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Intro to least-squares solutions and the x-hat formula
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Intro to least-squares solutions and the x-hat formula
23:32
About this lesson
• \(Ax=b\) give no solution
• Approximate closest solution \(\hat{x}\)
• The least Squares Solution \(\hat{x} =(A^T A)^{-1} A^T b\)
• Not always a unique solution
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Video 1 of 8
Intro to least-squares solutions and the x-hat formula
24 min
• Selected
Defining and computing the least-squares error
5 min
Two alternative methods for computing the least-squares solution
24 min
Finding the least-squares solution using the inverse formula
7 min
Finding all least-squares solutions when x-hat is not unique
16 min
Computing the least-squares error from a given solution
6 min
Finding orthogonal projection and least squares solution using the alternative method
9 min
Using QR factorization to solve a least-squares problem
11 min