Example 1 64 outlined the following algorithm for computing the square root of 2 Verify that cent The function f(x) 1 2 (x 2 x) is contraction mapping on the set X x x yen 1 cent The fixed point of f is 2 Estimate how many iterations are required to ensure that the approximation error is less than 0 001 The following result is often useful in establishing the properties of the fixed point of a particular model 4 0 2, x 1 x

Question: Example 1.64 outlined the following algorithm for computing the square root of 2: Verify that ¢ The function f(x) = 1/2 (x + 2/x) is

Example 1.64 outlined the following algorithm for computing the square root of 2:

Verify that
€¢ The function f(x) = 1/2 (x + 2/x) is contraction mapping on the set X = {x ˆŠ „œ: x ‰¥ 1}
€¢ The fixed point of f is ˆš2
Estimate how many iterations are required to ensure that the approximation error is less than 0.001.
The following result is often useful in establishing the properties of the fixed point of a particular model.

4-0 2, x*+1 " = x" +

Step by Step Solution

★★★★★

3.54 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

First observe that 1 for every 1 Therefore For any Since 1 1 for all so that or 12 is a co... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

914-M-N-A-O (325).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

The following algorithm will generate a random permutation of the elements 1, 2, . . . , n. It is somewhat faster than the one presented in Example 1a but is such that no position is fixed until the...

Devise a recursive algorithm for computing n2 where n is a nonnegative integer, using the fact that (n + 1)2 = n2 + 2n + 1. Then prove that this algorithm is correct.

Give a recursive algorithm for computing nx whenever n is a positive integer and x is an integer, using just addition.

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

All the information are in it (i) g(x) = x?(x + 5)%(x 1)(x 4) (a) Degree: ; Leading coefficient: ; based on this the end behavior is: (b) the x-intercepts: X-intercept Multiplicity Bounce or cross?...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

Danielson Electronics manufactures color television sets for sale in a highly competitive marketplace. Recently Ron Thomas, the marketing manager of Danielson Electronics, has been complaining that...

How can an increase in the U.S. saving rate lead to higher living standards?

1. What is meant by a dilutive security?

You are managing a complex project for a new method of heating and air conditioning in vehicles. You will use both solar and wind technologies in this project to reduce energy costs. Therefore, you...

Assume Z has a standard normal distribution. Use Appendix Table II to determine the value for z that solves each of the following: (a) P(Z z) = 0.1 (d) P(Z >...

Assume Z has a standard normal distribution. Use Appendix Table II to determine the value for z that solves each of the following: (a) P(-z

Assume X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the following: (a) P(X 9) (c) P(6

REQUIRED: Use two consecutive years ( 2 0 2 1 - 2 0 2 2 ) data for Zillow Group Inc ( Z ) to answer the following questions: What is the company core business? The main focus of Zillow Group Inc. ' s...

Q2) the 2-month interest rates in Switzerland and the United States are, respectively, 2\% and 3\% per annum with continuous compounding. The spot price of the Swiss franc is $1.0500. The futures...

2. Suppose a random variable U ~ unif(0, 1). (c) Next, consider another set of independent random variables Y1, ..., Ym, where each Y; is related to U; through Y= -0In Ui, where U; ~ unif(0, 1) and 0...