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Given the distinct points xi, 2 = Yi, i 0,1, · " = ., n+1, and the points n+ 1, let q be the Lagrange polynomial of degree n for the set of points {(xi, yi): i 0, 1,..., n} and let r be the Lagrange polynomial of degree n for the points {(xi, Yi): i = 1, 2, ..., n +1}. Define = p(x) = = (x − xo)r(x) — (x − xn+1)q(x) Xn+1 - x0 Show that is the Lagrange polynomial of degree n + 1 for the points {(x, yi): i = 0, 1, ..., n +1}.

Given the distinct points xi, 2 = Yi, i 0,1, · " = ., n+1, and the points n+ 1, let q be the Lagrange polynomial of degree n for the set of points {(xi, yi): i 0, 1,..., n} and let r be the Lagrange polynomial of degree n for the points {(xi, Yi): i = 1, 2, ..., n +1}. Define = p(x) = = (x − xo)r(x) — (x − xn+1)q(x) Xn+1 - x0 Show that is the Lagrange polynomial of degree n + 1 for the points {(x, yi): i = 0, 1, ..., n +1}.

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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6.3 Yi, Given the distinct points xi, i = 0, 1, . . . , n + 1, and the points i = 0, 1,..., n + 1, let q be the Lagrange polynomial of degreen for the set of points {(xi, Yi): i 0, 1, ... , ,n} and let r be the Lagrange polynomial of degree n for the points {(xi, Yi): i = 1, 2, ..., n +1}. Define = p(x) = (x − xo)r(x) - (x − xn+1)q(x) Xn+1 xo - Show that p is the Lagrange polynomial of degree n + 1 for the points {(x, y): i = 0, 1,..., n +1}.
Transcribed Image Text:6.3 Yi, Given the distinct points xi, i = 0, 1, . . . , n + 1, and the points i = 0, 1,..., n + 1, let q be the Lagrange polynomial of degreen for the set of points {(xi, Yi): i 0, 1, ... , ,n} and let r be the Lagrange polynomial of degree n for the points {(xi, Yi): i = 1, 2, ..., n +1}. Define = p(x) = (x − xo)r(x) - (x − xn+1)q(x) Xn+1 xo - Show that p is the Lagrange polynomial of degree n + 1 for the points {(x, y): i = 0, 1,..., n +1}.
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