Q1 xxxxxx Given the data: -3 0 2 f(x) 320 32 0 Construct Lagrange interpolating polynomial, then find f(1.5), if you know the exact value of f(1.5)=-17.5, calculate the error ???

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Q1 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxX
Given the data:
Sheet III
Chapter V: Interpolation & Data Fitting
Interpolation & Data Fitting
(Lagrange, Newton (divided, Forward) differences and Least squares
X₁
02
f(x)
0
Construct Lagrange interpolating polynomial, then find f(1.5), if you know the exact
value of f(1.5) = -17.5, calculate the error ???
Q2 xxxxxxxxxxxxxxxxxxxXX
Given the data:
Q3 xxxxxxxxxxxxxx
Given the data:
2
6
Xi
f(x)
Construct Newton's divided difference interpolating polynomial, then find f(1.5), if
you know the exact value of f(1.5)= -17.5, calculate the error ???
-3
320 32
X₂
f(x)
48
96
-2
0
Xi -2 0
0
32
Construct Newton's forward difference interpolating polynomial, then find f(1.5). if
you know the exact value of f(1.5)=-17.5, calculate the error ???
Q4 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Given the data:
f(x)) Af(x))
12
(a) 1+ 2x + x²
(c) 1-2x + x²
0
Use an appropriate interpolating polynomial form to construct the interpolating
polynomial, then find f(1.5), if you know the exact value of f(1.5) = -17.5
calculate the relative error and write your comments!
Q5 xxxxxxxxx
For a function f(x), the forward difference Table is
Xj
² f(x)
0
0
3
32 320
0
0 32
24
12
2
0 1440
48
12
1
0
36
xxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxx
³f(x)
(b) 1-2x-x²
(d) 1+2x-x²²
12
xxxxxxx
xxxxxxxxxxxxx
8
Determine the missing entries in the table; Establish the interpolating
polynomial which interpolates the values in this table.
A' f(x,)
Q6 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
The second degree polynomial which interpolates the set of values (0, 1). (1.2) and (2, 1) is
Transcribed Image Text:Q1 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxX Given the data: Sheet III Chapter V: Interpolation & Data Fitting Interpolation & Data Fitting (Lagrange, Newton (divided, Forward) differences and Least squares X₁ 02 f(x) 0 Construct Lagrange interpolating polynomial, then find f(1.5), if you know the exact value of f(1.5) = -17.5, calculate the error ??? Q2 xxxxxxxxxxxxxxxxxxxXX Given the data: Q3 xxxxxxxxxxxxxx Given the data: 2 6 Xi f(x) Construct Newton's divided difference interpolating polynomial, then find f(1.5), if you know the exact value of f(1.5)= -17.5, calculate the error ??? -3 320 32 X₂ f(x) 48 96 -2 0 Xi -2 0 0 32 Construct Newton's forward difference interpolating polynomial, then find f(1.5). if you know the exact value of f(1.5)=-17.5, calculate the error ??? Q4 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Given the data: f(x)) Af(x)) 12 (a) 1+ 2x + x² (c) 1-2x + x² 0 Use an appropriate interpolating polynomial form to construct the interpolating polynomial, then find f(1.5), if you know the exact value of f(1.5) = -17.5 calculate the relative error and write your comments! Q5 xxxxxxxxx For a function f(x), the forward difference Table is Xj ² f(x) 0 0 3 32 320 0 0 32 24 12 2 0 1440 48 12 1 0 36 xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx ³f(x) (b) 1-2x-x² (d) 1+2x-x²² 12 xxxxxxx xxxxxxxxxxxxx 8 Determine the missing entries in the table; Establish the interpolating polynomial which interpolates the values in this table. A' f(x,) Q6 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx The second degree polynomial which interpolates the set of values (0, 1). (1.2) and (2, 1) is
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