2. Consider the Newton polynomial Pn(x) = ao+a1(xr-xo) + a₂(x-xo)(x − x₁) +... +an(x-xo)(x - ₁)(x-In-1) that interpolates f(x) at ro, 1,,n. It is easy to see that ao = f[ro]. Show that a₁ = f[xo, 1], a2 = f[10, 11, 12], and a3 = f[10, 11, 12, 13].
2. Consider the Newton polynomial Pn(x) = ao+a1(xr-xo) + a₂(x-xo)(x − x₁) +... +an(x-xo)(x - ₁)(x-In-1) that interpolates f(x) at ro, 1,,n. It is easy to see that ao = f[ro]. Show that a₁ = f[xo, 1], 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 + a1(x-xo) + a2(x-xo)(x − x₁) + ...
+an(x-xo)(x-x₁)(x-In-1)
that interpolates f(x) at zo, 21,,n. It is easy to see that ao = f[ro]. Show that
a₁ = f[ro, 1], a2 = f[ro, 21, 2], and a3 = f[xo, 11, 12, 13].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c842333-6f00-4a4b-9f61-7bda344711a4%2Fa9082ad7-2f89-47d5-b2b2-674cd73fdaf2%2F3kzsou_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider the Newton polynomial
Pn(x) = ao + a1(x-xo) + a2(x-xo)(x − x₁) + ...
+an(x-xo)(x-x₁)(x-In-1)
that interpolates f(x) at zo, 21,,n. It is easy to see that ao = f[ro]. Show that
a₁ = f[ro, 1], a2 = f[ro, 21, 2], and a3 = f[xo, 11, 12, 13].
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