Sheet 3 Numerical analysis QI/ Use the polynomial that fits data shown by Newton divided difference ,and estimate f(2). Ans. 6 -1 1. f(1) -21 15 12 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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81 l
۳ ۱:۳ ص ۲ك.بث 0 ۵
2 53010361979450...
Sheet 3
Numerical analysis
Q1/ Use the polynomial that fits data shown by Newton divided difference ,and estimate
f(2). Ans. 6
-1
f(1)
-21
15
12
3
Q2/ Use the polynomial that fits data shown by Newton divided difference ,and estimate
f(6). Ans. 147
3.
9
10
f(x)
168
120
72
63
Q3) Find the Lagrange polynomial that fits the following set of four points and find the
value of y at x=0:
Ans. y=6.03888
-2
3
5.
7
11
34
Q4) Find the Lagrange polynomial that fits the following set of four points and find the
value of y at x=0, Ans. y=9.73222
-2
1.
6.
10
12
35
Q5) Fit a straight line to the data given below. Also estimate the value of y at x=2.5.
Ans. y-4.045
1
2
3.
4
y
1.8
3.3
4.5
6.3
Q6) Fit a second order polynomial to the following data. Also estimate the value of y at
x=1.25, Ans, y=1.5625
0.5 1
0.25 1
1.5 2
2.25 4
2.5
|了 |0
6.25
Transcribed Image Text:81 l ۳ ۱:۳ ص ۲ك.بث 0 ۵ 2 53010361979450... Sheet 3 Numerical analysis Q1/ Use the polynomial that fits data shown by Newton divided difference ,and estimate f(2). Ans. 6 -1 f(1) -21 15 12 3 Q2/ Use the polynomial that fits data shown by Newton divided difference ,and estimate f(6). Ans. 147 3. 9 10 f(x) 168 120 72 63 Q3) Find the Lagrange polynomial that fits the following set of four points and find the value of y at x=0: Ans. y=6.03888 -2 3 5. 7 11 34 Q4) Find the Lagrange polynomial that fits the following set of four points and find the value of y at x=0, Ans. y=9.73222 -2 1. 6. 10 12 35 Q5) Fit a straight line to the data given below. Also estimate the value of y at x=2.5. Ans. y-4.045 1 2 3. 4 y 1.8 3.3 4.5 6.3 Q6) Fit a second order polynomial to the following data. Also estimate the value of y at x=1.25, Ans, y=1.5625 0.5 1 0.25 1 1.5 2 2.25 4 2.5 |了 |0 6.25
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