TY - JOUR

T1 - ON RESTRICTED BEST APPROXIMATION TO FUNCTIONS WITH RESTRICTED DERIVATIVES.

AU - Kimchi, E.

AU - Leviatan, D.

PY - 1976

Y1 - 1976

N2 - Let a function f belonging to C**a left bracket minus 1,1 right bracket (where a equals 2k//r, for some fixed k//r greater than equivalent to 0), be such that the sum over n of (1/n) omega (f**a, 1/n** one-half ) less than infinity . It is shown that if f satisfies r restrictions on its 0 less than equivalent to k//1 less than k//2 less than . . . less than k, derivatives respectively with strict inequalities, then for sufficiently large n, the best polynomial approximator to f satisfies the same restriction. Thus the best polynomial approximator is also the best restricted derivatives approximator.

AB - Let a function f belonging to C**a left bracket minus 1,1 right bracket (where a equals 2k//r, for some fixed k//r greater than equivalent to 0), be such that the sum over n of (1/n) omega (f**a, 1/n** one-half ) less than infinity . It is shown that if f satisfies r restrictions on its 0 less than equivalent to k//1 less than k//2 less than . . . less than k, derivatives respectively with strict inequalities, then for sufficiently large n, the best polynomial approximator to f satisfies the same restriction. Thus the best polynomial approximator is also the best restricted derivatives approximator.

UR - http://www.scopus.com/inward/record.url?scp=0016928065&partnerID=8YFLogxK

U2 - 10.1137/0713006

DO - 10.1137/0713006

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0016928065

SN - 0036-1429

VL - 13

SP - 51

EP - 53

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 1

ER -