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On a problem in monotone approximation

โœ Scribed by Xingping Sun

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
237 KB
Volume
57
Category
Article
ISSN
0021-9045

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๐Ÿ“œ SIMILAR VOLUMES

One Example in Monotone Approximation
One Example in Monotone Approximation
โœ I.A. Shevchuk ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 306 KB

For each non-negative integer n a function f=f n is constructed such that f has a continuous and non-negative derivative f $ on I :=[&1, 1] and where is the value of the best uniform approximation on I of the function f $ ( f ) by arbitrary (monotone on I ) algebraic polynomials of degree n (n+1).

Approximation ofk-Monotone Functions
Approximation ofk-Monotone Functions
โœ Kirill A. Kopotun ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 259 KB

It is shown that an algebraic polynomial of degree k&1 which interpolates a k-monotone function f at k points, sufficiently approximates it, even if the points of interpolation are close to each other. It is well known that this result is not true in general for non-k-monotone functions. As an appli