{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture31

This preview shows pages 1–6. Sign up to view the full content.

Quadratic interpolation – need three points Use the parabola This is the same as ( 29 ( 29 ( 29 ( 29 2 1 3 1 2 1 2 x x b x x b b x f - - + - + = = - - = + - = + + = 3 3 2 3 1 3 2 2 2 1 3 1 2 1 1 3 2 1 2 b a x b x b b a x x b x b b a a x a a x f ) ( Quadratic Interpolation where

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

View Full Document
To get the coefficients b ’s 1) Set x = x 1 , get b 1 = f ( x 1 ) 2) Use b 1 and set x = x 2 to get b 2 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 2 1 1 1 3 1 1 2 1 1 2 x f b x x x x b x x b b x f = = - - + - + = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 1 2 2 2 2 2 1 2 3 1 2 2 1 2 2 x x x f x f b x f x x x x b x x b x f x f - - = = - - + - + = Quadratic Interpolation ( 29 ( 29 ( 29 ( 29 2 1 3 1 2 1 2 x x x x b x x b b x f - - + - + =
( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 3 3 3 2 3 1 3 3 1 3 1 2 1 2 1 3 2 x x b x f x x x x b x x x x x f x f x f x f - - = = - - + - - - + = b is a constant (0th order) b gives slope (finite difference) b gives curvature (difference of finite differences) Quadratic Interpolation 3) Use b 1 and b 2 , and set x = x 3 to get b 3

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

View Full Document
Example: interpolate e 2 using e 1 , e 3 , and e 5 ( 29 ( 29 ( 29 41 148 x f 5 x 086 20 x f 3 x 7183 2 x f 1 x 3 3 2 2 1 1 = = = = = = . . . 870 13 1 5 3 5 e e b ; 6836 8 b ; 7183 2 b 3 5 3 2 1 . . . = - - - - = = = = ( 29 ( 29 ( 29 ( 29 4681 2 3 2 1 2 870 13 1 2 6836 8 7183 2 2 f 2 . * . * . . - = - - + - + = 3891 7 e Exact 2 . = Hand Calculation Example
Example: interpolate e 2 using e 1 , e 1.5 , and e 2.5

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.

{[ snackBarMessage ]}