Suppose you have the following data points for a polynomial of degree 2 -1 1 3 y 3 7 -2 -4 Find the best fit polynomial, P2(x) for the above data points by the least squares method by answering the following (a) Write down the matrices: A, b and AT; and then compute the normal matrix AT A and ATb. (b) Now let V = A" A. Apply LU-decomposition method on the matrix V to find the value of columi T
Suppose you have the following data points for a polynomial of degree 2 -1 1 3 y 3 7 -2 -4 Find the best fit polynomial, P2(x) for the above data points by the least squares method by answering the following (a) Write down the matrices: A, b and AT; and then compute the normal matrix AT A and ATb. (b) Now let V = A" A. Apply LU-decomposition method on the matrix V to find the value of columi T
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 34EQ
Related questions
Question
![Suppose you have the following data points for a polynomial of degree 2
-1
1
3
Y
3
7
-2
-4
Find the best fit polynomial, P2(x) for the above data points by the least squares method by answering the following:
(a)
Write down the matrices: A, b and A"; and then compute the normal matrix A" A and ATb.
Now let V = AT A. Apply LU-decomposition method on the matrix V to find the value of column
(b)
matrix elements of x =
: (ao, a1, a2)".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde03737f-a199-4ea5-ae5a-3f42e546e759%2F4cc34e7d-7ec8-4ab7-9f50-0821e738bf49%2Fneoz1d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose you have the following data points for a polynomial of degree 2
-1
1
3
Y
3
7
-2
-4
Find the best fit polynomial, P2(x) for the above data points by the least squares method by answering the following:
(a)
Write down the matrices: A, b and A"; and then compute the normal matrix A" A and ATb.
Now let V = AT A. Apply LU-decomposition method on the matrix V to find the value of column
(b)
matrix elements of x =
: (ao, a1, a2)".
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![College Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652224/9781305652224_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![College Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652224/9781305652224_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage