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By using the method of least squares, find the best parabola through the points: (-1,-3). (1,3). (-2,-3). (0,-3) Step 1. The general equation of a parabola is c₂+₁ +₂2²=3. Plugging the data points into this formula gives a matrix equation Ac = y. ATA- Step 2. The matrix equation Ac=y has no solution, so instead we use the normal equation ATA è = A¹y ATy Step 3. Solving the normal equation gives the answer CO 0 0 which corresponds to the formula 866

By using the method of least squares, find the best parabola through the points: (-1,-3). (1,3). (-2,-3). (0,-3) Step 1. The general equation of a parabola is c₂+₁ +₂2²=3. Plugging the data points into this formula gives a matrix equation Ac = y. ATA- Step 2. The matrix equation Ac=y has no solution, so instead we use the normal equation ATA è = A¹y ATy Step 3. Solving the normal equation gives the answer CO 0 0 which corresponds to the formula 866

Advanced Engineering Mathematics
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,-3). (1,3). (-2,-3). (0,-3) Step 1. The general equation of a parabola is c₂+₁+c₂2²-3. Plugging the data points into this formula gives a matrix equation Ac=y. 1 ATA- ATy= 1 Step 3. Solving the normal equation gives the answer -8 which corresponds to the formula a Step 2. The matrix equation Ac=y has no solution, so instead we use the normal equation A¹A = A¹y O 0 3
Transcribed Image Text:By using the method of least squares, find the best parabola through the points: (-1,-3). (1,3). (-2,-3). (0,-3) Step 1. The general equation of a parabola is c₂+₁+c₂2²-3. Plugging the data points into this formula gives a matrix equation Ac=y. 1 ATA- ATy= 1 Step 3. Solving the normal equation gives the answer -8 which corresponds to the formula a Step 2. The matrix equation Ac=y has no solution, so instead we use the normal equation A¹A = A¹y O 0 3
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