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FUNGSI DM DAN TEOREMA MICCHELLI

DM FUNCTION AND MICCHELLI’S THEOREM

Master Theses from JBPTITBPP / 2017-09-14 16:01:05
Oleh : ILHAM DANGU RIANJAYA (NIM: 20115046), S2 - Mathematics
Dibuat : 2017-09-14, dengan 1 file

Keyword : Fungsi DM, completely monotone, interpolasi, Teorema Micchelli, ruang kuasi-metrik, ruang Euclid, penyisipan.

Fungsi 𝑓 disebut fungsi DM pada [0,∞) apabila fungsi 𝑓 kontinu pada [0,∞) dan setiap turunannya kontinu pada (0,∞) serta fungsi turunan pertama dari 𝑓, ditulis 𝑓′, merupakan fungsi completely monotone (CM). Pada tesis ini, dibahas mengenai fungsi DM dan aplikasinya dalam masalah interpolasi berdasarkan Teorema Micchelli. Teorema Micchelli menyatakan bahwa untuk 𝑓 anggota keluarga fungsi DM, matriks [𝐴𝑖𝑗]=𝑓(‖𝑥𝑖−𝑥𝑗‖2) merupakan matriks tak singular. Selain dalam masalah interpolasi, juga dipaparkan mengenai aplikasi fungsi DM dalam masalah penyisipan ruang kuasi-metrik berhingga ke ruang Euclid.

Deskripsi Alternatif :

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.

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PropertiNilai Properti
ID PublisherJBPTITBPP
OrganisasiS2 - Mathematics
Nama KontakUPT Perpustakaan ITB
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KotaBandung
DaerahJawa Barat
NegaraIndonesia
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