In an experiment, a scientist obtained the following data. x 0 1 -1 y -5 -3 -15 Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial : P2(x) = −5 + 2x − 4x(x−1) Now, the scientist wants to do more experiment and got two more points (2, 39) and (−2,−9). Therefore, the total data is the following. x 0 1 -1 2 -2 y -5 -3 -15 39 -9 Again by apply Newton's interpolating polynomial method, the scientist obtained the following polynomial P5(x) = a + 2x + bx(x−1) + cx(x−1)(x+1) + 3x(x−1)(x+1)(x+d). Then, a= b= c= d=
In an experiment, a scientist obtained the following data. x 0 1 -1 y -5 -3 -15 Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial : P2(x) = −5 + 2x − 4x(x−1) Now, the scientist wants to do more experiment and got two more points (2, 39) and (−2,−9). Therefore, the total data is the following. x 0 1 -1 2 -2 y -5 -3 -15 39 -9 Again by apply Newton's interpolating polynomial method, the scientist obtained the following polynomial P5(x) = a + 2x + bx(x−1) + cx(x−1)(x+1) + 3x(x−1)(x+1)(x+d). Then, a= b= c= d=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In an experiment, a scientist obtained the following data.
x | 0 | 1 | -1 |
y | -5 | -3 | -15 |
Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial : P2(x) = −5 + 2x − 4x(x−1)
Now, the scientist wants to do more experiment and got two more points (2, 39) and (−2,−9).
Therefore, the total data is the following.
x | 0 | 1 | -1 | 2 | -2 |
y | -5 | -3 | -15 | 39 | -9 |
Again by apply Newton's interpolating polynomial method, the scientist obtained the following polynomial
P5(x) = a + 2x + bx(x−1) + cx(x−1)(x+1) + 3x(x−1)(x+1)(x+d).
Then,
a=
b=
c=
d=
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