TY - JOUR
T1 - Nearly Comonotone Approximation
AU - Leviatan, D.
AU - Shevchuk, I. A.
N1 - Funding Information:
* Part of this work was done while the authors were guests of Professor R. A. DeVore at the University of South Carolina. They acknowledge partial support by ONR Grant N00014-91-1076 and by DoD Grant N00014-94-1-1163.
PY - 1998/10
Y1 - 1998/10
N2 - We discuss the degree of approximation by polynomials of a functionfthat is piecewise monotone in [-1, 1]. We would like to approximatefby polynomials which are comonotone with it. We show that by relaxing the requirement for comonotonicity in small neighborhoods of the points where changes in monotonicity occur and near the endpoints, we can achieve a higher degree of approximation. We show here that in that case the polynomials can achieve the rate ofω3. On the other hand, we show in another paper, that no relaxing of the monotonicity requirements on sets of measures approaching 0 allowsω4estimates.
AB - We discuss the degree of approximation by polynomials of a functionfthat is piecewise monotone in [-1, 1]. We would like to approximatefby polynomials which are comonotone with it. We show that by relaxing the requirement for comonotonicity in small neighborhoods of the points where changes in monotonicity occur and near the endpoints, we can achieve a higher degree of approximation. We show here that in that case the polynomials can achieve the rate ofω3. On the other hand, we show in another paper, that no relaxing of the monotonicity requirements on sets of measures approaching 0 allowsω4estimates.
UR - http://www.scopus.com/inward/record.url?scp=0002134702&partnerID=8YFLogxK
U2 - 10.1006/jath.1998.3194
DO - 10.1006/jath.1998.3194
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AN - SCOPUS:0002134702
SN - 0021-9045
VL - 95
SP - 53
EP - 81
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
IS - 1
ER -