Characterization of Constrained Approximation in Hilbert Space

• Main Authors: CHENG, YA-YUN, 鄭雅云
• Other Authors: 楊南屏
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/49407395696161717123

碩士 === 輔仁大學 === 數學系研究所 === 93 === In a Hilbert space , we primarily investigate the characterization of the best approximation to any from the set , where is a closed convex subset of , is a bounded linear operator from into a finite-dimensional Hilbert space and . Under the assumption that is in the relative interior of , denoted by ri , is shown to be identical to the best approximation to a certain perturbation of from . Such a property is called the perturbation property. Finally, we discuss a perturbation property from the sum of ri and ri . It also contains a briefly explanation on the relationship between and for and being orthogonal Chebyshev subspaces of .