DISTRIBUTION OF EXTREME-POINTS OF THE ERROR CURVE OF BEST APPROXIMATION BY INCOMPLETE POLYNOMIALS

[摘要] Let PHI(n,m) = {(x + 1)n P(m)(x):P(m)(x) is-an-element-of PHI(m)} be the set of incomplete polynomials of type (n, m) on [-1, 1]. We consider the distribution of the extreme points of the error curve in the best approximation of f is-an-element-of C[- 1, 1] with f(- 1) = 0 by incomplete polynomials of type (n, m) on [- 1, 1] and give a Kadec-type result for this setting. In particular, we improve the rate of convergence of the original Kadec result. (C) 1994 Academic Press, Inc.

[发布日期] 1994-12-01