{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW3 Solution

# HW3 Solution - ME218 Solutions to Homework 3 Problem1 f xn...

This preview shows pages 1–2. Sign up to view the full content.

ME218: Solutions to Homework 3 Problem1 . 1 1 1 ( ) ( ) 0 ( ) ( )( ) ( ) n n n n n n n n n f x f x f x f x x x x x f x + + + ʹ′ = + = ʹ′ For /4 2 ( ) 1 x f x e x = + , we have /4 ( ) 0.25 2 x f x e x ʹ′ = + 0 0 0 1 1 ( ) 0.7788, ( ) 1.8053 0.5686 x f x f x x ʹ′ = = = = Iteration n x ( ) n f x ( ) n f x ʹ′ 1 n x + 1 1 0.7788 1.8053 0.5686 2 0.5686 0.1908 0.9203 0.3613 3 0.3613 0.4417 0.4942 0.2719 4 0.2719 0.0082 0.3103 0.2454 The approximation result after 4 iterations is ࠵? 0 . 2454 . Problem2 1 1 1 1 1 1 1 ( ) ( ) ( ) ( ) ( ) 0 ( ) ( ) ( ) i i i i i i i i i i i i i i i f x f x x x f x x x f x x x f x x x f x f x + + + = + = . For 0 1 ( ) , 0, 1 x f x e x x x = = = , we have 0 1 2 ( ) 1, ( ) -0.6321 0.6127 f x f x x = = = Iteration 1 i x i x 1 ( ) i f x ( ) i f x 1 i x + 1 0 1 1.0000000 -0.6321205 0.6126998 2 1 0.6126998 -0.6321205 -0.0708139 0.5638383 3 0.6126998 0.5638383 -0.0708139 0.0051824 0.5671703 The approximation result after 3 iterations is 4 0.5671703 x . If 0.5671433 Actual x , the relative error of the solution is 3 0.5671703 0.5671433 100% 4.76 10 % 0.5671433 Actual Actual x x x x x x δ Δ = = = × = ×

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

View Full Document
Problem3. (a) 0 0 0 0 9 15 21 27 138, 18 30 42 54 27 45 63 81 cd dc Ρ Τ ΢ Υ ΢ Υ = = ΢ Υ ΢ Υ Σ Φ r r r r . They are not equal. The former is a scalar while the latter is a 4 4 × matrix. (b) 3 4 Ib Ρ Τ = ΢ Υ Σ Φ r r , which is equal to
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

HW3 Solution - ME218 Solutions to Homework 3 Problem1 f xn...

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

View Full Document
Ask a homework question - tutors are online