Least Squares Problems

Part of the Texts in Applied Mathematics book series (TAM, volume 55)

The origin of the least squares data-fitting problem is the need of a notion of “generalized solutions” for a linear system Ax = b that has no solution in the classical sense (that is, b does not belong to the range of A). The idea is then to look for a vector x such that Ax is “the closest possible” to b. Several norms are at hand to measure the distance between Ax and b, but the simplest choice (which corresponds to the denomination “least squares”) is the Euclidean vector norm. In other words, a least squares problem amounts to finding the solution (possibly nonunique) x ∈ ℝ p to the following minimization problem:


Orthogonal Projection Normal Equation Triangular Matrix Orthogonal Matrix Operation Count 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media, LLC 2008

Personalised recommendations