Concept explainers
Use MATLAb’S svd command to find the best rank-one approximation of the following matrices:
a.
Use MATLAB’s svd command to find the best rank-one approximation of the given matrx.
Answer to Problem 1CP
The best rank-one approximation of the matrix
Explanation of Solution
Given Information:
Calculation:
Use commands ‘A=[1 2;2 3]’ to define the matrix A and ‘[U S V]=svd(A)’ to find the singular value decomposition (SVD) of the matrix A in the MATLAB.
Therefore,
The first rank-one matrix is
Thus, the best rank-one approximation of the matrix
b.
Use MATLAB’s svd command to find the best rank-one approximation of the given matrx.
Answer to Problem 1CP
The best rank-one approximation of the matrix
Explanation of Solution
Given Information:
Calculation:
Use commands ‘A=[1 4;2 3]’ to define the matrix A and ‘[U S V]=svd(A)’ to find the singular value decomposition (SVD) of the matrix A in the MATLAB.
Therefore,
The first rank-one matrix is
Thus, the best rank-one approximation of the matrix
c.
Use MATLAB’s svd command to find the best rank-one approximation of the given matrx.
Answer to Problem 1CP
The best rank-one approximation of the matrix
Explanation of Solution
Given Information:
Calculation:
Use commands ‘A=[1 2 4;1 3 3;0 0 1]’ to define the matrix A and ‘[U S V]=svd(A)’ to find the singular value decomposition (SVD) of the matrix A in the MATLAB.
Therefore,
The first rank-one matrix is
Thus, the best rank-one approximation of the matrix
d.
Use MATLAB’s svd command to find the best rank-one approximation of the given matrx.
Answer to Problem 1CP
The best rank-one approximation of the matrix
Explanation of Solution
Given Information:
Calculation:
Use commands ‘A=[1 5 3;2 -3 2;-3 1 1]’ to define the matrix A and ‘[U S V]=svd(A)’ to find the singular value decomposition (SVD) of the matrix A in the MATLAB.
Therefore,
The first rank-one matrix is
Thus, the best rank-one approximation of the matrix
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Chapter 12 Solutions
Numerical Analysis, Books A La Carte Edition (3rd Edition)
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