Some remarks on greedy algorithms

There has recently been much interest in approximation by linear combinations of functions taken from a redundant set 79. That is, the elements of 79 are not linearly independent. Perhaps the first example of this type was considered by Schmidt in 1907 [6] who considered the approximation of functions f ( x , y ) of two variables by bilinear forms ~-~tfl=lUi(X)Vi(y ) in L2([0,112). This problem is closely connected with properties of the integral operator with ke rne l f (x , y). We mention two other prominent examples of this type of approximation. In neural networks, one approximates functions of d-variables by linear combinations of functions from the set