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L2_Interpolation

# L2_Interpolation - MA2213 Lecture 2 Interpolation...

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MA2213 Lecture 2 Interpolation

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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 values of a mathematical function f (ground height, air velocity-pressure-temperature) (cos, log, exp, solution of a differential equation)
Applications 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* ... Medicine, Entertainement, Earth Sciences Computer Aided Design and Manufacturing Image Processing, Computer Graphics and Vision An Efficient Spline Basis For Multi-dimensional 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://skagit.meas.ncsu.edu/~helena/gmslab/viz/sinter.html http://en.wikipedia.org/wiki/Linear_interpolation#Applications http://der.topo.auth.gr/DERMANIS/PDFs/Erice.pdf

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Given a sequence of numbers called nodes, and for each a second number we are looking for a function P so that A pair is called a data point and P is called an interpolant for the data points. One Dimensional Case n k y x P k k ,..., 1 , ) ( = = n n x x x x < < < < - 1 2 1 k x k y ) , ( k k y x
Suppose we have a table like this, which gives some values of an unknown function f . Example 0 0 1 0.8415 2 0.9093 3 0.1411 4 −0.7568 5 −0.9589 6 −0.2794 What 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

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Choosing a Method There are many different interpolation methods, including linear and polynomial . Some of the concerns to take into account when choosing an appropriate method are: How accurate is the method? How expensive is it? How smooth is
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