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1. 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.

1. 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
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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1. 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. 2. Fit a second-order Newton's Interpolating Polynomial to estimate log 10 using the data from problem at x = 8, 9 and 11. Compute the true percent relative error. 3. Fit a third-order Newton's Interpolating Polynomial to estimate log 10 using the data from Problem 1. 4. Repeat Problems 1 through 3 using the Lagrange Polynomial.
Transcribed Image Text:1. 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. 2. Fit a second-order Newton's Interpolating Polynomial to estimate log 10 using the data from problem at x = 8, 9 and 11. Compute the true percent relative error. 3. Fit a third-order Newton's Interpolating Polynomial to estimate log 10 using the data from Problem 1. 4. Repeat Problems 1 through 3 using the Lagrange Polynomial.
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