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Unformatted text preview: MA2213 Lecture 2 Interpolation Introduction Problem : Find / evaluate a function P whose values are specified on some set S The specified values S x x P ∈ ), ( may arise from measurements of a physical function f (ground height, air velocitypressuretemperature) values of a mathematical function f (cos, log, exp, solution of a differential equation) Applications Medicine, Entertainement, Earth Sciences Computer Aided Design and Manufacturing Image Processing, Computer Graphics and Vision • Applications of interpolation and area display in EEG. – Applications of interpolation and area display in EEG. McGee FE Jr, Lee RG, Harris JA, Melby G, Bickford RG.MeSH Terms Automatic Data Processing* ... An Efficient Spline Basis For Multidimensional Applications ... File Format: PDF/Adobe Acrobat In many applications , bilinear interpolation is. used instead of cubic splines because of its simplicity in. implementation. When HDTV is realized, ... http://der.topo.auth.gr/DERMANIS/PDFs/Erice.pdf http://en.wikipedia.org/wiki/Linear_interpolation#Applications http://skagit.meas.ncsu.edu/~helena/gmslab/viz/sinter.html One Dimensional Case iven a sequence of numbers alled nodes, and for each second number we are ooking for a function P so that n n x x x x < < < < − 1 2 1 L k x k y pair is called a data point and P is alled an interpolant for the data points. n k y x P k k ,..., 1 , ) ( = = ) , ( k k y x uppose we have a table like this, hich gives some values of an nknown function f . Example 0 1 0.8415 2 0.9093 3 0.1411 4 − 0.7568 5 − 0.9589 6 − 0.2794 hat value does the function have at, say, x = 2.5? Interpolation answers questions like this. Plot of the data points as given in the table k x k y ) , ( 3 3 y x ) , ( 4 4 y x Choosing a Method Linear Interpolation ) ( x P lin ) ( x P pol Polynomial Interpolation here are many different interpolation methods, including inear and polynomial . Some of the concerns to take into ccount when choosing an appropriate method are: How ccurate is the method? How expensive is it? How smooth is he interpolant? How many data points are needed? Linear Interpolation...
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 Fall '07
 Michael
 Numerical Analysis, yk, xk

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