| Line 6: | Line 6: | ||
for system | for system | ||
| − | :<math>A\bold{x}=\bold{b}</math> | + | :<math>A\bold{x}=\bold{b},</math> |
| − | :<math> {A^T(A\bold\hat{x} - \bold{b})} = 0 </math> | + | :<math> {A^T(A\bold\hat{x} - \bold{b})} = 0,</math> |
which is equivalent to | which is equivalent to | ||
| − | :<math> {A^TA\bold\hat{x}} = A^{T}\bold{b} </math> | + | :<math> {A^TA\bold\hat{x}} = A^{T}\bold{b}.</math> |
Revision as of 09:51, 8 December 2010
The Least Squares Solution
The Least Squares Approximation is a examples-intensive concept. However, it can be solved using the following concise formulas:
for system
- $ A\bold{x}=\bold{b}, $
- $ {A^T(A\bold\hat{x} - \bold{b})} = 0, $
which is equivalent to
- $ {A^TA\bold\hat{x}} = A^{T}\bold{b}. $
NOTE:
Thorough examples are available in the MA265 textbook, Webassign problems, and Past Exam Archive. Most problems only deal with linear and parabolic fits.
Ryan Jason Tedjasukmana
Back to Inner Product Spaces and Orthogonal Complements
