Lecture 26

Lecture 26 - Intersection of Two Curves Intersection of a...

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

Intersection of Two Curves Intersection of a circle and a parabola = - = = - + = = - = = - + = 0 x x x x f 0 1 x x x x f or 0 y x y x g 0 1 y x y x f 2 2 1 2 1 2 2 2 2 1 2 1 1 2 2 2 ) , ( ) , ( ) , ( ) , (

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

View Full Document
- = - = - + = 1 x 2 x 2 x 2 x f x f x f x f x x x x f 1 x x x x f 1 2 1 2 2 1 2 2 1 1 1 2 2 1 2 1 2 2 2 2 1 2 1 1 ) , ( ) , ( - - = - = i 2 i 1 i 2 i 1 i 1 i 2 i 1 f f x x 1 x 2 x 2 x 2 x J , , , , , , , } ]{ [ Intersection of Two Curves { } - - = - = = + + i 2 1 i 2 i 1 1 i 1 old new i 2 i 1 x y x x x x x x x , , , , , , Solve for x new
Newton-Raphson Method = = = = = ) ( ) ( ) ( ) ( ) ,.... , , , ( ) ,.... , , , ( ) ,.... , , , ( ) ,.... , , , ( x f x f x f x f ) x ( F 0 x x x x f 0 x x x x f 0 x x x x f 0 x x x x f n 3 2 1 n 3 2 1 n n 3 2 1 3 n 3 2 1 2 n 3 2 1 1 [ ] n 3 2 1 x x x x x , 0 x F = = ) ( n nonlinear equations in n unknowns

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

View Full Document
Jacobian (matrix of partial derivatives) Newton’s iteration Newton-Raphson Method 1 1 1 1 1 2 3 2 2 2 2 1 2 3 3 3 3 3 1 2 3 1 2 3 ( ) n n n n n n n n f f f f x x x x f f f f x x x x J x f f f f x x x x f f f f x x x x = O ( ) ( ); x old old new old J y x x x y F x = - ≡ ∆ ≡ -  
function x = Newton_sys(F, JF, x0, tol, maxit) % Solve the nonlinear system F(x) = 0 using Newton's method

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.

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

Page1 / 21

Lecture 26 - Intersection of Two Curves Intersection of a...

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

View Full Document
Ask a homework question - tutors are online