Numerical Linear Algebra pp 125-142 | Cite as

# Least Squares Problems

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:

## Keywords

Orthogonal Projection Normal Equation Triangular Matrix Orthogonal Matrix Operation Count## Preview

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