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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![2. Consider the Newton polynomial
Pn(x) = ao + ai (x-ro) + a2(x-To)(x-21)+...
+an(z-To)(z-I₁). (I-In-1)
...
that interpolates f(x) at zo, 21,,Zn. It is easy to see that ao = f[ro]. Show that
a1 = f[ro, zi], a2 = f[ro, r1, 12], and a3 = f[ro, 11, 12, 13].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b50cde9-6f11-4c6d-8f35-b591071c68b1%2F322a4958-cd3e-4e92-b4bc-3c0dd5a7685f%2F4p13xge_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider the Newton polynomial
Pn(x) = ao + ai (x-ro) + a2(x-To)(x-21)+...
+an(z-To)(z-I₁). (I-In-1)
...
that interpolates f(x) at zo, 21,,Zn. It is easy to see that ao = f[ro]. Show that
a1 = f[ro, zi], a2 = f[ro, r1, 12], and a3 = f[ro, 11, 12, 13].
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