CSC_349_HANDOUT#11

CSC_349_HANDOUT#11 - 1 COMPUTER SCIENCE 349A Handout Number...

Info iconThis preview shows pages 1–2. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 COMPUTER SCIENCE 349A Handout Number 11 ORDER OF CONVERGENCE OF THE SECANT METHOD AND BISECTION METHOD The Secant method iterative formula is ) ( ) ( ) ( 1 1 1 + = i i i i i i i x f x f x x x f x x . Therefore, if t x denotes an exact zero of ) ( x f , = = + t i t i t i i i i i i i i i t i t i i i i i i t i t i x x x x x f x f x x x f x f x x x f x f x x x x x f x f x x x f x x x x 1 1 1 1 1 1 1 1 1 ) ( ) ( ) ( ) ( ) ( ) ( 1 ) )( ( ) ( ) ( ) ( ) ( By the Mean Value Theorem, the first large square bracket term above is equal to ) ( 1 i f , for some value 1 and between i i i x x . The term in the second large square bracket above is equal to 2 ) ( i f , for some value i in an interval spanned by t i i x x x and , 1 as this is a second divided difference...
View Full Document

Page1 / 3

CSC_349_HANDOUT#11 - 1 COMPUTER SCIENCE 349A Handout Number...

This preview shows document pages 1 - 2. Sign up to view the full document.

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