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Show your work for each problem. For the data points (1,0), (2.0.693), (3.1.099), and (4,1.386): 1) Use the Lagrange method to find an interpolating polynomial of degree two through the last three points (ignoring (1.0). 2) Use the Divided Differences method to find an interpolating polynomial of degree three through all four points. 3) Find a natural cubic spline through all four points. 4) Given that the data function is y - Inix), evailuate each of 1). 2), and 3) at x - 3.5, and compute the error for each. Which one is the most accurate at that point?

Show your work for each problem. For the data points (1,0), (2.0.693), (3.1.099), and (4,1.386): 1) Use the Lagrange method to find an interpolating polynomial of degree two through the last three points (ignoring (1.0). 2) Use the Divided Differences method to find an interpolating polynomial of degree three through all four points. 3) Find a natural cubic spline through all four points. 4) Given that the data function is y - Inix), evailuate each of 1). 2), and 3) at x - 3.5, and compute the error for each. Which one is the most accurate at that point?

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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Show your work for each problem. For the data points (1,0), (2,0.693), (3,1.099), and (4,1.386): 1) Use the Lagrange method to find an interpolating polynomial of degree two through the last three points (ignoring (1.0). 2) Use the Divided Differences method to find an interpolating polynomial of degree three through all four points. 3) Find a natural cubic spline through all four points: 4) Given that the data function is y - Inix), evaluate each of 1). 2), and 3) at x = 3.5, and compute the error for each. Which one is the most accurate at that point?
Transcribed Image Text:Show your work for each problem. For the data points (1,0), (2,0.693), (3,1.099), and (4,1.386): 1) Use the Lagrange method to find an interpolating polynomial of degree two through the last three points (ignoring (1.0). 2) Use the Divided Differences method to find an interpolating polynomial of degree three through all four points. 3) Find a natural cubic spline through all four points: 4) Given that the data function is y - Inix), evaluate each of 1). 2), and 3) at x = 3.5, and compute the error for each. Which one is the most accurate at that point?
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