BEST INTERPOLATORY APPROXIMATION IN NORMED LINEAR-SPACES

A theory of best approximation with interpolatory contraints from a fi nite-dimensional subspace M of a normed linear space X is developed. I n particular, to each x is an element of X, best approximations are so ught from a subset M(x) of M which depends on the element x being appr oximated. It is shown that this ''parametric approximation'' problem c an be essentially reduced to the ''usual'' one involving a certain fix ed subspace M(0) of M. More detailed results can ve obtained when (1) X is a Hilbert space, or (2) M is an ''interpolating subspace'' of X ( in the sense of [1]). (C) 1996 Academic Press, Inc.