// Modified Newton's method with LU decomposition
public double[] ModifiedMethod()
{
Console.Out.Write("Модифицированный метод Ньютона :" + "\n");
sw.Start();
x.InitX();
iter = 0;
numOfOperations = 0;
//J = new SquareMatrix(InitializationExtension.InitJ(x),size);
J = new SquareMatrix(InitializationExtension.InitializationJ(x), size);
J.LUDecomposition();
numOfOperations += J.numOfOperations;
//J.Reverse();
while (true)
{
iter++;
norm = 0;
//F.InitF(x);
F1.InitializationF(x);
for (int i = 0; i < size; i++)
{
F[0, i] = F1[i];
}
var a = J.SolutionSystem(F1);
for (int i = 0; i < size; i++)
{
currentX[i] = a[0, i];
}
for (int i = 0; i < size; i++)
{
xk1[i] = x[i] - currentX[i];
//norm += (xk1[i] - x[i]) * (xk1[i] - x[i]);
if (Math.Abs(xk1[i] - x[i]) > norm)
{
norm = Math.Abs(xk1[i] - x[i]);
}
x[i] = xk1[i];
numOfOperations += 5;
}
if (norm < eps)
{
break;
}
}
sw.Stop();
Console.Out.Write("Количество итераций :" + iter + "\n");
Console.Out.Write("Число арифметических операций :" + numOfOperations + "\n");
Console.Out.Write("Затраченное время :" + sw.Elapsed + "\n");
return(xk1);
}
// Newton's method through the search of inverse matrix
public double[] Method()
{
Console.Out.Write("Метод Ньютона с поиском обратной матрицы :" + "\n");
sw.Start();
x.InitX();
iter = 0;
numOfOperations = 0;
while (true)
{
iter++;
// initialize function F and Jacoby's matrix
F1.InitializationF(x);
for (int i = 0; i < size; i++)
{
F[0, i] = F1[i];
}
norm = 0;
J = new SquareMatrix(InitializationExtension.InitializationJ(x), size);
// make LU decomposition
J.LUDecomposition();
numOfOperations += J.numOfOperations;
currentX = SquareMatrix.multiplyVec(J.reverseMatrix, F1, size);
for (int i = 0; i < size; i++)
{
xk1[i] = x[i] - currentX[i];
//norm += (xk1[i] - x[i]) * (xk1[i] - x[i]);
if (Math.Abs(xk1[i] - x[i]) > norm)
{
norm = Math.Abs(xk1[i] - x[i]);
}
x[i] = xk1[i];
numOfOperations += 5;
}
if (norm < eps)
{
break;
}
}
sw.Stop();
Console.Out.Write("Количество итераций :" + iter + "\n");
Console.Out.Write("Число арифметических операций :" + numOfOperations + "\n");
Console.Out.Write("Затраченное время :" + sw.Elapsed + "\n");
return(xk1);
}
// method with recounting reverse matrix every k iterations
public double[] MethodWithRewriteRevMat()
{
int step = 7;
Console.Out.Write("Поиск обратной матрицы каждые k = " + step + " итераций :" + "\n");
x.InitX();
//J = new SquareMatrix(InitializationExtension.InitJ(x),size);
J = new SquareMatrix(InitializationExtension.InitializationJ(x), size);
J.LUDecomposition();
numOfOperations += J.numOfOperations;
iter = 0;
numOfOperations = 0;
sw.Start();
while (true)
{
iter++;
norm = 0;
F1.InitializationF(x);
for (int i = 0; i < size; i++)
{
F[0, i] = F1[i];
}
if (iter % step == 1)
{
//J = new SquareMatrix(InitializationExtension.InitJ(x),size);
J = new SquareMatrix(InitializationExtension.InitializationJ(x), size);
J.LUDecomposition();
numOfOperations += J.numOfOperations;
J.Reverse();
}
var a = J.SolutionSystem(F1);
for (int i = 0; i < size; i++)
{
currentX[i] = a[0, i];
}
for (int i = 0; i < size; i++)
{
xk1[i] = x[i] - currentX[i];
//norm += (xk1[i] - x[i]) * (xk1[i] - x[i]);
if (Math.Abs(xk1[i] - x[i]) > norm)
{
norm = Math.Abs(xk1[i] - x[i]);
}
x[i] = xk1[i];
numOfOperations += 5;
}
if (norm < eps)
{
break;
}
}
sw.Stop();
Console.Out.Write("Количество итераций :" + iter + "\n");
Console.Out.Write("Число арифметических операций :" + numOfOperations + "\n");
Console.Out.Write("Затраченное время :" + sw.Elapsed + "\n");
return(xk1);
}
// Method with transition to modified
public double[] TransitionToModMeth()
{
Console.Out.Write("Переход от обычного метода Ньютона к модифицированному :" + "\n");
int step = 8;
Console.WriteLine("Шаг k = " + step);
x.InitX();
double[] xFix = new double[size];
xFix.InitX();
double[] x0 = new double[size];
x0.InitX();
iter = 0;
numOfOperations = 0;
sw.Start();
while (true)
{
iter++;
norm = 0;
F1.InitializationF(x);
for (int i = 0; i < size; i++)
{
F[0, i] = F1[i];
}
if (step > 0)
{
J = new SquareMatrix(InitializationExtension.InitializationJ(x), size);
J.LUDecomposition();
numOfOperations += J.numOfOperations;
for (int i = 0; i < size; i++)
{
xFix[i] = x[i];
}
//J.Reverse();
currentX = SquareMatrix.multiplyVec(J.reverseMatrix, F1, size);
step--;
}
else
{
if (step == 0)
{
J = new SquareMatrix(InitializationExtension.InitializationJ(xFix), size);
J.LUDecomposition();
}
numOfOperations += J.numOfOperations;
//currentX = J.SolutionSystem(F);
currentX = SquareMatrix.multiplyVec(J.reverseMatrix, F1, size);
step--;
}
for (int i = 0; i < size; i++)
{
xk1[i] = x[i] - currentX[i];
if (Math.Abs(xk1[i] - x[i]) > norm)
{
norm = Math.Abs(xk1[i] - x[i]);
}
x[i] = xk1[i];
numOfOperations += 5;
}
if (norm < eps)
{
break;
}
}
sw.Stop();
Console.Out.Write("Количество итераций :" + iter + "\n");
Console.Out.Write("Число арифметических операций :" + numOfOperations + "\n");
Console.Out.Write("Затраченное время :" + sw.Elapsed + "\n");
return(xk1);
}