hw3solution - Homework 3 Solution 1. Determine the...

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: Homework 3 Solution 1. Determine the approximated root of the following equation: f ( x ) = 5 x 3- 3 x 2 + 6 x- 2 (a) [1pt] Using three iterations of the Newton-Raphson method with the initial guess, x = 1. (b) [1pt] Using three iterations of the secant method with the initial guesses, x- 1 = 0 and x = 1. Solution: (a) Newton-Raphson iteration First order derivative: f ( x ) = 15 x 2- 6 x + 6 x 1 = x- f ( x ) f ( x ) = 1- 6 15 = 0 . 6 x 2 = x 1- f ( x 1 ) f ( x 1 ) = 0 . 6- 1 . 6 7 . 8 = 0 . 3949 x 3 = x 2- f ( x 2 ) f ( x 2 ) = 0 . 3949- . 2095 5 . 9698 = 0 . 3598 , f (0 . 3598) = 0 . 0033 (b) secant method iteration x 1 = x- f ( x )( x- 1- x ) f ( x- 1 )- f ( x ) = 1- 6 (0- 1)- 2- 6 = 0 . 25 x 2 = x 1- f ( x 1 )( x- x 1 ) f ( x )- f ( x 1 ) = 0 . 25-- . 6094 (1- . 25) 6 + 0 . 6094 = 0 . 3192 x 3 = x 2- f ( x 2 )( x 1- x 2 ) f ( x 1 )- f ( x 2 ) = 0 . 3192-- . 2281 (0 . 25- . 3192)- . 6094 + 0 . 2281 = 0 . 3606 2. For a given equation, A~x = ~ b where A is an n-by-n matrix and ~x and ~ b are n-by-1 vectors, well-conditioned systems have det A 6 = 0 and ill-conditioned systems have det A 0, i.e., the determinant is not zero but close to zero. Given the equations . 5 x 1- x 2 =- 9 . 5 , 1 . 02 x 1...
View Full Document

This note was uploaded on 11/14/2011 for the course EAME 250 taught by Professor Lee during the Spring '11 term at Case Western.

Page1 / 5

hw3solution - Homework 3 Solution 1. Determine the...

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