2. Consider the Newton polynomial Pn(z)= ao+a1 (1-10) + a₂(1-10) (1-11)+... +an(1-10)(1-1₁). (I-In-1) ... that interpolates f(x) at zo, 1,,Zn. It is easy to see that ao = f[zo]. Show that a₁ = f[ro, z1], a2 = f[10, 11, 12], and a3 = f[10, 11, 12, 13].
2. Consider the Newton polynomial Pn(z)= ao+a1 (1-10) + a₂(1-10) (1-11)+... +an(1-10)(1-1₁). (I-In-1) ... that interpolates f(x) at zo, 1,,Zn. It is easy to see that ao = f[zo]. Show that a₁ = f[ro, z1], a2 = f[10, 11, 12], and a3 = f[10, 11, 12, 13].
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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