ABSTRACT
The purpose of linear least squares approaches is mainly to approximate solutions of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.
Specifically, consider a matrix A ∈ Rm×n, and let y ∈ Rm. The least squares solution w ∈ Rn of the linear system Aw“ = ”y is defined as:
Find w ∈ Rn, such that ‖y −Aw‖ = min z∈Rn
‖y −Az‖, (4.1)
where for x ∈ Rn, ‖x‖ = ‖x‖2 = √ xTx is the l2 vector norm. The existence
and uniqueness of such a solution will be discussed in Sections 4.2 and 4.3. We first give an application of linear least squares problems in statistical computations.
