Question: Repeat Exercise 15, constructing instead the clamped cubic spline with f'(0) = f' (1) = 0. In Exercise 15 Construct a natural cubic spline to

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

Ge-x dx = 1-1/e.

Step by Step Solution

★★★★★

3.35 Rating (161 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 x x ... 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 (329).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

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...

Repeat Exercise 15 using n = m = p = 3. In Exercise 15 0 1 0 y dz dy dx z dz dy dx r-y sin y d: dy da Jo Jo Jo )

Repeat Exercise 15 using n = m = p = 4 and n = m = p = 5. In Exercise 15 0 1 0 y dz dy dx z dz dy dx r-y sin y d: dy da Jo Jo Jo )

Repeat Exercise 32, constructing three natural splines using Algorithm 3.4. In Exercise 32 The upper portion of this noble beast is to be approximated using clamped cubic spline interpellants. The...

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

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...

1. A transportation engineering study was conducted to determine the proper design of bike lanes. Data were gathered on bike-lane widths and average distance between bikes and passing cars. The data...

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...

interpolation and the Lagrange polynomial 5. Polynomial Irrte rpolation. {a} Use the Lagrange interpolation process to obtain a polynomial of least degree that assumes these values. 1 I] 2 3 4 y i"...

I was given the following file "ScriptFigs.m": % % Script for generating figures and testing stuff. % n = 10; x = 1:n; y = randn(n,1); pp = spline (x, y); %% Plot the results delta = 0.05; x2 =...

In 1970 Milton Friedman wrote that "there is only one social responsibility for business - to use its resources and engage in activities designed to increase its profits as long as it remains within...

Consider the following forecasts for a project (in thousands): Year 1 55,000 55,000 27,000 27,000 28,000 5,000 7,000 Revenues - Cost of goods sold Gross profit - General, sales, and administrative...

8. Fig. 1F.17 shows how pressure increases with depth below the surface of the sea. (a) Why is the pressure 100 kPa on the surface of the sea? (b) What is the pressure 45 m below the surface? 550 500...

You just found out that a major subcontractor for your project consistently provides deliverables late. The subcontractor approaches you and asks you to continue accepting late deliverables in...

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

Assume X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the value for x that solves each of the following: (a) P(X > x) = 0.5 (b) P(X > x) = 0.95 (c) P(x

Assume X is normally distributed with a mean of 5 and a standard deviation of 4. Determine the following: (a) P(X 0) (c) P(3

A bag contains 7 red marbles, 9 blue marbles, and 3 green marbles. If one marble is randomly selected from the bag, what is the probability that it is blue? Write your answer as a decimal rounded to...

Use the dataset Homework2_Data1 and a simple linear regression model to calculate the beta of the stock ABC based on CAPM (see Lecture 5). Please notice that the variables are stock return and...

The bid and offer orders of XYZ stock are shown in the table below. The last executed price was $9.55. Q2. Mary would like to buy 10,000 shares of XYZ stock. However, she thinks that as long as the...