For the function f2 on p. 161 of Lyche et al. Write a code to construct...
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For the function f2 on p. 161 of Lyche et al. Write a code to construct the C¹ and C² cubic interpolating splines with 3, 7, 15, and 31 interior nodes. Submit one plot for each number of interior nodes. Each plot must contain f2 and both interpolating splines. Additionally, submit the lists of the Bernstein coefficients for the case of 3 interior nodes for each spline. Modify your code to compute the numerical error of approximation for both C¹ and C² cubic interpolating splines. Derive the nu- merical order of convergence and compare it with the theoretical one. cubic C² splines: 6, 7, 11 and 16 nodes, Lyche et. al, p. 161 0.9 0.8 0.7 0.6 0.5 0,4 0.3 0.2 0.1 0 -5 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 5 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -6 0.9 0.8 0,7 0.6 0.5 0.4 0.3 0.2 0.1 For the function f2 on p. 161 of Lyche et al. Write a code to construct the C¹ and C² cubic interpolating splines with 3, 7, 15, and 31 interior nodes. Submit one plot for each number of interior nodes. Each plot must contain f2 and both interpolating splines. Additionally, submit the lists of the Bernstein coefficients for the case of 3 interior nodes for each spline. Modify your code to compute the numerical error of approximation for both C¹ and C² cubic interpolating splines. Derive the nu- merical order of convergence and compare it with the theoretical one. cubic C² splines: 6, 7, 11 and 16 nodes, Lyche et. al, p. 161 0.9 0.8 0.7 0.6 0.5 0,4 0.3 0.2 0.1 0 -5 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 5 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -6 0.9 0.8 0,7 0.6 0.5 0.4 0.3 0.2 0.1
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To solve this problem you will need to perform the following steps Define the function f 2 x based on the information provided on page 161 of the book ... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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