Find the least-square solution of Ax = b for | Mathematics II 2075

Mathematics II207510 marksNumerical: least squares solutionLeast squares problems

Find the least-square solution of $Ax = b$ for

$A = \begin{bmatrix} 1 & 3 & 5 \\ 1 & 1 & 0 \\ 1 & 1 & 2 \\ 1 & 3 & 3 \end{bmatrix}, \quad b = \begin{pmatrix} 3 \\ 5 \\ 7 \\ 3 \end{pmatrix}$

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Find the least-square solution of $Ax = b$ for

$$A = \begin{bmatrix} 1 & 3 & 5 \ 1 & 1 & 0 \ 1 & 1 & 2 \ 1 & 3 & 3 \end{bmatrix}, \quad b = \begin{pmatrix} 3 \ 5 \ 7 \ 3 \end{pmatrix}$$

[10]

$A = \begin{bmatrix} 1 & 3 & 5 \\ 1 & 1 & 0 \\ 1 & 1 & 2 \\ 1 & 3 & 3 \end{bmatrix}, \qquad b = \begin{pmatrix} 3 \\ 5 \\ 7 \\ 3 \end{pmatrix}$ The least-square solution $\hat{x}$ solves the normal equations: $A^T A \hat{x} = A^T b$ $$A^T = \begin{bmatrix} 1 & 1 & 1 & 1 \ 3 & 1 & 1 & 3 \ 5 ...

$$A = \begin{bmatrix} 1 & 3 & 5 \ 1 & 1 & 0 \ 1 & 1 & 2 \ 1 & 3 & 3 \end{bmatrix}, \qquad b = \begin{pmatrix} 3 \ 5 \ 7 \ 3 \end{pmatrix}$$ The least-square solution $\hat{x}$ solves the normal equations: $$A^T A \hat{x} = A^T b$$ $$A^T = \begin{bmatrix} 1 & 1 & 1 & 1 \ 3 & 1 & 1 & 3 \ 5 ...

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