Matlab牛顿迭代法求方程的根（GUI）

牛顿迭代法的具体内容不赘述
它的核心算法是：

k = 1;
x = x0;
x0 = x + e*2; % 为了让初启动时满足循环条件
while (abs(x-x0))>e && (k<=N)  % 同时限定误差和最大循环次数x0 = x;x = x0 - f(x0)/df(x0);  % 牛顿迭代法式子k = k+1;
end

这是一个非常简单的牛顿法实现，根据上学期学的数值分析和这学期上的Matlab，把它用GUI简单包装了一下。

用户输入函数表达式、初值、最大容许误差、最大循环次数之后，就可以计算根。代码实现如下。

function varargout = Newton_TEST(varargin)% NEWTON_TEST MATLAB code for Newton_TEST.fig%      NEWTON_TEST, by itself, creates a new NEWTON_TEST or raises the existing%      singleton*.%%      H = NEWTON_TEST returns the handle to a new NEWTON_TEST or the handle to%      the existing singleton*.%%      NEWTON_TEST('CALLBACK',hObject,eventData,handles,...) calls the local%      function named CALLBACK in NEWTON_TEST.M with the given input arguments.%%      NEWTON_TEST('Property','Value',...) creates a new NEWTON_TEST or raises the%      existing singleton*.  Starting from the left, property value pairs are%      applied to the GUI before Newton_TEST_OpeningFcn gets called.  An%      unrecognized property name or invalid value makes property application%      stop.  All inputs are passed to Newton_TEST_OpeningFcn via varargin.%%      *See GUI Options on GUIDE's Tools menu.  Choose "GUI allows only one%      instance to run (singleton)".%% See also: GUIDE, GUIDATA, GUIHANDLES% Edit the above text to modify the response to help Newton_TEST% Last Modified by GUIDE v2.5 12-Mar-2020 23:03:08% Begin initialization code - DO NOT EDITgui_Singleton = 1;gui_State = struct('gui_Name',       mfilename, ...'gui_Singleton',  gui_Singleton, ...'gui_OpeningFcn', @Newton_TEST_OpeningFcn, ...'gui_OutputFcn',  @Newton_TEST_OutputFcn, ...'gui_LayoutFcn',  [] , ...'gui_Callback',   []);if nargin && ischar(varargin{1})gui_State.gui_Callback = str2func(varargin{1});endif nargout[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});elsegui_mainfcn(gui_State, varargin{:});end% End initialization code - DO NOT EDIT% --- Executes just before Newton_TEST is made visible.function Newton_TEST_OpeningFcn(hObject, eventdata, handles, varargin)% This function has no output args, see OutputFcn.% hObject    handle to figure% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)% varargin   command line arguments to Newton_TEST (see VARARGIN)handles.FUN = [];handles.X0 = [];% Choose default command line output for Newton_TESThandles.output = hObject;% Update handles structureguidata(hObject, handles);% UIWAIT makes Newton_TEST wait for user response (see UIRESUME)% uiwait(handles.figure1);% --- Outputs from this function are returned to the command line.function varargout = Newton_TEST_OutputFcn(hObject, eventdata, handles)% varargout  cell array for returning output args (see VARARGOUT);% hObject    handle to figure% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)% Get default command line output from handles structurevarargout{1} = handles.output;function editFUN_Callback(hObject, eventdata, handles)% hObject    handle to editFUN (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)% Hints: get(hObject,'String') returns contents of editFUN as text%        str2double(get(hObject,'String')) returns contents of editFUN as a doublehandles.FUN = get(hObject,'String');guidata(hObject, handles);% --- Executes during object creation, after setting all properties.function editFUN_CreateFcn(hObject, eventdata, handles)% hObject    handle to editFUN (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    empty - handles not created until after all CreateFcns called% Hint: edit controls usually have a white background on Windows.%       See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction editX0_Callback(hObject, eventdata, handles)% hObject    handle to editX0 (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)% Hints: get(hObject,'String') returns contents of editX0 as text%        str2double(get(hObject,'String')) returns contents of editX0 as a doublehandles.X0 = str2num(get(hObject,'String'));guidata(hObject, handles);% --- Executes during object creation, after setting all properties.function editX0_CreateFcn(hObject, eventdata, handles)% hObject    handle to editX0 (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    empty - handles not created until after all CreateFcns called% Hint: edit controls usually have a white background on Windows.