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E7Lecture13Summary

# E7Lecture13Summary - E7 Lecture 13 Interpolation...

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E7 Lecture 13: Interpolation & Approximation. . . Tad Patzek, Civil & Environmental Engineering, U.C. Berkeley March 17, 2008

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Announcements. . . For this week read: Class book Chapters 7 and Chapra’s IV Class handouts for Lectures 13 and 14 Prof. T.W. Patzek’s E7 Lecture 13: . . . – p.1/23
Today’s Lecture Today we shall learn about: Approximation and Interpolation Prof. T.W. Patzek’s E7 Lecture 13: . . . – p.2/23

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Approximation We approximate a complicated or unknown function with a simpler function, e.g., a polynomial which is in some sense “close” to the known function values, but in general does not coincide with these values. A least square fit of a set of data points is a “best” approximation in the sense of minimizing the variance of deviations between the model and data. Prof. T.W. Patzek’s E7 Lecture 13: . . . – p.3/23
Interpolation We design a simpler function, e.g., a polynomial that must coincide with the known function values at discrete points. In-between the data points our interpolating function should behave “nicely,” for example, it should not oscillate wildly. Prof. T.W. Patzek’s E7 Lecture 13: . . . – p.4/23

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Files to download. . . Screendigitizer.m + getcurve.m digitizes screen images LinearInt.m performs piecewise linear interpolation LagrangeInt.m performs interpolation with the Lagrange polynomial vibration.m piecewise linear and the L AGRANGE
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E7Lecture13Summary - E7 Lecture 13 Interpolation...

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