Status: Tags: #cards/math232/unit7/3 Links: Subspace Projections
Method of Least Squares
Principles
Usual formula for quadratics
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- X is derived from the design matrix, whatever the polynomial equation is
- a is a,b,c
- y is y values given
When is $X^TX$ invertible ?
- When number of $t_i$ values >= number of unknown coefficients
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- Produces a unique solution
Overdetermined systems
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- When a system has more equations than unknowns
- If no x such that Ax = b, find a vector x that minimizes the error ||Ax-b||
- This satisfies the normal system $A^TA\vec{x} = A^T\vec{b}$
Examples
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- a always 1
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References:
Created:: 2022-03-30 00:44