%       See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction editError_Callback(hObject, eventdata, handles)% hObject    handle to editError (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)% Hints: get(hObject,'String') returns contents of editError as text%        str2double(get(hObject,'String')) returns contents of editError as a doublehandles.ERROR = str2num(get(hObject,'String'));guidata(hObject, handles);% --- Executes during object creation, after setting all properties.function editError_CreateFcn(hObject, eventdata, handles)% hObject    handle to editError (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    empty - handles not created until after all CreateFcns called% Hint: edit controls usually have a white background on Windows.%       See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction editN_Callback(hObject, eventdata, handles)% hObject    handle to editN (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)% Hints: get(hObject,'String') returns contents of editN as text%        str2double(get(hObject,'String')) returns contents of editN as a doublehandles.N = str2num(get(hObject,'String'));guidata(hObject, handles);% --- Executes during object creation, after setting all properties.function editN_CreateFcn(hObject, eventdata, handles)% hObject    handle to editN (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    empty - handles not created until after all CreateFcns called% Hint: edit controls usually have a white background on Windows.%       See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');end% --- Executes on selection change in listboxK.function listboxK_Callback(hObject, eventdata, handles)% hObject    handle to listboxK (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)% Hints: contents = cellstr(get(hObject,'String')) returns listboxK contents as cell array%        contents{get(hObject,'Value')} returns selected item from listboxK% --- Executes during object creation, after setting all properties.function listboxK_CreateFcn(hObject, eventdata, handles)% hObject    handle to listboxK (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    empty - handles not created until after all CreateFcns called% Hint: listbox controls usually have a white background on Windows.%       See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');end% --- Executes on selection change in listboxX.function listboxX_Callback(hObject, eventdata, handles)% hObject    handle to listboxX (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)% Hints: contents = cellstr(get(hObject,'String')) returns listboxX contents as cell array%        contents{get(hObject,'Value')} returns selected item from listboxX% --- Executes during object creation, after setting all properties.function listboxX_CreateFcn(hObject, eventdata, handles)% hObject    handle to listboxX (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    empty - handles not created until after all CreateFcns called% Hint: listbox controls usually have a white background on Windows.%       See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');end% --- Executes on button press in pushbuttonRUN.function pushbuttonRUN_Callback(hObject, eventdata, handles)% hObject    handle to pushbuttonRUN (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)claf = handles.FUN;x0 = handles.X0;N = handles.N;e = handles.ERROR;f = eval(['@(x)',f]); % 将用户输入的str类型转化为有意义的匿名函数df = eval(['@(x)',char(diff(sym(f)))]); % 计算微分node = line(x0,f(x0),'Marker','o','MarkerSize',8,'MarkerFaceColor','r','MarkerEdgeColor','r');connectline = line(x0,f(x0),'linewidth',1,'color','b'); %用来画连接的线k = 1;x = x0;x0 = x+e*2;K = [];X = [];xcon = x0;ycon = f(x0);while (abs(x-x0))>e && (k<=N)x0 = x;x = x0 - f(x0)/df(x0);xcon = [xcon,x];  % 用将新的x值同旧值连接ycon = [ycon,f(x)];K = [{num2str(k)};K];X = [{num2str(x)};X];% 将循环结果呈现在界面set(handles.listboxK,'string',K);set(handles.listboxX,'string',X);set(node,'xdata',x,'ydata',f(x));set(connectline,'xdata',xcon,'ydata',ycon);pause(0.5)  % 为了能让人眼看到过程，用pause暂停0.5sk = k+1;endhold onxline = sort(xcon);[xx,yy] = fplot(f,[min(xline),max(xline)]);  %画出模拟曲线plot(xx,yy,'--k');

用一个的高次方程举例是这样