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?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 65E

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