Lecture34 - Cubic Splines 4. Two additional conditions are...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Cubic Splines 4. Two additional conditions are needed (arbitrary) The last two equations Total equations: 2(n-1) + (n-2) + (n-2) +2 = 4(n-1) + = = = = ---- 1 n 1 n 1 n n 1 n 1 1 1 h d 6 c 2 x s c 2 x s ) ( ) ( = + = = = = ---- h d 3 c c c x s x s 1 n 1 n 1 n n 1 n 1 n 1 1 ) ( ) ( Cubic Splines 3 i i 2 i i i i i i x x d x x c x x b a x s ) ( ) ( ) ( ) (- +- +- + = Solve for ( a i , b i , c i , d i ) see textbook for details Tridiagonal system with boundary conditions c 1 = c n = ]) , [ ] , [ ( ) ( 1 i i i 1 i 1 i 1 i i i i 1 i 1 i i i i 1 i 1 i 1 i x x f x x f 3 h f f 3 h f f 3 c h c h h 2 c h- +-- + +---- =--- = +- + ( 29 1 i i i i i 1 i i i i 1 i i i i c c 2 3 h h f f b h 3 c c d f a + + + +-- =- = = , , Cubic Splines ( 29 ( 29 ( 29 --- = + + +-------- x x f x x f 3 x x f x x f 3 x x f x x f 3 c c c c c 1 h h h 2 h h h h 2 h h h h 2 h 1 2 n 1 n 1 n n 2 3 3 4 1 2 2 3 n 1 n 3 2 1 1 n 1 n 2 n 2 n 3 3 2 2 2 2 1 1 ] , [ ] , [ ] , [ ] , [ ] , [ ] , [ ) ( ) ( ) ( Tridiagonal matrix Hand Calculations f(4) estimate 58 19 2 4 ) x ( f 6 5 2 x- f(4) , 4 x 3 x 5 x f(x) : solution Exact 2 3 = + +- = 39 1 19 58 h f f x x f 7 3 2 19 h f f x x f 3 2 4 2 h f f x x f 58 f 19 f 2 f 4 f 1 5 6 x x h 3 2 5 x x h 2 2 x x h 3 3 4 3 4 2 2 3 2 3 1 1 2 1 2 4 3 2 1 3 4 3 2 3 2 1 2 1 =- =- = =-- =- =- =-- =- = = =- = = =- =- = =- =- = =- =- = ] , [ ) ( ] , [ ] , [ , , , , , Hand Calculations ( 29...
View Full Document

This note was uploaded on 09/05/2011 for the course EGM 3344 taught by Professor Raphaelhaftka during the Spring '09 term at University of Florida.

Page1 / 20

Lecture34 - Cubic Splines 4. Two additional conditions are...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online