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scotchtapeman
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I'm studying for my numerical analysis final on tuesday, and I know this is going to be one of the problems, so any help is greatly appreciated.
State and prove existence and uniqueness for the solution of the linear least squares problem.
[itex]y \approx x B[/itex]
[itex]x' x B = x' y[/itex]
linear least squares finds B such that [itex]\| y - x B \|[/itex] is minimized.
Since this is linear least squares, [itex]y = B_0 + B_1 x[/itex]
[itex]r_i = y_i - (B_0 + B_1 x_i)[/itex]
For [itex]1 \le i \le n, \delta r_i / \delta x_i = 0[/itex]
Then [itex](\delta y_i / \delta x_i) - B_1 = 0[/itex]
I missed this lecture and I can't find much help online, so I could be headed in the wrong direction. Thanks!
Homework Statement
State and prove existence and uniqueness for the solution of the linear least squares problem.
Homework Equations
[itex]y \approx x B[/itex]
[itex]x' x B = x' y[/itex]
The Attempt at a Solution
linear least squares finds B such that [itex]\| y - x B \|[/itex] is minimized.
Since this is linear least squares, [itex]y = B_0 + B_1 x[/itex]
[itex]r_i = y_i - (B_0 + B_1 x_i)[/itex]
For [itex]1 \le i \le n, \delta r_i / \delta x_i = 0[/itex]
Then [itex](\delta y_i / \delta x_i) - B_1 = 0[/itex]
I missed this lecture and I can't find much help online, so I could be headed in the wrong direction. Thanks!
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