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 EDIT
gui_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});
end

if nargout
    [varargout{
     1:nargout}] = gui_mainfcn(gui_State, varargin{
     :});
else
    gui_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_TEST
handles.output = hObject;

% Update handles structure
guidata(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 structure
varargout{
     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 double
handles.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');
end



function 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 double
handles.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');
end

function 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 double
handles.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');
end

function 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 double
handles.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)
cla
f = 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0.5s
    
    k = k+1; 
end

hold on
xline = 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

纯纯纯纯小白，发上来是希望可以互相交流，以及督促自己继续联系其他的数值方法。