Computation
A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by
simply because
is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X). A few popular ways to find such a matrix S are described below.
Read more about this topic: Linear Least Squares (mathematics)
Famous quotes containing the word computation:
“I suppose that Paderewski can play superbly, if not quite at his best, while his thoughts wander to the other end of the world, or possibly busy themselves with a computation of the receipts as he gazes out across the auditorium. I know a great actor, a master technician, can let his thoughts play truant from the scene ...”
—Minnie Maddern Fiske (1865–1932)