用matlab做一个app 2、功能包括：二分法求根、不动点迭代求根、牛顿法求根、fsolve求根 3、求以下方程的全部根 x^2-e^x=0

好的，以下是一个简单的 MATLAB App Designer 程序，可以实现二分法求根、不动点迭代求根、牛顿法求根和 fsolve 求根。程序包括以下部分：

1. 一个输入框，用于输入方程参数。
2. 一个下拉菜单，用于选择求根方法。
3. 一个输入框，用于输入初始值（仅在不动点迭代和牛顿法中需要）。
4. 一个按钮，用于计算结果。
5. 一个输出框，用于显示结果。

以下是程序代码：

classdef RootFindingApp < matlab.apps.AppBase

    % Properties that correspond to app components
    properties (Access = public)
        UIFigure       matlab.ui.Figure
        EquationLabel  matlab.ui.control.Label
        EquationEdit   matlab.ui.control.EditField
        MethodLabel    matlab.ui.control.Label
        MethodDropDown matlab.ui.control.DropDown
        InitialLabel   matlab.ui.control.Label
        InitialEdit    matlab.ui.control.NumericEditField
        ComputeButton  matlab.ui.control.Button
        ResultLabel    matlab.ui.control.Label
        ResultEdit     matlab.ui.control.EditField
    end

    % Callbacks that handle component events
    methods (Access = private)

        % Callback function for ComputeButton
        function ComputeButtonPushed(app, event)
            % Get equation and initial value
            eqn = @(x) x^2 - exp(x);
            x0 = app.InitialEdit.Value;
            
            % Compute root using selected method
            method = app.MethodDropDown.Value;
            switch method
                case 'Bisection'
                    [x, ~] = bisection(eqn, 0, 2, 1e-6);
                case 'Fixed-Point Iteration'
                    [x, ~] = fixedpoint(eqn, x0, 1e-6, 50);
                case 'Newton-Raphson'
                    [x, ~] = newtonraphson(eqn, x0, 1e-6, 50);
                case 'fsolve'
                    x = fsolve(eqn, x0);
            end
            
            % Display result
            app.ResultEdit.Value = num2str(x);
        end
    end

    % App initialization and construction
    methods (Access = private)

        % Create UIFigure and components
        function createComponents(app)
            % Create UIFigure
            app.UIFigure = uifigure;
            app.UIFigure.Position = [100 100 640 480];
            app.UIFigure.Name = 'Root-Finding App';

            % Create EquationLabel
            app.EquationLabel = uilabel(app.UIFigure);
            app.EquationLabel.HorizontalAlignment = 'right';
            app.EquationLabel.Position = [80 416 49 22];
            app.EquationLabel.Text = 'Equation';

            % Create EquationEdit
            app.EquationEdit = uieditfield(app.UIFigure, 'text');
            app.EquationEdit.Position = [138 416 407 22];
            app.EquationEdit.Value = 'x^2 - exp(x)';

            % Create MethodLabel
            app.MethodLabel = uilabel(app.UIFigure);
            app.MethodLabel.HorizontalAlignment = 'right';
            app.MethodLabel.Position = [80 372 49 22];
            app.MethodLabel.Text = 'Method';

            % Create MethodDropDown
            app.MethodDropDown = uidropdown(app.UIFigure);
            app.MethodDropDown.Items = {'Bisection', 'Fixed-Point Iteration', 'Newton-Raphson', 'fsolve'};
            app.MethodDropDown.Position = [138 372 407 22];
            app.MethodDropDown.Value = 'Bisection';

            % Create InitialLabel
            app.InitialLabel = uilabel(app.UIFigure);
            app.InitialLabel.HorizontalAlignment = 'right';
            app.InitialLabel.Position = [80 328 49 22];
            app.InitialLabel.Text = 'Initial';

            % Create InitialEdit
            app.InitialEdit = uieditfield(app.UIFigure, 'numeric');
            app.InitialEdit.Position = [138 328 100 22];
            app.InitialEdit.Value = 1;

            % Create ComputeButton
            app.ComputeButton = uibutton(app.UIFigure, 'push');
            app.ComputeButton.ButtonPushedFcn = createCallbackFcn(app, @ComputeButtonPushed, true);
            app.ComputeButton.Position = [367 328 100 22];
            app.ComputeButton.Text = 'Compute';

            % Create ResultLabel
            app.ResultLabel = uilabel(app.UIFigure);
            app.ResultLabel.HorizontalAlignment = 'right';
            app.ResultLabel.Position = [80 284 49 22];
            app.ResultLabel.Text = 'Result';

            % Create ResultEdit
            app.ResultEdit = uieditfield(app.UIFigure, 'text');
            app.ResultEdit.Position = [138 284 407 22];
            app.ResultEdit.Value = '';
        end
    end

    % App creation and deletion
    methods (Access = public)

        % Construct app
        function app = RootFindingApp

            % Create UIFigure and components
            createComponents(app)

            % Register the app with App Designer
            registerApp(app, app.UIFigure)

            % Execute the startup function
            runStartupFcn(app, @startupFcn)

            if nargout == 0
                clear app
            end
        end

        % Code that executes before app deletion
        function delete(app)

            % Delete UIFigure when app is deleted
            delete(app.UIFigure)
        end
    end
end

% Bisection method for root-finding
function [x, n] = bisection(f, a, b, tol)
    fa = f(a);
    fb = f(b);
    if sign(fa) == sign(fb)
        error('f(a) and f(b) have the same sign')
    end
    n = ceil(log2((b-a)/tol));
    for k = 1:n
        c = (a + b)/2;
        fc = f(c);
        if sign(fc) == sign(fa)
            a = c;
            fa = fc;
        else
            b = c;
            fb = fc;
        end
    end
    x = (a + b)/2;
end

% Fixed-point iteration for root-finding
function [x, n] = fixedpoint(g, x0, tol, maxiter)
    x = x0;
    for n = 1:maxiter
        xprev = x;
        x = g(xprev);
        if abs(x - xprev) < tol
            break
        end
    end
    if n == maxiter
        warning('Fixed-point iteration did not converge')
    end
end

% Newton-Raphson method for root-finding
function [x, n] = newtonraphson(f, x0, tol, maxiter)
    df = matlabFunction(diff(sym(f)));
    x = x0;
    for n = 1:maxiter
        fx = f(x);
        dfx = df(x);
        xprev = x;
        x = xprev - fx/dfx;
        if abs(x - xprev) < tol
            break
        end
    end
    if n == maxiter
        warning('Newton-Raphson method did not converge')
    end
end

在 MATLAB 中运行该程序，然后输入方程 `x^2 - exp(x) = 0`，选择求根方法为 `Bisection`、`Fixed-Point Iteration`、`Newton-Raphson` 或 `fsolve` 中的一个，点击 `Compute` 按钮即可计算结果。