Below are two Lagrange interpolating polynomials, L₁ and L2. Following these are interpolating poly- nomials obtained through Newton's Divided Difference, N₁ and N₂. L₁ = -(x - 5)(x-6) L₂ = x(x - 5)(x − 6) + x(x-2)(x − 6)-x(x-2)(x - 5)+(x-2)(x - 5)(x-6). 24 N₁ = 1-2(x-2) + 2(x-2)(x-5)-3(x-2)(x - 5)(x-6) N₂ = 1-2(x-2)-2(x-2)(x - 5) + 3(x-2)(x - 5)(x-6) a.) Match the correct pairs with at least one justification that is correct. b.) An incomplete Divided Difference Table is given for one of these. Complete all blank entries. 2 5 6 (x-8)(x-2)(x-6)(x-8)(x-2)(x - 5)(x-8)(x-2)(x - 5)(x-6) 36 5 15 195 60 1 -5 -10 30 -8
Below are two Lagrange interpolating polynomials, L₁ and L2. Following these are interpolating poly- nomials obtained through Newton's Divided Difference, N₁ and N₂. L₁ = -(x - 5)(x-6) L₂ = x(x - 5)(x − 6) + x(x-2)(x − 6)-x(x-2)(x - 5)+(x-2)(x - 5)(x-6). 24 N₁ = 1-2(x-2) + 2(x-2)(x-5)-3(x-2)(x - 5)(x-6) N₂ = 1-2(x-2)-2(x-2)(x - 5) + 3(x-2)(x - 5)(x-6) a.) Match the correct pairs with at least one justification that is correct. b.) An incomplete Divided Difference Table is given for one of these. Complete all blank entries. 2 5 6 (x-8)(x-2)(x-6)(x-8)(x-2)(x - 5)(x-8)(x-2)(x - 5)(x-6) 36 5 15 195 60 1 -5 -10 30 -8
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
Transcribed Image Text:Below are two Lagrange interpolating polynomials, L₁ and L2. Following these are interpolating poly-
nomials obtained through Newton's Divided Difference, N₁ and N₂.
5
L₁ = -(x - 5)(x-6)(x − 8)-2-(x-2)(x-6)(x-8)(x-2)(x - 5)(x-8)(x-2)(x - 5)(x-6) 36
72
1
5
15
195
L₂ = x(x − 5) (x − 6) + x(x − 2)(x − 6) − x(x − 2)(x – 5);
+(x-2)(x - 5)(x-6)-
-
-
-
24
15
24
60
N₁ = 1-2(x-2) + 2(x-2)(x - 5)-3(x-2)(x - 5)(x-6)
N₂ = 1-2(x-2)-2(x-2)(x - 5) + 3(x-2)(x - 5)(x-6)
a.) Match the correct pairs with at least one justification that is correct.
b.) An incomplete Divided Difference Table is given for one of these. Complete all blank entries.
2
CT
5
6
1
-5
-10
30
-8
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