METODE NUMERIKInterpolasi Gauss Mundur
Kelas 2012 C
Anggota Kelompok 3:
1. Suprat Dwi Cahyono
12030174060
2. Muryati
12030174062
3. Nurfi Rifatul Himmah H. A.12030174242
4. Hetri Nur Fajarwati
12030174244
5. Dita Nilamsari
12030174245
Universitas Negeri Surabaya
Fakultas Matematika dan Ilmu Pengetahuan Alam
Jurusan MatematikaProgram Studi S1 Pendidikan Matematika
2015
Interpolasi Gauss MundurMetode ini hanya dapat digunakan jika
data yang diberikan berupa data yang memiliki beda sama ( konstan)
dengan mendefinisikan .Bentuk umum formula interpolasi gauss mundur
adalah sebagai berikut. Rumus ini cocok di hingga
Dengan
Contoh Soal
1. Hitunglah nilai dan tentukan nilai apabila diberikan tabel
diferensi berikut ini (pendekatan hingga )
0.1 0.09983
0.379600.5 0.47943 - 0.07570 0.30390 - 0.047970.9 0.78333 -
0.12367 0.01951 0.18023 - 0.02846
1.3 0.96356 - 0.15231 0.02404
0.02810 - 0.004421.7 0.99166 - 0.15655
0.128452.1 0.86321
Penyelesaian:
= - 0.25
2. Apply Gausss backward formulas to obtain sin 45, given in the
following table.x203040506070
y = sin x0,34200,50200,64280,76600,86600,9397
Penyelesaian:
20 0,3420 0,16 30 0,5020 - 0,0192 0,1408 0,0016 40 0,6428 -
0,0176 - 0,0072 0,1232 - 0,0056 0,0097 50 0,7660 - 0,0232
0,0025
0,1 - 0,0031 60 0,8660 - 0,0263
0,0737 70 0,9397
= 0,7660 0,06155 + 0,0029 0,00035 + 0,0000585938
0,0001136719
= 0,70694492193. Find the values of y when x = 2.9 from the
following data using Gausss backward formula respectively
:x2,02,53,03,54,0
y246,2409,3537,2636,3715,9
Penyelesaian:
2,0 246,2 163,12,5 409,3 - 35,2 127,9 6,43,0 537,2 - 28,8 2,9
99,1 9,3
3,5 636,3 - 19,5
79,6 4,0 715,9
= 537,2 25,58 + 2,304 + 0,2048 + 0,04176
= 514,170564. Given that = 2,2361; and find by using Gausss
backward formula.
Penyelesaian:
4 2 0,2361 5 2,2361 - 0,0227 0,2134 0,00566 2,4495 - 0,0171 -
0,0022 0,1963 0,0034 0,0015 7 2,6458 - 0,0137 - 0,0007
0,1826 0,0027 8 2,8284 - 0,011
0,1716 9 3
= 2,6458 0,03926 + 0,001096 + 0,0001088 0,00001008
0,000009504
= 2,607725216Daftar Pustaka
Fuad, Yusuf. 2014. Metode Numerik 1. Surabaya: Jurusan
Matematika FMIPA Unesa.
https://books.google.co.id/books?id=cL1boM2uyQwC&pg=SA6-PA4&lpg=SA6
PA4&dq=gauss+backward+interpolation&source=bl&ots=Q_kjG-G3sz&sig=
Xzy2kV1ZklRHVBZWM21oZ9EO4&hl=id&sa=X&ei=D1dRVd2OAZLjoATQg4GIBg&ved=0CF4Q6AEwCA#v=onepage&q=gauss%20backward%20interpolation&f=false.(Diakses
pada Selasa 12 Mei 2015 pukul
09.00)http://sakshieducation.com/Engg/EnggAcademia/CommonSubjects/MathMethods
Interpolation.pdf. (Diakses pada Senin 11 Mei 2015 pukul 10.00)
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