A cubic spline of tri-monotone approximation
For any 3-monotone on $[????,????]$ function $????$ (its third divided differences are nonnegative for all choices of four distinct points, or equivalently, $????$ has a convex derivative on $(????,????)$) we construct a cubic 3-monotone (like $????$) spline $????$ with $???? \in N$ ”almost” equidis...
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| Date: | 2017 |
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| Keywords: | keywords |
| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут математики НАН України
2017
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/34 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | For any 3-monotone on $[????,????]$ function $????$ (its third divided differences are nonnegative for all choices of four distinct points, or equivalently, $????$ has a convex derivative on $(????,????)$) we construct a cubic 3-monotone (like $????$) spline $????$ with $???? \in N$ ”almost” equidistant knots $????_????$ such that${‖???? - ????‖}_{[????_????, ????_{????-1}]} ≤ ???? ω_4 (????, (???? - ????) / ????, [????_{????+4}, ????_{????-5}] \cap [????, ????]), ???? = 1,...,????,$where $????$ is an absolute constant, $????_4 (????,????,[\cdot,\cdot])$ is the 4-th modulus of smoothness of $????$, and ${|| \cdot ||}_{[\cdot, \cdot]}$ is the max-norm. |
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