Batas galat pada aproksimasi integral riemann-stieltjes oleh aturan trapesium = Error bound on riemann-stieltjes integral approximation by trapezoidal rule / Gisca Annur Tri Ayu Putri
| Main Author: | Gisca Annur Tri Ayu Putri, author |
|---|---|
| Format: | Bachelors |
| Terbitan: |
, 2016
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| Subjects: | |
| Online Access: |
http://lib.ui.ac.id/file?file=digital/2018-4/20422509-S62456-Gisca Annur Tri Ayu Putri.pdf |
Daftar Isi:
- [<b>ABSTRAK</b><br> Integral Riemann-Stieltjes, salah satu konsep penting dalam analisis dan kalkulus, merupakan bentuk yang lebih umum dari integral Riemann. Untuk beberapa fungsi, nilai eksak suatu integral Riemann-Stieltjes tidak mudah didapatkan. Oleh karena itu, terdapat beberapa metode yang dapat digunakan untuk mencari nilai tersebut secara numerik, salah satunya adalah aturan trapesium. Walaupun demikian, metode aproksimasi ini memiliki galat dalam mencari nilai tersebut. Studi literatur ini bertujuan untuk mencari batas galat terbaik dalam mengaproksimasi nilai eksak integral Riemann-Stieltjes menggunakan aturan trapesium. Dalam studi ini, akan ditinjau beberapa fungsi khusus tertentu yakni fungsi variasi terbatas, fungsi p-H-Hölder, fungsi Lipschitz, dan fungsi tak turun. <hr> <b>ABSTRACT</b><br> Riemann-Stieltjes intgeral, one of the most important concepts in analysis and calculus, is a general form of Riemann integral. For some functions, the exact value of Riemann-Stieltjes integral cannot be simply obtained. Therefore, there are some methods that could be used to find the value numerically, one of them is trapezoidal rule. However, this rule has an error in finding the value. The study of literature is to learn the sharp bounds for the error in approximating the Riemann-Stieltjes integral by trapezoidal rule. In this study, various classes of functions, such as functions of bounded variation, p-H-Hölder type, Lipschitzian, and nondecreasing functions are recalled., Riemann-Stieltjes intgeral, one of the most important concepts in analysis and calculus, is a general form of Riemann integral. For some functions, the exact value of Riemann-Stieltjes integral cannot be simply obtained. Therefore, there are some methods that could be used to find the value numerically, one of them is trapezoidal rule. However, this rule has an error in finding the value. The study of literature is to learn the sharp bounds for the error in approximating the Riemann-Stieltjes integral by trapezoidal rule. In this study, various classes of functions, such as functions of bounded variation, p-H-Hölder type, Lipschitzian, and nondecreasing functions are recalled. ]