Komputasi Numeris: Iterasi Jacobi
Pendahuluan:
Metode Jacobi merupakan salah satu metode penyelesaian sistem persamaan linear (baca: matriks) berdimensi banyak (baca: lebih dari 2). Untuk matriks dengan dimensi kecil (kurang atau sama dengan dua), lebih efektif diselesaikan dengan aturan eliminasi atau metode Cramer.
Sistem persamaan linear dapat di-representasikan (dimodelkan) dalam bentuk matriks sebagai berikut:
Sebagai contoh:
3x1 + x2 - x3 = 5
4x1 + 7x2 - 3x3 = 20
2x1 - 2x2 + 5x3 = 10
dapat di-representasikan sebagai:
Iterasi Jacobi memiliki rumus persamaan sebagai berikut:
Jika inisialisasi nilai awal x1, x2 dan x3 = 0, maka:
Iterasi berikutnya ditunjukkan pada tabel berikut ini:
Jika diperhatikan pada tabel di atas, nilai x1, x2 dan x3 semakin stabil (perbedaan nilai saat ini dengan nilai sebelumnya semakin kecil). Proses ini dapat diteruskan sesuka hati sampai diperoleh toleransi error yang diinginkan.
Menulis Kode Program
Setelah kita mengetahui algoritma Methode Jacobi, saatnya menulis kode program supaya kita dapat mengganti-ganti persamaannya secara mudah. Saya menggunakan C++ sebagai contoh.
Step #1 : Menulis identitas program
//--------JACOBI Iteration
//--------Haruno Sajati, S.T., M.Eng
//--------jati@stta.ac.id
//--------Teknik Informatika
//--------Sekolah Tinggi Teknologi Adisutjipto
Step #2 : Deklarasi header dan inisialisasi variabel
#include<iostream.h>
void main()
{
int i, j, k, l, ukuran, iterasi;
float f[10], a[10][10],b[10],x[10], toleransi, sigma[10];
Step #3 : Input ukuran matriks
//input ukuran matrik
cout << "Masukkan besar matriks : ";
cin >> ukuran;
Step #4 : Input matriks A dan matriks B
//masukkan matrik a
for (i=1;i<=ukuran;i++){
for (j=1;j<=ukuran;j++){
cout << "Masukkan elemen matrik a[" << i << "][" << j << "] = ";
cin >> a[i][j];
}
}
//masukkan matrik b
for (i=1;i<=ukuran;i++){
cout << "Masukkan elemen matrik b[" << i << "] = ";
cin >> b[i];
}
Step #5 Inisialisasi nilai awal
//inisialisasi nilai awal
for (i=1;i<=ukuran;i++){
x[i]=0;
}
toleransi = 10;
iterasi = 0;
Step #6 Iterasi Jacobi
while (toleransi > 0.00001)
{
iterasi++;
cout << "---------------------------------------\n";
cout << "iterasi ke " << iterasi << endl;
if (iterasi > 50)
break;
//menghitung jumlah total sigma
for (k=1;k<=ukuran;k++) {
sigma[k] = 0;
for (l=1;l<=ukuran;l++)
{
if (k != l) {
sigma[k] = sigma[k] + (a[k][l]*x[l]);
} // tutup if k != l
} // tutup for l
f[k] = (b[k] - sigma[k])/a[k][k];
cout << "x[" << k << "] = " << f[k] << endl;
} // tutup for k
toleransi = (f[1]-x[1])+(f[2]-x[2])+(f[3]-x[3]);
if (toleransi < 0) {
toleransi *= -1;
}
for (i=0;i<=ukuran;i++) {
x[i] = f[i];
}
} //tutup while
} //tutup void
Uji Coba Program
1. Proses input matriks:
![](data:image/png;base64,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)
2. Iterasi 1 -5
![](data:image/png;base64,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)
3. Iterasi 15 - 19
![](data:image/png;base64,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)
Selamat mencoba
Metode Jacobi merupakan salah satu metode penyelesaian sistem persamaan linear (baca: matriks) berdimensi banyak (baca: lebih dari 2). Untuk matriks dengan dimensi kecil (kurang atau sama dengan dua), lebih efektif diselesaikan dengan aturan eliminasi atau metode Cramer.
