public static Polynomial newtonemethod(double[] x, double[] y, double[,] tab, int n)
{
Polynomial temp = new Polynomial();
Polynomial temp1 = new Polynomial();
Polynomial temp2 = new Polynomial();
Polynomial temp3 = new Polynomial();
temp = Polynomial.insert(y[0], .0, temp);
for (int i = 1; i < n; i++)
{
temp1 = new Polynomial();
temp1 = Polynomial.insert(1.0, .0, temp1);
temp3 = new Polynomial();
temp3 = Polynomial.insert(tab[0, i], .0, temp3);
for (int j = 0; j < i; j++)
{
temp2 = new Polynomial();
temp2 = Polynomial.insert(1.0, 1.0, temp2);
temp2 = Polynomial.insert(-1.0 * x[j], .0, temp2);
temp1 = Polynomial.multi(temp2, temp1);
}
temp3 = Polynomial.multi(temp1, temp3);
temp = Polynomial.add(temp, temp3);
}
return(temp);
}
public static Polynomial Newtonsecond(double [] Y, double h, int n, double x0)
{
Double[] DalthY = new double[3];
Double[] Dalth2Y = new double[2];
double Dalth3Y = 0;
for (int i = 0; i < 3; i++)
{
DalthY[i] = Y[i + 1] - Y[i];
}
for (int i = 0; i < 2; i++)
{
Dalth2Y[i] = DalthY[i + 1] - DalthY[i];
}
Dalth3Y = Dalth2Y[1] - Dalth2Y[0];
Polynomial p = new Polynomial();
Polynomial temp = new Polynomial();
Polynomial temp1 = new Polynomial();
Polynomial temp2 = new Polynomial();
temp = Polynomial.insert(Dalth2Y[0], 0, temp);
p = Polynomial.insert(1 / h, 1, p);
p = Polynomial.insert(-1 * (x0 / h), 0, p);
temp1 = Polynomial.insert(Dalth3Y, 0, temp1);
temp1 = Polynomial.multi(temp1, p);
temp1 = Polynomial.insert(-1 * Dalth3Y, 0, temp1);
temp1 = Polynomial.add(temp1, temp);
h = h * h;
temp2 = Polynomial.insert((1 / h), 0, temp2);
temp1 = Polynomial.multi(temp1, temp2);
return(temp1);
}
public static string lagrang(double[] x, int node, double[] y)
{
Polynomial temp = new Polynomial();
Polynomial onepoly = new Polynomial();
bool loop = false;
for (int i = 0; i < node; i++)
{
for (int j = 0; j < node; j++)
{
loop = false;
if (i != j)
{
loop = true;
temp = new Polynomial();
double amthallagrang = x[i] - x[j];
temp = Polynomial.insert(y[i] * amthallagrang, 1, temp);
temp = Polynomial.insert(y[i] * amthallagrang * -x[j], 0, temp);
}
if (loop)
{
onepoly = Polynomial.add(temp, onepoly);
}
}
}
return(Polynomial.tostring(onepoly));
}
public static Polynomial Newton(double [] Y, double h, int n, double x0)
{
Double[] DalthY = new double[3];
Double[] Dalth2Y = new double[2];
double Dalth3Y = 0;
for (int i = 0; i < 3; i++)
{
DalthY[i] = Y[i + 1] - Y[i];
}
for (int i = 0; i < 2; i++)
{
Dalth2Y[i] = DalthY[i + 1] - DalthY[i];
}
Dalth3Y = Dalth2Y[1] - Dalth2Y[0];
Polynomial first = new Polynomial();
Polynomial second = new Polynomial();
Polynomial third = new Polynomial();
Polynomial p = new Polynomial();
Polynomial p2 = new Polynomial();
Polynomial temp = new Polynomial();
Polynomial temp1 = new Polynomial();
Polynomial temp2 = new Polynomial();
p = Polynomial.insert(1 / h, 1, p);
p = Polynomial.insert(-1 * (x0 / h), 0, p);
p2 = Polynomial.multi(p, p);
second = Polynomial.insert((2 * Dalth2Y[0]) / 2, 0, second);
second = Polynomial.multi(second, p);
second = Polynomial.insert(-1 * (Dalth2Y[0] / h), 0, second);
first = Polynomial.insert(DalthY[0], 0, first);
third = Polynomial.insert((3 * Dalth3Y) / 6, 0, third);
third = Polynomial.multi(p2, third);
temp = Polynomial.insert(-1 * (Dalth3Y), 0, temp);
temp = Polynomial.multi(temp, p);
third = Polynomial.add(third, temp);
temp1 = Polynomial.insert((2 * Dalth3Y) / 6, 0, temp1);
third = Polynomial.add(third, temp1);
third = Polynomial.add(third, first);
third = Polynomial.add(third, second);
temp2 = Polynomial.insert((1 / h), 0, temp2);
third = Polynomial.multi(third, temp2);
return(third);
}