Here are some data points kk f(xk) 02 10 15 60 2 10 140 (a) Form the Lagrange interpolating polynomial P(x) using the original definition: P(x) = f(xk). Lk (x), = £1(² k=0 n L₁(x) = II: j=0 j/k 10 ? ? 60 ? ? 140 ? ? x-xj. Ik - Dj (b) Here is a partially completed divided differences matrix for the above data. Complete the matrix and hence form the Lagrange interpolating polynomial P(x) using the divided differences method: P(x) = f[ro]+f[x0, x₁] (x-xo)++ƒ[xo,..., n] (x-xo) (x-En-1).
Here are some data points kk f(xk) 02 10 15 60 2 10 140 (a) Form the Lagrange interpolating polynomial P(x) using the original definition: P(x) = f(xk). Lk (x), = £1(² k=0 n L₁(x) = II: j=0 j/k 10 ? ? 60 ? ? 140 ? ? x-xj. Ik - Dj (b) Here is a partially completed divided differences matrix for the above data. Complete the matrix and hence form the Lagrange interpolating polynomial P(x) using the divided differences method: P(x) = f[ro]+f[x0, x₁] (x-xo)++ƒ[xo,..., n] (x-xo) (x-En-1).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Numerical Analysis
![Here are some data points
k | 2k [f(k)
0
2
10
1
5
60
2 10
140
n
2.0
(a)
Form the Lagrange interpolating polynomial P(x) using
the original definition:
P(x) = f(xk). Lk (™),
Σf(xx)
k=0
n
Lk (T) = II:
j=0
j‡k
x-xj
Ik - Tj
(b)
Here is a partially completed divided differences matrix for
the above data. Complete the matrix and hence form the Lagrange
interpolating polynomial P(x) using the divided differences method:
P(x) = f[ro]+f[x0, x₁] (x−xo)+ +ƒf[xo,..., En] (x-xo) (x-xn-1).
10
? ?
60
? ?
140 ? ?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f3fcee3-df4f-43f5-a70c-56c5ba155c30%2Fe8dc0052-bf23-4ecc-9140-9d3dab4be405%2F2vwcg8c_processed.png&w=3840&q=75)
Transcribed Image Text:Here are some data points
k | 2k [f(k)
0
2
10
1
5
60
2 10
140
n
2.0
(a)
Form the Lagrange interpolating polynomial P(x) using
the original definition:
P(x) = f(xk). Lk (™),
Σf(xx)
k=0
n
Lk (T) = II:
j=0
j‡k
x-xj
Ik - Tj
(b)
Here is a partially completed divided differences matrix for
the above data. Complete the matrix and hence form the Lagrange
interpolating polynomial P(x) using the divided differences method:
P(x) = f[ro]+f[x0, x₁] (x−xo)+ +ƒf[xo,..., En] (x-xo) (x-xn-1).
10
? ?
60
? ?
140 ? ?
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