public HalfDeviation(double a, double b, Func <double, double> f)
{
Console.WriteLine("\n\n\nМетод деления пополам: ");
var iterationNumber = Math.Ceiling(Math.Log((3 - 2) / Math.Pow(10, -5), 2) - 1);
Console.WriteLine($"Итераций: {iterationNumber}");
PrintTable.PrintRow("n", "an", "xn", "bn", "f(an)", "f(xn)", "f(bn)");
double x = (a + b) / 2;
double fa = 0, fx = 0, fb = 0;
do
{
fa = f(a);
fx = f(x);
fb = f(b);
PrintTable.PrintRow(iterationNumber, a, x, b, fa, fx, fb);
if (fx == 0)
{
break;
}
a = SameSign(fa, fx) ? x : a;
b = SameSign(fb, fx) ? x : b;
x = (a + b) / 2;
} while (iterationNumber-- > 0);
Console.WriteLine($"Х є околу: {x}");
}
public Newton(double a, double b, double eps, Func <double, Double> f, Func <double, double> f1, Func <double, double> f2)
{
Console.WriteLine("\n\n\nМетод Ньютона");
Console.WriteLine($"f'({a}) = {f1(a)}");
Console.WriteLine($"f'({b}) = {f1(b)}");
double m1 = Math.Min(f1(a), f1(b));
Console.WriteLine($"m1 = min{{f'({a}); f'({b})}} = {m1}");
Console.WriteLine();
Console.WriteLine($"f''({a}) = {f2(a)}");
Console.WriteLine($"f''({b}) = {f2(b)}");
double M2 = Math.Max(f2(a), f2(b));
Console.WriteLine($"M1 = max{{f''({a}); f''({b})}} = {M2}");
double delta = Math.Sqrt(2 * m1 * eps / M2);
Console.WriteLine($"Delta = {delta}");
var x = a;
if (f(x) * f2(x) <= 0)
{
x = b;
}
while (f(x) * f2(x) <= 0)
{
x -= eps;
}
PrintTable.PrintRow("n", "Xn", "|Xn-X(n-1)|", "|Xn-X(n-1)| < delta");
PrintTable.PrintRow(0, x, "-", "-");
double xPrev;
var i = 1;
do
{
xPrev = x;
x = xPrev - f(x) / f1(x);
PrintTable.PrintRow(i, x, Math.Abs(x - xPrev), Math.Abs(x - xPrev) < delta);
i++;
} while (Math.Abs(x - xPrev) >= delta);
Console.WriteLine($"Х є околу: {x}");
}
/// <summary>
/// Метод простой итерации
/// </summary>
/// <param name="a">Левая граница</param>
/// <param name="b">Правая граница</param>
/// <param name="f">Функция</param>
/// <param name="f1">Первая производная</param>
public SimpleIteration(double a, double b, double eps, Func <double, Double> f, Func <double, double> f1)
{
Console.WriteLine("\n\n\nМетод простой итерации");
// Переходим от заданого уравнения к уравнению удобному для итерирования: x = x - alpha*f(x)
var M1 = Math.Max(f1(a), f1(b));
var m1 = Math.Min(f1(a), f1(b));
if (f1(a) > f1(b))
{
M1 = f1(a);
m1 = f1(b);
Console.WriteLine($"M1 = f({a}) = {f1(a)}");
Console.WriteLine($"m1 = f({b}) = {f1(b)}");
}
else
{
M1 = f1(b);
m1 = f1(a);
Console.WriteLine($"M1 = f({b}) = {f1(b)}");
Console.WriteLine($"m1 = f({a}) = {f1(a)}");
}
var alpha = 2 / (M1 + m1);
Console.WriteLine($"Alpha = {alpha}");
double x = a;
double stopValue = Math.Abs(f(x)) / m1;
int i = 0;
PrintTable.PrintRow("n", "x", "|f(xn)|/m1", "epsilon", "Stop");
while (stopValue > eps)
{
PrintTable.PrintRow(i, x, Math.Abs(f(x)) / m1, eps, stopValue < eps);
x = x - alpha * f(x);
stopValue = Math.Abs(f(x)) / m1;
i++;
}
PrintTable.PrintRow(i, x, Math.Abs(f(x)) / m1, eps, stopValue < eps);
Console.WriteLine($"Х є околу: {x}");
}
public Chords(double a, double b, double eps, Func <double, Double> f, Func <double, double> f1, Func <double, double> f2)
{
Console.WriteLine("\n\n\nМетод хорд");
Console.WriteLine($"f'({a}) = {f1(a)}");
Console.WriteLine($"f'({b}) = {f1(b)}");
var M1 = Math.Max(f1(a), f1(b));
var m1 = Math.Min(f1(a), f1(b));
Console.WriteLine($"M1 = {M1}");
Console.WriteLine($"m1 = {m1}");
var gamma = m1 * eps / (M1 - m1);
Console.WriteLine($"Gamma = {gamma}");
var x = a;
// while (f(x) * f2(x) >= 0)
// {
x = x + eps;
// }
PrintTable.PrintRow("n", "Xn", "|Xn-X(n-1)|", "|Xn-X(n-1)| < gamma");
PrintTable.PrintRow(0, x, "-", "-");
double prevX;
int i = 1;
do
{
prevX = x;
x = prevX - f(prevX) * (3 - prevX) / (f(3) - f(prevX));
PrintTable.PrintRow(i, x, Math.Abs(x - prevX), Math.Abs(x - prevX) < gamma);
i++;
} while (Math.Abs(x - prevX) >= gamma);
Console.WriteLine($"Х є околу: {x}");
}
