Suppose you want to interpolate the points (−1, −3), (0, 0) and (1, 3) by a polynomial. (a) What will the degree of the interpolating polynomial be? Write down the linear system. Solve the system to get the polynomial. Find the interpolated value at t = 1/2. (b) Write down directly the Lagrange basis interpolation. Simplify the polynomial to get the same answer as (a).
Suppose you want to interpolate the points (−1, −3), (0, 0) and (1, 3) by a polynomial. (a) What will the degree of the interpolating polynomial be? Write down the linear system. Solve the system to get the polynomial. Find the interpolated value at t = 1/2. (b) Write down directly the Lagrange basis interpolation. Simplify the polynomial to get the same answer as (a).
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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Suppose you want to interpolate the points (−1, −3), (0, 0) and (1, 3) by a polynomial.
(a) What will the degree of the interpolating polynomial be? Write down the linear system. Solve the system to get the polynomial. Find the interpolated value at t = 1/2.
(b) Write down directly the Lagrange basis interpolation. Simplify the polynomial to get the same answer as (a).
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