cot4501fa10_hw1_sol

# cot4501fa10_hw1_sol - COT4501 Fall 2010 Homework 1...

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

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.

Unformatted text preview: COT4501 Fall 2010 Homework 1 solutions 1.3: Since the relative error = approximate value − true value true value , we get r = a − t t from which we obtain that a = t (1 + r ) . 1.4: We have an error in the function value due to a perturbation h in the argument x . a) The absolute error in evaluating sin( x ) is sin( x + h )- sin( x ) ≈ h cos( x ) when h is small, b) the relative error is sin( x + h ) − sin( x ) sin( x ) ≈ h cot( x ) , c) the condition number is approximately equal to | xf ′ ( x ) f ( x ) | = x cot( x ) and d) the problem is highly sensitive to values of x = π 2 + kπ, k ∈ N since the relative error and condition number go to infinity. 1.6: (a) x y = sin( x ) ˆ y = x forward error backward error ˆ y- y ˆ x- x = arcsin( x )- x 0.1 .0998 0.1 0.002 0.0002 0.5 .4794 0.5 0.0206 0.0236 1.0 .8415 1.0 0.1585 0.5708 Table 1: Forward and backward error of the sine function when using the first term of the Taylor series (b) x y = sin( x ) ˆ y = x- x 3 / 6 forward error...
View Full Document

## This note was uploaded on 01/22/2012 for the course COT 4501 taught by Professor Davis during the Spring '08 term at University of Florida.

### Page1 / 2

cot4501fa10_hw1_sol - COT4501 Fall 2010 Homework 1...

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

View Full Document
Ask a homework question - tutors are online