By using the method of least squares, find the best parabola through the points: (-1,–2), (1,0), (2,3), (0,0)
By using the method of least squares, find the best parabola through the points: (-1,–2), (1,0), (2,3), (0,0)
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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![By using the method of least squares, find the best parabola through the points:
(-1, –2), (1,0), (2,3), (0,0)
Step 1. The general equation of a parabola is co +cjx + c2x²
y. Plugging the data points into this formula gives a matrix equation Ac = y.
-2
Co
C2
Step 2. The matrix equation Ac
y has no solution, so instead we use the normal equation ATA ĉ = ATy
АТА —
ATy =
Step 3. Solving the normal equation gives the answer
which corresponds to the formula
y =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e444f08-7dae-4966-aecb-157f33ba5d56%2F8b4f30e2-305f-4366-ad82-7f18444f8fe8%2Frt6nnor_processed.png&w=3840&q=75)
Transcribed Image Text:By using the method of least squares, find the best parabola through the points:
(-1, –2), (1,0), (2,3), (0,0)
Step 1. The general equation of a parabola is co +cjx + c2x²
y. Plugging the data points into this formula gives a matrix equation Ac = y.
-2
Co
C2
Step 2. The matrix equation Ac
y has no solution, so instead we use the normal equation ATA ĉ = ATy
АТА —
ATy =
Step 3. Solving the normal equation gives the answer
which corresponds to the formula
y =
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