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1. Consider the following data points (0,3), (1,0), (2, 1), (3,0) (a) Derive the monomial interpolation that passes through those 4 data points; (b) Derive the Lagrange interpolation that passes through those 4 data points; (c) Derive the polynomial interpolation with Newton's form that passes through those 4 data points. Note: For all the questions above, make sure to include the final polynomial function, that is p3(r) = ... in its corresponding interpolation form.

1. Consider the following data points (0,3), (1,0), (2, 1), (3,0) (a) Derive the monomial interpolation that passes through those 4 data points; (b) Derive the Lagrange interpolation that passes through those 4 data points; (c) Derive the polynomial interpolation with Newton's form that passes through those 4 data points. Note: For all the questions above, make sure to include the final polynomial function, that is p3(r) = ... in its corresponding interpolation form.

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. Consider the following data points (0, 3), (1,0), (2, 1), (3,0) (a) Derive the monomial interpolation that passes through those 4 data points; (b) Derive the Lagrange interpolation that passes through those 4 data points; (c) Derive the polynomial interpolation with Newton's form that passes through those 4 data points. Note: For all the questions above, make sure to include the final polynomial function, that is pa(2) = .. in its corresponding interpolation form.
Transcribed Image Text:1. Consider the following data points (0, 3), (1,0), (2, 1), (3,0) (a) Derive the monomial interpolation that passes through those 4 data points; (b) Derive the Lagrange interpolation that passes through those 4 data points; (c) Derive the polynomial interpolation with Newton's form that passes through those 4 data points. Note: For all the questions above, make sure to include the final polynomial function, that is pa(2) = .. in its corresponding interpolation form.
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