why aren't the results the same?
i have to differnt sets of code but the only difference is how i create my A matrix
code 1
publicclass GaussEl2{
publicstaticvoid main(String[] args){
int N = 10;
double[][] A ={{ 12, -2, 1, 0, 0, 0, 0, 0, 0, 0},
{ -2, 12, -2, 1, 0, 0, 0, 0, 0, 0},
{ 1, -2, 12, -2, 1, 0, 0, 0, 0, 0},
{ 0, 1, -2, 12, -2, 1, 0, 0, 0, 0},
{ 0, 0, 1, -2, 12, -2, 1, 0, 0, 0},
{ 0, 0, 0, 1, -2, 12, -2, 1, 0, 0},
{ 0, 0, 0, 0, 1, -2, 12, -2, 1, 0},
{ 0, 0, 0, 0, 0, 1, -2, 12, -2, 1},
{ 0, 0, 0, 0, 0, 0, 1, -2, 12, -2},
{ 0, 0, 0, 0, 0, 0, 0, 1, -2, 12}
};
double[] b ={ 13.97, 5.93, -6.02, 8.32, -23.75, 28.45, -8.9, -10.5, 10.34, -38.74};
double [][] L =newdouble [10][10];
double [][] U =newdouble [10][10];
double [] b1 =newdouble [10];
// cpoying original A to U
for(int i = 0; i < 10; ++i)
for(int j = 0; j < 10; ++j)
U[i][j] = A[i][j];
// cpoying original b to b1
for(int i = 0; i < 10; ++i)
for(int j = 0; j < 1; ++j)
b1[i] = b[i];
// Gaussian elimination with partial pivoting
for (int p = 0; p < N; p++){
// find pivot row and swap
int max = p;
for (int i = p + 1; i < N; i++){
if (Math.abs(A[i][p]) > Math.abs(A[max][p])){
max = i;
}
}
double[] temp = U[p]; U[p] = U[max]; U[max] = temp;
doublet= b1[p]; b1[p] = b1[max]; b1[max] = t;
// pivot within A and b
for (int i = p + 1; i < N; i++){
L[i][p] = U[i][p] / U[p][p];
b1[i] -= L[i][p] * b1[p];
for (int j = p; j < N; j++){
U[i][j] -= L[i][p] * U[p][j];
}
}
}
// back substitution
double[] x =newdouble[N];
for (int i = N - 1; i >= 0; i--){
double sum = 0.0;
for (int j = i + 1; j < N; j++){
sum += U[i][j] * x[j];
}
x[i] = (b1[i] - sum) / U[i][i];
}
// print results
System.out.println("This is my A:\n");
for (int i = 0; i < N; i++){
for(int j = 0; j < N; ++j)
System.out.print(A[i][j]+"\t");
System.out.println();
}
System.out.println("\nThis is my b:\n");
for (int i = 0; i < N; i++){
System.out.println(b[i]);
System.out.println();
}
System.out.println("\nThis is my x:\n");
for (int i = 0; i < N; i++){
System.out.println(x[i]);
System.out.println();
}
System.out.println("\nThis is my L:\n");
for(int i = 0; i < 10; ++i){
for(int j = 0; j < 10; ++j)
System.out.print(Math.round((L[i][j])*10000)/10000.0+"\t");
System.out.println();
}
System.out.println("\nThis is my U:\n");
for(int i = 0; i < 10; ++i){
for(int j = 0; j < 10; ++j)
System.out.print(Math.round((U[i][j])*10000)/10000.0+"\t");
System.out.println();
}
}
}
code 2
publicclass GaussEl{
publicstaticvoid main(String[] args){
int N = 10;
double[][] A =newdouble [10][10];
double[] b ={ 13.97, 5.93, -6.02, 8.32, -23.75, 28.45, -8.9, -10.5, 10.34, -38.74};
double [][] L =newdouble [10][10];
double [][] U =newdouble [10][10];
double [] b1 =newdouble [10];
for (int i=0; i<=9; i++){
A[i][i] = 12;
}
for (int i=0; i<=8; i++){
A[i][i+1] = -2;
}
for (int i=1; i<=9; i++){
A[i][i-1] = -2;
}
for (int i=0; i<=7; i++){
A[i][i+1] = -1;
}
for (int i=2; i<=9; i++){
A[i][i-1] = -1;
}
// cpoying original A to U
for(int i = 0; i < 10; ++i)
for(int j = 0; j < 10; ++j)
U[i][j] = A[i][j];
// cpoying original b to b1
for(int i = 0; i < 10; ++i)
for(int j = 0; j < 1; ++j)
b1[i] = b[i];
// Gaussian elimination with partial pivoting
for (int p = 0; p < N; p++){
// find pivot row and swap
int max = p;
for (int i = p + 1; i < N; i++){
if (Math.abs(A[i][p]) > Math.abs(A[max][p])){
max = i;
}
}
double[] temp = U[p]; U[p] = U[max]; U[max] = temp;
doublet= b1[p]; b1[p] = b1[max]; b1[max] = t;
// pivot within A and b
for (int i = p + 1; i < N; i++){
L[i][p] = U[i][p] / U[p][p];
b1[i] -= L[i][p] * b1[p];
for (int j = p; j < N; j++){
U[i][j] -= L[i][p] * U[p][j];
}
}
}
// back substitution
double[] x =newdouble[N];
for (int i = N - 1; i >= 0; i--){
double sum = 0.0;
for (int j = i + 1; j < N; j++){
sum += U[i][j] * x[j];
}
x[i] = (b1[i] - sum) / U[i][i];
}
// print results
System.out.println("This is my A:\n");
for (int i = 0; i < N; i++){
for(int j = 0; j < N; ++j)
System.out.print(A[i][j]+"\t");
System.out.println();
}
System.out.println("\nThis is my b:\n");
for (int i = 0; i < N; i++){
System.out.println(b[i]);
System.out.println();
}
System.out.println("\nThis is my x:\n");
for (int i = 0; i < N; i++){
System.out.println(x[i]);
System.out.println();
}
System.out.println("\nThis is my L:\n");
for(int i = 0; i < 10; ++i){
for(int j = 0; j < 10; ++j)
System.out.print(Math.round((L[i][j])*10000)/10000.0+"\t");
System.out.println();
}
System.out.println("\nThis is my U:\n");
for(int i = 0; i < 10; ++i){
for(int j = 0; j < 10; ++j)
System.out.print(Math.round((U[i][j])*10000)/10000.0+"\t");
System.out.println();
}
}
}
