Problem 1: (10 pts) In lab, we showed that if interpolated over the data (xj, fj),...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Problem 1: (10 pts) In lab, we showed that if interpolated over the data (xj, fj), (xj+1, fj+1), (xj+2, fj+2) where our nodes are equally spaced so that 8x=xj+1xj = xjxj-1 then using f(x) P2(x), we have 1 f'(xj) (- 3 1 fj + 2 fj + 1 (5 pts) Using the same interpolation information, find an approximation to "(xj). (5 pts) Using f(x) = cos(x), determine the accuracy of your centered difference approximations with respect to the magnitude of 8x for the second derivative. Clearly explain your methodology. Note, in order to measure the error in our approximation, we look at points x; [0,2] where dx = 2/N so that xj = 2j N " j = 0,..., N. We plot the maximum of the absolute value of the error in our approximation over our chosen interval for increasing choices of N. Problem 1: (10 pts) In lab, we showed that if interpolated over the data (xj, fj), (xj+1, fj+1), (xj+2, fj+2) where our nodes are equally spaced so that 8x=xj+1xj = xjxj-1 then using f(x) P2(x), we have 1 f'(xj) (- 3 1 fj + 2 fj + 1 (5 pts) Using the same interpolation information, find an approximation to "(xj). (5 pts) Using f(x) = cos(x), determine the accuracy of your centered difference approximations with respect to the magnitude of 8x for the second derivative. Clearly explain your methodology. Note, in order to measure the error in our approximation, we look at points x; [0,2] where dx = 2/N so that xj = 2j N " j = 0,..., N. We plot the maximum of the absolute value of the error in our approximation over our chosen interval for increasing choices of N.
Expert Answer:
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these mathematics questions
-
"internet radios" for streaming audio, and personal video recorders and players. Describe design and evaluation processes that could be used by a start-up company to improve the usability of such...
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
Requirement 1 Two contribution format statements: current and proposed based on business decision. Requirement 2 For each option current and proposed business decision) calculate the following: a....
-
Yk = q0 + q1k + q2k2 + Zk, Where q 0 + q 1 k + q 2 k 2 is an unknown quadratic function of k and Z k is a sequence of iid Gaussian (0,1) noise random variables. We wish to estimate the unknown...
-
f(x) = (x + 5) 2 - 7 for x 5. Find an expression for f -1 (x).
-
Consider the Gallo strategic decision. Describe how you would go about evaluating that decision.
-
Chrome-It, Inc., manufactures special chromed parts made to the order and specifications of the customer. It has two production departments, stamping and plating, and two service departments, power...
-
(b) If the game below is repeated twice, the following strategies form an SPNE when = 1: Strategies Player 1 period 1: Play C period 2: Play B if (C,Y) in stage 1. Play A otherwise. Player 2 period...
-
Enter the following sales transaction into the Ledger/Journal. You have negotiated the sale of Mr and Mr Emerald's home at 8 Knowle Court, Ocean Grove for $1,000 000. The purchasers, Mr and Mrs Teal...
-
change the order of integration in I= integration(pi/2,0) integration(cos(theta),0) x sin(theta) cos(theta) , and hence evaluate
-
Identify passive voice in the following sentences and convert it to active voice. In some cases, you may need to add information to do so. You may use different words as long as you retain the basic...
-
Listed here are several things an organization might like its employees to do: 1. Write fewer emails. 2. Volunteer at a local food pantry. 3. Volunteer to recruit interns at a job fair. 4. Attend...
-
Revise each of the following sentences to focus on the options that remain, not those that are closed off. 1. Applications that are postmarked after January 15 will not be accepted. 2. All new...
-
In the U.S., credit card companies make offers to people fresh out of bankruptcy. They do this because they know that those targeted people cannot file for Chapter 7 bankruptcy again for eight years....
-
In each of the following pairs, identify the more favorable term. When is its use justifiable? 1. wasted/sacrificed 2. illegal alien/immigrant 3. bring about/cause 4. terminate/fire 5....
-
Write a C++ program that utilizes a function named find_pi to find the value of pi given the desired accuracy. Prompt the user for the accuracy. You must create the find_pi function and all arguments...
-
a) Calculate the goodwill that was paid by Major Ltd on the acquisition of Minor Ltd. [10 marks] b) Prepare the consolidated statement of financial position for Major Ltd at 31 July 20X8. [30 marks]...
-
Dr. Ivan I. Incisor and his wife Irene are married and file a joint return for 2012. Ivan's Social Security number is 477-34-4321 and he is 48 years old. Irene I. Incisor's Social Security number is...
-
Brian and Kim have a 12-year-old child, Stan. For 2012, Brian and Kim have taxable income of $52,000, and Stan has nonqualifying dividend income of $4,500 and investment expenses of $250. No election...
-
David and Darlene Jasper have one child, Sam, who is 6 years old. The Jaspers reside at 4639 Honeysuckle Lane, Los Angeles, CA 90248. David's Social Security number is 577-11-3311, Darlene's is...
-
Based on Exhibit 1, the fi nancial leverage ratio for Company B is closest to: A . 0.55. B . 1.22. C . 2.22. EXHIBIT 1 Common-Size Balance Sheets for Company A, Company B, and Sector Average Company...
-
Based on Exhibit 1, which ratio indicates lower liquidity risk for Company A compared with Company B? A . Cash ratio. B . Quick ratio. C . Current ratio. EXHIBIT 1 Common-Size Balance Sheets for...
-
Under which section of a manufacturing companys cash fl ow statement are the following activities reported? Item 1: Purchases of securities held for trading Item 2: Sales of securities considered...
Study smarter with the SolutionInn App