Chapter 6

Approximation and fitting

6.1 Norm approximation

6.1.1 Basic norm approximation problem

The simplest norm approximation problem is an unconstrained problem of the form

(6.1) |

where A ∈ R^{m×n} and b ∈ R^{m} are problem data, x ∈ R^{n} is the variable, and · is a norm on R^{m}. A solution of the norm approximation problem is sometimes called an approximate solution of Ax ≈ b, in the norm · . The vector

is called the residual for the problem; ...

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