FIGURE:4 The use of quadratic interpolation to estimate In 2. The linear interpolation fromx = 1 to 4 is also included for comparison. f(x) 2 0 True value f(x) = In x- f₂(x) Quadratic estimate Linear estimate 5 X Q1: Estimate the common logarithm of 10 using linear interpolation. (a) Interpolate between log 8= 0.9030900 and log 12=1.0791812. (b) Interpolate between log 9 = 0.9542425 and log 11 = 1.0413927. For each of the interpolations, compute the percent relative error based on the true value.
FIGURE:4 The use of quadratic interpolation to estimate In 2. The linear interpolation fromx = 1 to 4 is also included for comparison. f(x) 2 0 True value f(x) = In x- f₂(x) Quadratic estimate Linear estimate 5 X Q1: Estimate the common logarithm of 10 using linear interpolation. (a) Interpolate between log 8= 0.9030900 and log 12=1.0791812. (b) Interpolate between log 9 = 0.9542425 and log 11 = 1.0413927. For each of the interpolations, compute the percent relative error based on the true value.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:FIGURE:4
The use of quadratic interpolation to estimate In 2. The linear interpolation from x = 1 to 4 is also
included for comparison.
f(x)
2
0
True
value
f(x)= Inx-
1₂(x)
Quadratic estimate
Linear estimate
5
X
Q1: Estimate the common logarithm of 10 using linear interpolation.
(a) Interpolate between log 8= 0.9030900 and log 12=1.0791812.
(b) Interpolate between log 9 = 0.9542425 and log 11 = 1.0413927.
For each of the interpolations, compute the percent relative error based on the true
value.
Q2: Fit a second-order Newton's interpolating polynomial to estimate log 10 using the
data from Prob. 1 at x = 8, 9, and 11. Compute the true percent relative error.
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