kvadratne formule-zavrsni rad-matematika i informatika-matematika pdf

7/25/2019 Kvadratne Formule-Zavrsni Rad-Matematika i Informatika-Matematika PDF

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3

1. , 41.1 .................................................................................................. 4

1.2 ........................................................................................ 5

1.3 ............................................................................................... 8

2. 11

2.1 ................................................................................................... 11

2.2 . 14

2.2.1 ...................... ...................... ...................... .......... 14

2.2.2 .................... ...................... ...................... .......... 15

2.2.3 ..................... ..................... ...................... ....... 16

2.3 - .................... 17

2.3.1 ............................................................................................... 17

2.3.2 .......................................................................................... 18

2.3.3 ............................................................................................. 18

2.4 ......... 22

2.4.1 .............................................................................. 23

2.4.2 ................... ...................... ...................... .............. 23

2.4.3 ............................................................................ 24

3. 25

3.1.1 Nasr-Al-Din Ide ................... ...................... ...................... .............. 25

3.1.2 ..................... ..................... ...................... ...................... ....... 26

3.1.3 ........................................................................................... 27


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4/38

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6/38

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7/38

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8/38

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9/38

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10/38

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11/38

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12/38

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13/38

13

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14/38

14

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15/38

15

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16/38

16

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17/38

17

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18/38

18

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19/38

19

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20/38

20

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21/38

21

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22/38

22

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23/38

23

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1, 33

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24/38

24

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25/38

25

3.

[10] [17].

2, [17] 3. , ,

2.

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3.1.1 Nasr Al Din Ide

[10]

1

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26/38

26

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27/38

27

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28/38

28

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[1], [6], [7], [8], [13], [17] [18].


29/38

29

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,

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(COC)

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, .


30/38

30

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[17] 1/ 2 . 1 , 0 , 1/ 3 . [16] ( ), [2] ( ) [3] ( ).

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1f 2f 3f 8f 10f

156.858 143.505 76.5611 37.7291 41.5255

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1/ 2

2795.84 2436.88 1300.31 607.272 692.079

1/ 3 2686.51 2457.16 1312.18 630.584 708.99 0 2524.01 2500.55 1339.00 683.024 745.809 . 2n 2686.57 2457.16 1312.82 630.79 708.992 . 3n 2686.55 2457.16 1312.82 630.71 708.991 238.781 229.883 133.557 78.1489 84.7777

2940.17 2417.43 1288.14 585.626 676.032

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31/38

31

p d EEF *EEF AKG

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32/38

32

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33/38

33

6.

[1] Babajee, D. K. R., Dauhoo, M. Z., An analysis of the properties of the variants of

Newton's method with third order convergence, Applied Mathematics andComputation 183 (1) (2006), 659684.[2] Frontini, M., Sormani, E., Some variants of Newton's method with third-order

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UNIVERSITY OF NOVI SADFACULTY OF SCIENCE

DEPARTAMENT OF MATHEMATICS AND INFORMATICSKEY WORDS DOCUMENTATION

Accession number:ANO

Identification number:INODocument type: Monograph typeDT

Type of record: Printed textTR

Contents Code:CC

Author: Jelena Kovaevi

AU

Mentor: dr. Dragoslav HercegMN

Title: Quadrature based iterative method for numerical solving nonlinear equationsXI

Language of text: Serbian (Cyrillic)LT

Language of abstract: Serbian and EnglishLA

Country of publication: SerbiaCP

Locality of publication: VojvodinaLP

Publication year: 2012.PY

Publisher: Author's reprintPU

Publ. place: Novi Sad, Department of mathematics and informatics, Faculty ofScience, Trg Dositeja Obradovia 3

PP

Physical description4/ 38/ 18/3/0/0PD

Scientific field: MathematicsSF

Scientific discipline: Numerical mathematicsSD

Key words:SKW UC:Holding data:HD

Note:N

Abstract: In this paper, we consider some numerical methods for solving nonlinearequations 0f x with one unknown, which are based on modifications of


38/38

Newton's procedure. Starting from the expression k

x

k

x

f x f x f u du and

replacing the integral by quadrature formulas for numerical integration, we obtain

an approximation for f x . Equating to zero this approximation we get firstly

implicit equation to calculate the approximate value of solutions to the equation 0f x . Using Newton's method we obtain from the implicit equation explicit

one, and then two-step iterative method. Depending on the choice of quadratureformulas we obtained family of iterative methods. For selected procedures, undercertain assumptions, we prove convergence and determine the order ofconvergence.AB

Accepted by the Scientific Board on: 9. 07. 2012ASB

Defended:

DEThesis defense board:DBPresident: dr ore Herceg, Full Professor, Faculty of Science, University of

Novi SadMember: dr, Helena Zarin, Associate Professor, Faculty of Science,

University of Novi SadMember: dr Dragoslav Herceg, Full Professor, Faculty of Science, University

of Novi Sad

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