TU Wien:Computernumerik VU (Schranz-Kirlinger)/Übungen SS16/Beispiel 23

Lösung

Matlab Code

function Bsp3

bisektion(0.1, 1.9, 0.000001);
sekanten(0.1, 1.9, 0.000001);
end

function [error] = bisektion(la, rb, eps)

error = [];

while(abs(f(rb) - f(la)) >= eps)
    %error = cat(1, error, f(rb) - f(la));
    fprintf('%.15f\n', f(rb) - f(la));
    
    m = abs((rb - la)/2);
    
    if(sign(f(la)) ~= sign(f(rb - m)))
        rb = rb - m;
        error = cat(1, error, rb);
    elseif (sign(f(la + m)) ~= sign(f(rb)))
        la = la + m;
        error = cat(1, error, la);
    else
        break;
    end
end

fprintf('%.5f %.5f %.5f\n', la, rb, f(rb) - f(la));

end

function [error] = sekanten(x0, x1, eps)

xn = 0;
error = [];
while(1)
    xn = x1 - ((x1 - x0)/(f(x1) - f(x0))) * f(x1);
    fprintf('%.10f', xn);
    if(abs(f(xn)) <= eps)
        break;
    end
    error = cat(1, error, xn);
    x0 = x1;
    x1 = xn;
end

disp(xn);
end

function [fn] = f(x)

fn = x^3 - 3 * x^2 + 2 * x;
end