DM FUNCTION AND MICCHELLỈ̉S THEOREM
A function 𝑓 is said to be a DM function on [0,∞) if 𝑓 is continuous function on [0,∞) and its derivatives is continuous on (0,∞) and the first derivative, 𝑓′, is a completely monotone (CM) function. This thesis discusses DM...
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id-itb.:225282017-09-27T14:41:49ZDM FUNCTION AND MICCHELLIÃâÃâS THEOREM DANGU RIANJAYA (NIM: 20115046), ILHAM Indonesia Theses INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/22528 A function 𝑓 is said to be a DM function on [0,∞) if 𝑓 is continuous function on [0,∞) and its derivatives is continuous on (0,∞) and the first derivative, 𝑓′, is a completely monotone (CM) function. This thesis discusses DM functions and their application in the problem of interpolation based on Micchelli’s Theorem. Micchelli’s Theorem states that for a DM function 𝑓, the matrix [𝐴𝑖𝑗]=𝑓(‖𝑥𝑖−𝑥𝑗‖2) is nonsingular. Besides the problem of interpolation, this thesis also discusses the application of DM functions in the problem of embedding a finite dimensional quasi-metric space into Euclidean space. text |
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A function 𝑓 is said to be a DM function on [0,∞) if 𝑓 is continuous function on [0,∞) and its derivatives is continuous on (0,∞) and the first derivative, 𝑓′, is a completely monotone (CM) function. This thesis discusses DM functions and their application in the problem of interpolation based on Micchelli’s Theorem. Micchelli’s Theorem states that for a DM function 𝑓, the matrix [𝐴𝑖𝑗]=𝑓(‖𝑥𝑖−𝑥𝑗‖2) is nonsingular. Besides the problem of interpolation, this thesis also discusses the application of DM functions in the problem of embedding a finite dimensional quasi-metric space into Euclidean space. |
| format |
Theses |
| author |
DANGU RIANJAYA (NIM: 20115046), ILHAM |
| spellingShingle |
DANGU RIANJAYA (NIM: 20115046), ILHAM DM FUNCTION AND MICCHELLỈ̉S THEOREM |
| author_facet |
DANGU RIANJAYA (NIM: 20115046), ILHAM |
| author_sort |
DANGU RIANJAYA (NIM: 20115046), ILHAM |
| title |
DM FUNCTION AND MICCHELLỈ̉S THEOREM |
| title_short |
DM FUNCTION AND MICCHELLỈ̉S THEOREM |
| title_full |
DM FUNCTION AND MICCHELLỈ̉S THEOREM |
| title_fullStr |
DM FUNCTION AND MICCHELLỈ̉S THEOREM |
| title_full_unstemmed |
DM FUNCTION AND MICCHELLỈ̉S THEOREM |
| title_sort |
dm function and micchelliãâãâs theorem |
| url |
https://digilib.itb.ac.id/gdl/view/22528 |
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1823634292318666752 |