Sistem persamaan linear dapat di-representasikan (dimodelkan) dalam bentuk matriks sebagai berikut:
3x1 + x2 - x3 = 5
4x1 + 7x2 - 3x3 = 20
2x1 - 2x2 + 5x3 = 10
dapat di-representasikan sebagai:
Tujuannya supaya mudah untuk diselesaikan secara matematis.
Aturan Jacobi:
atau
Iterasi berakhir jika:
Atau perhitungan saat ini tidak berbeda jauh (baca: mirip) dengan perhitungan sebelumnya.
Jika di-implementasikan ke contoh di atas menjadi:
Jika inisialisasi nilai awal x1, x2 dan x3 = 0, maka:
Iterasi berikutnya ditunjukkan pada tabel berikut ini:
Jika diperhatikan pada tabel di atas, nilai x1, x2 dan x3 semakin stabil (perbedaan nilai saat ini dengan nilai sebelumnya semakin kecil). Proses ini dapat diteruskan sesuka hati sampai diperoleh toleransi error yang diinginkan.
Menulis Kode Program
Setelah kita mengetahui algoritma Methode Jacobi, saatnya menulis kode program supaya kita dapat mengganti-ganti persamaannya secara mudah. Saya menggunakan C++ sebagai contoh.
Step #1 : Menulis identitas program
//--------JACOBI Iteration
//--------Haruno Sajati, S.T., M.Eng
//--------jati@stta.ac.id
//--------Teknik Informatika
//--------Sekolah Tinggi Teknologi Adisutjipto
Step #2 : Deklarasi header dan inisialisasi variabel
#include<iostream.h>
void main()
{
int i, j, k, l, ukuran, iterasi;
float f[10], a[10][10],b[10],x[10], toleransi, sigma[10];
Step #3 : Input ukuran matriks
//input ukuran matrik
cout << "Masukkan besar matriks : ";
cin >> ukuran;
Step #4 : Input matriks A dan matriks B
//masukkan matrik a
for (i=1;i<=ukuran;i++){
for (j=1;j<=ukuran;j++){
cout << "Masukkan elemen matrik a[" << i << "][" << j << "] = ";
cin >> a[i][j];
}
}
//masukkan matrik b
for (i=1;i<=ukuran;i++){
cout << "Masukkan elemen matrik b[" << i << "] = ";
cin >> b[i];
}
Step #5 Inisialisasi nilai awal
//inisialisasi nilai awal
for (i=1;i<=ukuran;i++){
x[i]=0;
}
toleransi = 10;
iterasi = 0;
Step #6 Iterasi Jacobi
while (toleransi > 0.00001)
{
iterasi++;
cout << "---------------------------------------\n";
cout << "iterasi ke " << iterasi << endl;
if (iterasi > 50)
break;
//menghitung jumlah total sigma
for (k=1;k<=ukuran;k++) {
sigma[k] = 0;
for (l=1;l<=ukuran;l++)
{
if (k != l) {
sigma[k] = sigma[k] + (a[k][l]*x[l]);
} // tutup if k != l
} // tutup for l
f[k] = (b[k] - sigma[k])/a[k][k];
cout << "x[" << k << "] = " << f[k] << endl;
} // tutup for k
toleransi = (f[1]-x[1])+(f[2]-x[2])+(f[3]-x[3]);
if (toleransi < 0) {
toleransi *= -1;
}
for (i=0;i<=ukuran;i++) {
x[i] = f[i];
}
} //tutup while
} //tutup void
Uji Coba Program
1. Proses input matriks:
2. Iterasi 1 -5
3. Iterasi 15 - 19
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mas/mbak itu yang masukkan matriks b nya illegal structure gitu terus inisialisasinya malah undefined kenapa ya tolong pencerahannya
ohh lagi mau tanya nih ini kenapa waktu di run kok malah cuma menghitung iterasi 1 iterasi selanjutnya malah error kenapa ya tolong pencerahannya
Pakai apa nih nulisnya? Kalau pakai visual studio, coba tambahkan using namespace std;
Script di atas, saya tulis pakai Turbo C++ 4.5.
saya pakai aplikasi code blocks. berhasil ketika di run kan. tapi, ingin melihat nilai dari iterasi 1, pas diarahkan keatas kok malah langsung terkeluar ya...?