Assume the polynomial P5(x) interpolates a function f(x) at the six data points (xi, f(xi)) with a-coordinates x₁ = 0.0, 2 = 0.2, x3 = 0.4, 4 = 0.6, 50.8, 06 = 1.0. Assume that the interpolation error at x = 0.3 is f(0.3) - P(0.3)| 0.3 is f(0.3) P5(0.3)| = 0.01. Estimate the new interpolation error f(0.3) - P(0.3)| that would result if two additional interpolation points (x7, y7) = (0.1, f(0.1)) and (x8, ys) = (0.5, f(0.5)) are added. What assumptions have you made to produce this estimate?
Assume the polynomial P5(x) interpolates a function f(x) at the six data points (xi, f(xi)) with a-coordinates x₁ = 0.0, 2 = 0.2, x3 = 0.4, 4 = 0.6, 50.8, 06 = 1.0. Assume that the interpolation error at x = 0.3 is f(0.3) - P(0.3)| 0.3 is f(0.3) P5(0.3)| = 0.01. Estimate the new interpolation error f(0.3) - P(0.3)| that would result if two additional interpolation points (x7, y7) = (0.1, f(0.1)) and (x8, ys) = (0.5, f(0.5)) are added. What assumptions have you made to produce this estimate?
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
100%
Transcribed Image Text:Assume the polynomial P5(x) interpolates a function f(x) at the six data points (xi, f(xi))
with x-coordinates ₁ = 0.0, 2
0.0, x2 = 0.2, x3 = 0.4, x4 = 0.6, x5 = 0.8, x6 = 1.0. Assume
that the interpolation error at x = 0.3 is |f(0.3) - P5(0.3)| = 0.01. Estimate the new
interpolation error |ƒ(0.3) — P7(0.3)| that would result if two additional interpolation points
-
(x7, y7) = (0.1, f(0.1)) and (x8, ys) = (0.5, f(0.5)) are added. What assumptions have you
made to produce this estimate?
Expert Solution
Step 1
Step by step
Solved in 2 steps with 2 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,
