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Unformatted text preview: E7 Lecture 13: Interpolation & Approximation. . . Tad Patzek, Civil & Environmental Engineering, U.C. Berkeley March 17, 2008 Announcements. . . For this week read: Class book Chapters 7 and Chapras IV Class handouts for Lectures 13 and 14 Prof. T.W. Patzeks E7 Lecture 13: . . . p.1/23 Todays Lecture Today we shall learn about: Approximation and Interpolation Prof. T.W. Patzeks E7 Lecture 13: . . . p.2/23 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. Patzeks 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. Inbetween the data points our interpolating function should behave nicely, for example, it should not oscillate wildly. Prof. T.W. Patzeks E7 Lecture 13: . . . p.4/23 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 interpolations of a periodic and step function LagrangeDemo.m shows how 2, 3, and 4 points of an...
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This note was uploaded on 03/04/2009 for the course E 7 taught by Professor Patzek during the Spring '08 term at University of California, Berkeley.
 Spring '08
 Patzek

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