Optimal Numerical Approximation of a Linear Operator

Abstract

Many linear problems of numerical analysis can be formulated in the following way: One is given a set of n linear data Nu = and a bound for the norm ||u||B of an otherwise unknown element of u of a hilbert space B. One wishes to find a best approximation to the element Su, where S is a bounded linear operator from B to another Hilbert space . For example, Su may be the solution of an ordinary or partial differential equation with right-hand side, initial data, or boundary data u.