1. Consider the matrix: 3 × 3: [1 2 3] A = 334 [5 6 7 Use the svd() function in MATLAB to compute A₁, the rank-1 approximation of A. Clearly state what A₁ is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A₁. 2. Use the svd() function in MATLAB to compute A₂, the rank-2 approximation of A. Clearly state what A₂ is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A2. Which approximation is better, A₁ or A₂? Explain.
1. Consider the matrix: 3 × 3: [1 2 3] A = 334 [5 6 7 Use the svd() function in MATLAB to compute A₁, the rank-1 approximation of A. Clearly state what A₁ is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A₁. 2. Use the svd() function in MATLAB to compute A₂, the rank-2 approximation of A. Clearly state what A₂ is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A2. Which approximation is better, A₁ or A₂? Explain.
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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I need help with question 2. Here's the code used for question 1.
%Define matrix A
A = [1, 2, 3; 3, 3, 4; 5, 6, 7];
%Compute SVD of A
[U, S, V] = svd(A);
%Rank-1 approx
A1 = U(:,1) * S(1,1) * V(:,1)';
RMSE = sqrt(mean((A(:) - A1(:)).^2));
%Display A1 rounded to 4 decimal places
disp(round(A1, 4));
%Display RMSE
disp(RMSE);
![1. Consider the matrix: 3 × 3:
[1 2 3]
A = 334
[5 6 7
Use the svd() function in MATLAB to compute A₁, the rank-1 approximation of A. Clearly state what A₁ is, rounded to 4 decimal places.
Also, compute the root mean square error (RMSE) between A and A₁.
2. Use the svd() function in MATLAB to compute A₂, the rank-2 approximation of A. Clearly state what A₂ is, rounded to 4 decimal places.
Also, compute the root mean square error (RMSE) between A and A2. Which approximation is better, A₁ or A₂? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbdef5b53-2acf-4587-9caf-137577214115%2F09c774eb-702b-4f90-9824-c7d260b714dc%2Fe8szhvt_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the matrix: 3 × 3:
[1 2 3]
A = 334
[5 6 7
Use the svd() function in MATLAB to compute A₁, the rank-1 approximation of A. Clearly state what A₁ is, rounded to 4 decimal places.
Also, compute the root mean square error (RMSE) between A and A₁.
2. Use the svd() function in MATLAB to compute A₂, the rank-2 approximation of A. Clearly state what A₂ is, rounded to 4 decimal places.
Also, compute the root mean square error (RMSE) between A and A2. Which approximation is better, A₁ or A₂? Explain.
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