d) This part of the equation concerns the following data values obtained from a scientific experiment: 1 2 3 4 Xị 4 6. 8. 9. Yi 2.5 7.5 4.5 1 7 (i) Use Least Squares Approximation method to find the best fit cubic polynomial of the form: Yi= a. +a,x + a,x? + a3x³ for the five data points (xi, Y¡), where a., ai, az and a3 are unknown coefficients to be determined.
d) This part of the equation concerns the following data values obtained from a scientific experiment: 1 2 3 4 Xị 4 6. 8. 9. Yi 2.5 7.5 4.5 1 7 (i) Use Least Squares Approximation method to find the best fit cubic polynomial of the form: Yi= a. +a,x + a,x? + a3x³ for the five data points (xi, Y¡), where a., ai, az and a3 are unknown coefficients to be determined.
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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Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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![(d)
This part of the equation concerns the following data values obtained from a scientific
experiment:
1
2
3
4
Xị
4
8.
9.
Yi
2.5
7.5
4.5
1
7
(i)
Use Least Squares Approximation method to find the best fit cubic polynomial of
the form:
Yi= a, +ajx + a,x² + a3x³
for the five data points (xi, Y;), where a., ai, az and a3 are unknown coefficients to
be determined.
(ii) Hence, explain briefly why the cubic polynomial you found in part (i) may not give
a good approximation to the value of Y at x = 10.
[Remark: You may use Mathcad to help you to carry out the computation. If you
use Mathcad in your computation, submit a printout of Mathcad solutions to show
your working.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4df1412f-98f8-45f1-b949-6e67ef4913aa%2F70f87be5-d04b-43bd-ab1f-3c854f3e122d%2Fc7p1ojf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(d)
This part of the equation concerns the following data values obtained from a scientific
experiment:
1
2
3
4
Xị
4
8.
9.
Yi
2.5
7.5
4.5
1
7
(i)
Use Least Squares Approximation method to find the best fit cubic polynomial of
the form:
Yi= a, +ajx + a,x² + a3x³
for the five data points (xi, Y;), where a., ai, az and a3 are unknown coefficients to
be determined.
(ii) Hence, explain briefly why the cubic polynomial you found in part (i) may not give
a good approximation to the value of Y at x = 10.
[Remark: You may use Mathcad to help you to carry out the computation. If you
use Mathcad in your computation, submit a printout of Mathcad solutions to show
your working.]
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