On the Existence of Strong Unicity of Arbitrarily Small Order.
Abstract
It is shown that the strong uniqueness theorem need not hold in its standard form when constraints are imposed on a uniform approximation problem. In particular, it is shown that when approximation with polynomials subject to a monotone constraint (P1(x) > or = 0) and Hermite-Birkhoff interpolating constraints, a best possible result is the inequality with the constraints f-p > or = to f - p sub f + delta x p - p sub f to the 1/2 m power where p is any approximating polynomial satisfying the constraints and the additional condition that norm of p < or = M (M fixed) and P sub f is the unique best approximation to f from the given class of approximants.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1980
- Accession Number
- ADA082105
Entities
People
- B. L. Chalmers
- Gerald D. Taylor
Organizations
- Colorado State University