Question (a) (b) We are given four data points: (c) Here is an uncompleted divided difference matrix: 3 7 (1,3) (3,7) 9 27 Complete the matrix. divided difference formula: 0 f[0, 1] f1, ₂] [TO, I1, I2] 0 f[2,3] [1, 2, 3] [10, 11, 12, 13]., 0 (4,9) 0 (10, 27). 0 0 Hence write down the Lagrange interpolating polynomial on the full data set, here is the P(x) = f[ro] + f[ro, #1] (T−TO) +ƒ [TO, T1, T2] (T−TO) (T-T1) + ƒ [TO, T1, T2, T3] (T-TO) (T-T1)(x − T2). Give one difference between Lagrange and Hermite interpolating polynomials.
Question (a) (b) We are given four data points: (c) Here is an uncompleted divided difference matrix: 3 7 (1,3) (3,7) 9 27 Complete the matrix. divided difference formula: 0 f[0, 1] f1, ₂] [TO, I1, I2] 0 f[2,3] [1, 2, 3] [10, 11, 12, 13]., 0 (4,9) 0 (10, 27). 0 0 Hence write down the Lagrange interpolating polynomial on the full data set, here is the P(x) = f[ro] + f[ro, #1] (T−TO) +ƒ [TO, T1, T2] (T−TO) (T-T1) + ƒ [TO, T1, T2, T3] (T-TO) (T-T1)(x − T2). Give one difference between Lagrange and Hermite interpolating polynomials.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Numerical Analysis
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![Question
(a)
(b)
We are given four data points:
(c)
Here is an uncompleted divided difference matrix:
3
(1,3)
7
(3,7)
0
f[0, 1]
9
[1, ₂] [10, 11, 12]
27 f[2,3] [1, 2, 3] [10, 11, 12, 13].,
Complete the matrix.
divided difference formula:
0
(4,9)
0
(10, 27).
0
0
0
Hence write down the Lagrange interpolating polynomial on the full data set, here is the
P(x) = f[ro] + f[0, T₁] (T-TO) +ƒ[TO, E₁, E2] (x− I0) (x − E₁)+ƒ[10, 11, 12, 13] (1−10) (T—F₁) (T-T₂).
Give one difference between Lagrange and Hermite interpolating polynomials.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f3fcee3-df4f-43f5-a70c-56c5ba155c30%2F1835f2d6-7fe2-47e3-9b38-7b16ad0723cf%2Fl0qaab3_processed.png&w=3840&q=75)
Transcribed Image Text:Question
(a)
(b)
We are given four data points:
(c)
Here is an uncompleted divided difference matrix:
3
(1,3)
7
(3,7)
0
f[0, 1]
9
[1, ₂] [10, 11, 12]
27 f[2,3] [1, 2, 3] [10, 11, 12, 13].,
Complete the matrix.
divided difference formula:
0
(4,9)
0
(10, 27).
0
0
0
Hence write down the Lagrange interpolating polynomial on the full data set, here is the
P(x) = f[ro] + f[0, T₁] (T-TO) +ƒ[TO, E₁, E2] (x− I0) (x − E₁)+ƒ[10, 11, 12, 13] (1−10) (T—F₁) (T-T₂).
Give one difference between Lagrange and Hermite interpolating polynomials.
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