Best Interpolatory Approximation in Normed Linear Spaces

✍ Scribed by Frank Deutsch; Sizwe Mabizela

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 542 KB
• Volume: 85
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1996.0041

✦ Synopsis

A theory of best approximation with interpolatory contraints from a finitedimensional subspace M of a normed linear space X is developed. In particular, to each x # X, best approximations are sought from a subset M(x) of M which depends on the element x being approximated. It is shown that this parametric approximation'' problem can be essentially reduced to the usual'' one involving a certain fixed subspace M 0 of M. More detailed results can be obtained when (1) X is a Hilbert space, or (2) M is an ``interpolating subspace'' of X (in the sense of [1]).