I am getting the error , Unable to perform assignment because the indices on the left side are not compatible with the size of the right side trying to compute the bisection m

for method_number = 1 : 3
    fprintf("---\nmethod %d\n",method_number);
    tol = 10^-9;
    epsilon = 10^4;
    steps = 1;
    
    %% If we get in an infinite loop we'll break out of it
    %% break_flag = 0 indicates the default state
    %% break_flag = 1 indicates a break
    break_flag = 0;
    
    %% We'll use X to store the current and new value of x
    %% at each step.
    clear X;  
    
    x1 = 3.65:0.002:3.75;   %% set the seed point = starting x value.
    fprintf("{0, %.8f},\n",x1)
    while epsilon > tol
        x0 = x1;    %% replace x0 with x1
        x1 = method(x0,method_number); %% compute the new value of x = g(x0)
        X(steps,1) = x0; %% At each step store x0 and x1 in matrix X
        X(steps,2) = x1;
        fprintf("{%d, %.8f},\n",steps,x1)
        epsilon = abs(x1-x0); 
        steps = steps + 1;
        %% If we're in an infinite loop or the solution is diverging
        %% let's break out if it.
        if steps > 200000 || epsilon == inf
            break_flag = 1;
            break 
        end
    end
    %% Now let's plot all of the data from our iterations
    subplot(2,2,method_number)
    plot(X(:,1),X(:,2));    %% plot all the data with lines
    hold on
    scatter(X(:,1),X(:,2)); %%replot all the data with dots
    scatter(X(1,1),X(1,2),75,'g','d','filled','MarkerEdgeColor','b'); %% the starting point
    scatter(X(end,1),X(end,2),75,'r','d','filled','MarkerEdgeColor','b'); %% the end point
    if break_flag   %% a different plot heading for divergent and convergent results 
        heading = sprintf('method %d: the method did not converge after %d steps',method_number,steps-1);
    else
        heading = sprintf('method %d: after %d steps, x = %.12f',method_number,steps-1,x1);
    end
    title(heading);
end

function ans = method(x,number)
    switch number
        case 1 %%%%%  Method 1 (Example 8: x = x^2 + x - 2)
            ans = exp(-x/10)-cos(x) + x; %x^2+x-2;
        case 2 %%%%%  Method 2 (Example 9: x = (x^2 - 5x - 2)/(-5))
            k = -0.867%% try different values of k
            ans = (-1/k)*(exp(-x/10)-cos(x)-k*x);
        case 3 %%%%%  Method 3 Newton's (Example 11: f(x)=x^2-2, f'(x)=2x, x=x-f/f')
            ans = x -(exp(-x/10)-cos(x))/((exp(-x/10)*(-1/10))+sin(x));
    end
end

Answer 1

[KSSV]

You are trying to save more number of elements than the matrix is initilaized. Your LHS is a scalar and RHS is a vector, so error pops out. Check the modififed code below:

function Test()
for method_number = 1 : 3
    fprintf("---\nmethod %d\n",method_number);
    tol = 10^-9;
    epsilon = 10^4;
    steps = 1;
    
    %% If we get in an infinite loop we'll break out of it
    %% break_flag = 0 indicates the default state
    %% break_flag = 1 indicates a break
    break_flag = 0;
    
    %% We'll use X to store the current and new value of x
    %% at each step.
    clear X;
    
    x1 = 3.65:0.002:3.75;   %% set the seed point = starting x value.
    fprintf("{0, %.8f},\n",x1)
    X = zeros([],length(x1)) ; 
    Y = zeros([],length(x1)) ; 
    while epsilon > tol
        x0 = x1;    %% replace x0 with x1
        x1 = method(x0,method_number); %% compute the new value of x = g(x0)
        X(steps,:) = x0; %% At each step store x0 and x1 in matrix X
        Y(steps,:) = x1;
        fprintf("{%d, %.8f},\n",steps,x1)
        epsilon = abs(x1-x0);
        steps = steps + 1;
        %% If we're in an infinite loop or the solution is diverging
        %% let's break out if it.
        if ((steps > 200000) | (epsilon == inf))
            break_flag = 1;
            break
        end
    end
    %% Now let's plot all of the data from our iterations
    subplot(2,2,method_number)
    plot(X,Y);    %% plot all the data with lines
    hold on
    scatter(X(:),Y(:)); %%replot all the data with dots
    scatter(X(1),Y(1),75,'g','d','filled','MarkerEdgeColor','b'); %% the starting point
    scatter(X(end),Y(end),75,'r','d','filled','MarkerEdgeColor','b'); %% the end point
    if break_flag   %% a different plot heading for divergent and convergent results
        heading = sprintf('method %d: the method did not converge after %d steps',method_number,steps-1);
    else
        heading = sprintf('method %d: after %d steps, x = %.12f',method_number,steps-1,x1);
    end
    title(heading);
end
end
function ans = method(x,number)
switch number
    case 1 %%%%%  Method 1 (Example 8: x = x^2 + x - 2)
        ans = exp(-x/10)-cos(x) + x; %x^2+x-2;
    case 2 %%%%%  Method 2 (Example 9: x = (x^2 - 5x - 2)/(-5))
        k = -0.867%% try different values of k
        ans = (-1/k)*(exp(-x/10)-cos(x)-k*x);
    case 3 %%%%%  Method 3 Newton's (Example 11: f(x)=x^2-2, f'(x)=2x, x=x-f/f')
        ans = x -(exp(-x/10)-cos(x))/((exp(-x/10)*(-1/10))+sin(x));
end
end