Lecture 8 Slides - 10/6/2010 SecantMethod...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
10/6/2010 1 Secant Method Requires two initial values ( x 0 , x 1 ) Initial values do not have to lie on either side of root (not a bracketing method) Iterative formula: ) )( ( 1 i i i x x x f Like Newton Raphson but with numerically estimated derivative. ) ( ) ( 1 1 i i i i x f x f x x ) ) ( / ) ( ) ( ) ( : Raphson Newton 1 i i i i i i i f f x f x f x x f x f x x ) ( ) ( ) ( / ) ( ) ( ) ( ) )( ( : Secant 1 1 1 1 1 i i i i i i i i i i i i i x x x f x x f x x f x f x x x x x Approximate derivate Modified Secant Method Only one initial value required ( x 0 ) Iterative formula: ) ( ) ( ) ( 1 i i i i i i i x f x x f x f x x x where δ is a small perturbation fraction Same basic idea but derivative estimated in a slightly different way i i i i i i i i i i i i x f x x f x f x x f x x x x f x f x x f x f x x ) ( ) ( / ) ( ) ( : Secant Modified ) ( / ) ( ) ( ) ( : Raphson Newton 1 Approximate derivative i i i i i i i i x x f x x f ) ( ) ( 1 Choice of δ important: too small > numerical errors too large > inefficient, method may diverge
Background image of page 1

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

View Full DocumentRight Arrow Icon
10/6/2010 2 Technique Key Formula Notes Bisection
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

Lecture 8 Slides - 10/6/2010 SecantMethod...

This preview shows document pages 1 - 3. Sign up to view the full document.

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