Question: Construct a natural cubic spline to approximate f (x) = ex by using the values given by f (x) at x = 0, 0.25, 0.75,

Construct a natural cubic spline to approximate f (x) = eˆ’x by using the values given by f (x) at x = 0, 0.25, 0.75, and 1.0. Integrate the spline over [0, 1], and compare the result to

Use the derivatives of the spline to approximate f'(0.5) and f'' (0.5). Compare the approximations to the actual values.

Se dx = 1- 1/e.

Step by Step Solution

★★★★★

3.41 Rating (182 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Assume that the equation of the spline is Sx S i x a i b i ... 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)

731-M-N-A-N-L-A (328).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Construct a natural cubic spline to approximate f (x) = cos x by using the values given by f (x) at x = 0, 0.25, 0.5, 0.75, and 1.0. Integrate the spline over [0, 1], and compare the result to 0. Use...

Repeat Exercise 15, constructing instead the clamped cubic spline with f'(0) = f' (1) = 0. In Exercise 15 Construct a natural cubic spline to approximate f (x) = cos x by using the values given by f...

Repeat Exercise 16, constructing instead the clamped cubic spline with f'(0) = 1, f'(1) = e1. In Exercise 16 Construct a natural cubic spline to approximate f (x) = ex by using the values given by f...

2. Construct a natural cubic spline to approximate f(x) 0,0.25, 0.5, 0.75 and 1.0. Integrate the spline the derivatives of the spline to approximate f'(0.5) and f"(0.5). Compare to the analytic...

Part A: (2 marks) Construct a natural cubic spline to approximate f(X) = e * by using the values given by f(X) at X = 0,0.25,0.5,0.75,1.0. Use the derivatives of the spline to approximate f'(0.5) and...

Numerical Methods Question: Will need matlab!!!! (a) Construct a free cubic spline to approximate f(x) = e -x by using the values given by f(x) at x = 0, 0.25, 0.75, and x= 1.0. (You may use Matlab...

Math 104A Homework #4 Instructor: Lihui Chai 1. Write a code to compute a natural spline S(x) which interpolates a collection of given points (x0 , y0 ), (x1 , y1 ), ..., (xn , yn ) where x0

EGN 5458: STATISTICAL APPLICATIONS FOR ENGINEERS HOMEWORK 6 Due: 11.02.2023, 08:00 PM Please submit your homework on CANVAS using the assignment page for Homework 6. Please send your homework in ONE...

Please quality check my solutions for this advanced heat transfer problem. Show all work. Thank you. All original documents are located at the bottom. 3.9 COMPACT HEAT EXCHANGERS 3.9.10-1 3.9.10...

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...

If a country has a surplus balance of payments, what will be the appropriate government policy to restore the balance of payments back to equilibrium? What effects might this have on the country's...

In the Bohr model of the hydrogen atom, a single electron revolves around a single proton in a circle of radius r. Assume that the proton remains at rest (a) By equating the electric force to the...

Where is it being done? Is it the right place? Is reception the right place to collect all that information? Why cant everything but medically necessary information be collected during the process...

The management theory that states that people can direct their own efforts is: A. Theory Y. B. Herzberg's theory. C. Maslow's hierarchy. D. Theory X.

Use Appendix Table II to determine the following probabilities for the standard normal random variable Z: (a) P(-1 3) (e) P(0

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

Calculate the value of a six-month futures contract on a Treasury bond. You have the following information: (Do not round intermediate calculations. Round your answer to 3 decimal places.) 0 ....

A stock has a beta of .6 and an expected return of 10 percent. A risk-free asset currently earns 4.1 percent. a. What is the expected return on a portfolio that is equally invested in the two assets?...

Solve by hand not by excel Galvanized Products is considering purchasing a new computer system for their enterprise data management system. The vendor has quoted a purchase price of $80,000....