1. Suppose we want to approximate the function f(x) = sin(x) on the interval [0, 1] by using polynomial interpolation with xo = 0, x₁ = 0.5, and x2 = 1. (a) Let pi(x) be the polynomial that interpolates f(x) at xo and ₁. (i) Find the error bound at x = 0.3 (i.e., the bound for error f(0.3) - pi(0.3)). (ii) Find the error bound on the whole interval [0, 0.5]. (iii) Use any method of your choice to find p₁(x) and compare the actual error at x = 0.3 with the error bounds in previous steps. (b) Let p2(x) be the polynomial that interpolates f(x) at x0, x1 and 2. (i) Find the error bound at x = 0.3. (ii) Find the error bound on the interval [0, 1]. (iii) Use any method of your choice to find p2(x) and compare the actual error at x = 0.3 with the error bounds in previous steps.
1. Suppose we want to approximate the function f(x) = sin(x) on the interval [0, 1] by using polynomial interpolation with xo = 0, x₁ = 0.5, and x2 = 1. (a) Let pi(x) be the polynomial that interpolates f(x) at xo and ₁. (i) Find the error bound at x = 0.3 (i.e., the bound for error f(0.3) - pi(0.3)). (ii) Find the error bound on the whole interval [0, 0.5]. (iii) Use any method of your choice to find p₁(x) and compare the actual error at x = 0.3 with the error bounds in previous steps. (b) Let p2(x) be the polynomial that interpolates f(x) at x0, x1 and 2. (i) Find the error bound at x = 0.3. (ii) Find the error bound on the interval [0, 1]. (iii) Use any method of your choice to find p2(x) and compare the actual error at x = 0.3 with the error bounds in previous steps.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Need answer b
![1. Suppose we want to approximate the function f(x) = sin(x) on the interval [0, 1] by
using polynomial interpolation with xo = 0, x₁ = 0.5, and x2 = 1.
(a) Let pi(x) be the polynomial that interpolates f(x) at xo and ₁. (i) Find the
error bound at x = 0.3 (i.e., the bound for error f(0.3) - pi(0.3)). (ii) Find the
error bound on the whole interval [0, 0.5]. (iii) Use any method of your choice
to find p₁(x) and compare the actual error at x = 0.3 with the error bounds in
previous steps.
(b) Let p2(x) be the polynomial that interpolates f(x) at x0, x1 and 2. (i) Find the
error bound at x = 0.3. (ii) Find the error bound on the interval [0, 1]. (iii) Use
any method of your choice to find p2(x) and compare the actual error at x = 0.3
with the error bounds in previous steps.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c842333-6f00-4a4b-9f61-7bda344711a4%2Fa544fbe5-06cc-4e48-b874-1ac7097ccfd2%2F880bgjm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Suppose we want to approximate the function f(x) = sin(x) on the interval [0, 1] by
using polynomial interpolation with xo = 0, x₁ = 0.5, and x2 = 1.
(a) Let pi(x) be the polynomial that interpolates f(x) at xo and ₁. (i) Find the
error bound at x = 0.3 (i.e., the bound for error f(0.3) - pi(0.3)). (ii) Find the
error bound on the whole interval [0, 0.5]. (iii) Use any method of your choice
to find p₁(x) and compare the actual error at x = 0.3 with the error bounds in
previous steps.
(b) Let p2(x) be the polynomial that interpolates f(x) at x0, x1 and 2. (i) Find the
error bound at x = 0.3. (ii) Find the error bound on the interval [0, 1]. (iii) Use
any method of your choice to find p2(x) and compare the actual error at x = 0.3
with the error bounds in previous steps.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 1 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
