ИДЗ-1

ИДЗ 1, вариант 32

Код программы

Newton([5.80; 9.20], [7 2 5 -765; 4 5 2 -576]);

function Newton(X0, Coef)

M = 10;

Xnext = X0;

delta = 1;

eps = 0.001;

m = 0;

while (delta > eps) && (m < M)

X = Xnext;

F = SystEqu(X, Coef);

dF = diffEqu(X, Coef);

Xnext = X - inv(dF) * F;

delta = (Xnext - X)' * (Xnext - X);

m = m + 1;

end

fprintf('x1=%6.4f; x2=%6.4f; delta=%6.4f\n', Xnext(1), Xnext(2), delta);

end

function [F] = SystEqu(X, Coef)

F(1, 1) = Coef(1, 1) * X(1, 1)^2 + Coef(1, 2) * X(1, 1) * X(2, 1) + Coef(1, 3) * X(2, 1)^2 + Coef(1, 4);

F(2, 1) = Coef(2, 1) * X(1, 1)^2 + Coef(2, 2) * X(1, 1) * X(2, 1) + Coef(2, 3) * X(2, 1)^2 + Coef(2, 4);

end

function [dF] = diffEqu(X, Coef)

dF(1, 1) = 2 * Coef(1, 1) * X(1, 1) + Coef(1, 2) * X(2, 1);

dF(1, 2) = 2 * Coef(1, 3) * X(2, 1) + Coef(1, 2) * X(1, 1);

dF(2, 1) = 2 * Coef(2, 1) * X(1, 1) + Coef(2, 2) * X(2, 1);

dF(2, 2) = 2 * Coef(2, 3) * X(2, 1) + Coef(2, 2) * X(1, 1);

end

Дано:

Результат: .