# Lecture23 - Engineering Analysis ENG 3420 Fall 2009 Dan C....

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1 Engineering Analysis ENG 3420 Fall 2009 Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00

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2 Lecture 23 Lecture 23 ± Attention: The last homework HW5 and the last project are due on Tuesday November 24!! ± Last time: ² Linear regression versus sample mean. Coefficient of determination ² Polynomial least squares fit ² Multiple linear regression ² General linear squares ² More on non-linear models ² Interpolation (Chapter 15) ± Today ² Lagrange interpolating polynomials ² Splines ² Cubic splines ² Searching and sorting. ± Next Time ² More on Splines ² Numerical integration (chapter 17)
3 Newton interpolating polynomial of degree n-1 ± In general, an ( n -1) th Newton interpolating polynomial has all the terms of the ( n -2) th polynomial plus one extra. ± The general formula is: ± where ± and the f […] represent divided differences . f n 1 x () = b 1 + b 2 x x 1 + L + b n x x 1 ( ) x x 2 ( ) L x x n 1 ( ) b 1 = fx 1 ( ) b 2 = 2 , x 1 [] b 3 = 3 , x 2 , x 1 M b n = n , x n 1 , L , x 2 , x 1

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4 Divided differences ± Divided difference are calculated as follows: ± Divided differences are calculated using divided difference of a smaller number of terms: fx i , x j [] = i ( ) j ( ) x i x j i , x j , x k = i , x j j , x k x i x k n , x n 1 , L , x 2 , x 1 = n , x n 1 , L , x 2
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## This note was uploaded on 02/17/2012 for the course EGN 3420 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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Lecture23 - Engineering Analysis ENG 3420 Fall 2009 Dan C....

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