Newton and Lagrange polynomials are well-suited for determining values between points (interpolation) However, they do not provide a convenient polynomial of conventional form Use n data points to determine n coefficients + + + + = + + + + = + + + + = - - - - - - - - - n n 1 n 2 n n 2 1 n n 1 n n 2 1 n 2 n 2 2 1 n 2 1 2 n 1 1 n 2 n 1 2 1 n 1 1 1 p x p x p x p x f p x p x p x p x
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Lecture 31 - Chapter 15 Polynomial Interpolation...

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