L2_Interpolation

L2_Interpolation - MA2213 Lecture 2 Interpolation...

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 velocity-pressure-temperature) 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 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://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...
View Full Document

This note was uploaded on 01/06/2012 for the course MA 2213 taught by Professor Michael during the Fall '07 term at National University of Singapore.

Page1 / 23

L2_Interpolation - MA2213 Lecture 2 Interpolation...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online