ku2021_mech457_hw1_q8_approximation.m

clc, clear, close('all')

%% PLOT
x = -4:0.1:8;
plot(x, ku2021_mech457_hw1_q8_f(x))
xlabel('x'); ylabel('y');
title('f(x) = -0.6*x^2 + 2.4*x + 5.5');
hold on, plot([x(1), x(end)], [0,0], 'k')
clear x

%% LEFT root; -4 <= \alpha < 2
fprintf('Find LEFT root:\n');
x_l = -4;
x_r = 2;
for j=1:6
    x = x_l:0.1^j:x_r;
    for i=1:length(x)
        if(ku2021_mech457_hw1_q8_f(x(i)) * ku2021_mech457_hw1_q8_f(x(i+1)) <0)
            x_l = x(i);
            x_r = x(i+1);
            fprintf('x_l#%d=%f\tf(x_l)=%f\tx_r#%d=%f\tf(x_l)=%f\n',j,x_l,q8_f(x_l),j,x_r,ku2021_mech457_hw1_q8_f(x_r));
            clear x
            break
        end
    end
end

%% RIGHT root; 2 < \beta <= 8
fprintf('Find RIGHT root:\n');
x_l = 2;
x_r = 8;
for j=1:6
    x = x_l:0.1^j:x_r;
    for i=1:length(x)
        if(ku2021_mech457_hw1_q8_f(x(i)) * ku2021_mech457_hw1_q8_f(x(i+1)) <0)
            x_l = x(i);
            x_r = x(i+1);
            fprintf('x_l#%d=%f\tf(x_l)=%f\tx_r#%d=%f\tf(x_l)=%f\n',j,x_l,q8_f(x_l),j,x_r,ku2021_mech457_hw1_q8_f(x_r));
            clear x
            break
        end
    end
end

ku2021_mech457_hw1_q8_bisection.m

clc, clear, close('all')
x_l = 5;
x_u = 10;
x_TRUE = (12+sqrt(474))/6;

x = [x_l x_u];
y = ku2021_mech457_hw1_q8_f(x);

i = 0;
err_apprx = 1000;
while i<=3
    i = i+1;
    fprintf('[iteration #%d] ',i);
    
    xnew(i) = mean(x);
    ynew = ku2021_mech457_hw1_q8_f(xnew(i));
    
    if y(1)*ynew > 0
        x = [xnew(i), x(2)];
        y = ku2021_mech457_hw1_q8_f(x);       
    elseif y(1)*ynew < 0
        x = [x(1), xnew(i)];
        y = ku2021_mech457_hw1_q8_f(x);
    else
        fprintf('the solution is %f\n', xnew(i));
        break
    end
    
    if i > 1
        err_apprx = 100*abs((xnew(i) - xnew(i-1))/xnew(i));
        err_true = abs(mean(x) - x_TRUE);
        fprintf('x=[%f,%f]\tepsilon_a=%f\tepsilon_t=%f ', x(1), x(2), err_apprx, err_true);
    end
    
    fprintf('\n');
end
fprintf('solution = %f\n', xnew(end));
clear x y xnew i e

ku2021_mech457_hw1_q8_f.m

function y = ku2021_mech457_hw1_q8_f(x)

y = -0.6*x.^2 + 2.4*x + 5.5;