


Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
The solution to assignment #2 for the mth603 course taken in spring 2012. The assignment includes constructing divided difference tables and using newton's interpolation polynomial to find function values, as well as finding derivatives using forward and backward differences. The document also includes the steps and calculations for each question.
Typology: Exercises
1 / 4
This page cannot be seen from the preview
Don't miss anything!
MTH603 (Spring 2012)
Total marks: 10 Lecture # 23- Due date: 20-06-
Dear students as it was told there are 3 questions in the assignment but only one question will be graded. Question 3 will be graded.
Question#1 Marks 10
A function y=f(x) is given by the following table.
x 321.0 322.8 324.2 325. y=f(x) 2.50651 2.50893 2.51081 2.
a) Construct the divided differences table for the above data. b) Find f (323.5) by Newton’s interpolation polynomial.
Solution:
The divided difference table for the given data is constructed as;
x f(x) 1 st^ D.D 2 nd^ D.D 3 rd^ D.D 321.0 2. 322.8 2.50893 0. 324.2 2.51081 0.001343 -3.12510- 325.0 2.51188 0.001338 -2.27310-6^ -4.901*10 -
Now, using Newton’s divided difference formula, we have
0 0 0 1 0 1 0 1 2 0 1 2 0 1 2 3
7 7
y y x x y x x x x x x y x x x x x x x x x y x x x x y x x x x x x y x
7 2 4 7 3 4 2
4 7 2
x x x x x
x x x x
7 3 2 7 3
x x x x x
Hence, the value of f(323.5)
2 7 3
y f
Question#2 Marks 10
Find / / /
x 0.4 0.5 0.6 0.7 0. y 1.5836494 1.7974426 2.0442376 2.3275054 2.
Solution:
y (^) n yn y^ n^ yn^ yn h
y
y
y
y
2 3 4 2
2
2
2
y (^) n (^) h yn yn yn
y
y
y
y