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rehomework2.zip （3个子文件）

HW2.zip 3KB

HW1_OUTPUTFILE.pdf 316KB

HW2_OUTPUT_FILE.pdf 453KB

FUNCTION

F= x.^3-x-2; …..Function which I implemented in matlab

MATLAB CODE

clc

close all

clear all

syms x % symbol representation

a=input('Initial value of a: '); % enter value of 'a'

b=input('Initial value of b: '); % enter value of 'b'

tolerance=input('Enter tolarence value: '); % enter Tollarance value'

[X1,X2,c,F_c,err1,t_bisection]=Bisection(a,b,tolerance); % Bisection method

[Xin,F,F_d,err,t_NRmethod]=NRmethod(a,tolerance); % NR method

%% Bi-Section Method -------Output variable display----------------------------

-------------------------------

fprintf('\n %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% BI-

SECTION METHOD RESULTS

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\n');

fprintf('-----------------------------------------------------------------------

--------------------------------------------\n');

fprintf('\n Iteration\t| a | b | c

| F(c) | Tolerance | \n');

fprintf('-----------------------------------------------------------------------

----------------------------------------------\n');

for j=1:length(F_c);

fprintf('%5d \t|\t%5f \t|\t%5f\t\t|\t%5f \t|\t%5f \t|\t%5f \t|\n',j,X1(j),X

2(j),c(j),F_c(j),err1(j));

end

format long;

fprintf('-----------------------------------------------------------------------

----------------------------------------------\n');

fprintf('time elapsed in milliseconds:\tt = %-10f\n',t_bisection*10^3);

%% NR Method results----- Output variable display----------------------------

----------------------------

fprintf('\n %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% NR METHOD RESULTS

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \n');

fprintf('\n --------------------------------------------------------------------

-----------------------\n');

fprintf('\n Iteration\t| Value of x | function F(x) | F_d(x)

| Tolerance | \n');

fprintf('-----------------------------------------------------------------------

----------------------\n');

for i=1:length(F);

),err(i));

end

format long;

fprintf('-----------------------------------------------------------------------

----------------------\n');

fprintf('time elapsed in milliseconds:\tt = %-10f\n',t_NRmethod*10^3);

%% Analysis Part in terms of plots

figure(1)

y=0.7:0.001:2.2;

z= y.^3-y-2;

subplot (2,2,1)

plot(y,z);

xlabel('Range of x');

ylabel('Function-F');

grid on

title('Original function w.r.t x')

subplot (2,2,2)

plot(err1,'-o');

xlabel('Number of Iteration');

ylabel('Tolerance');

grid on

hold on

plot(err,'-or');

title('Comparistion between 2 methods in terms of Tolerance Vs Iterataion')

legend('Bi-section method','NR method')

subplot (2,2,3)

plot(y,z,Xin,err,'-or',X1,err1,'-o');

legend('Orginal Curve','NR method', 'Bi-section method')

xlabel('x value');

ylabel('Tolerance');

grid on

title('Comparistion between 2 methods interms of Tolerance Vs "x" is super

imposed in original curve')

subplot (2,2,4)

for j=1:length(F_c);

s(j)=j+1;

end

z=[err1;X1;X2];

surf(z)

grid on

xlabel('Iteration');

ylabel('a-value');

zlabel('b-value');

title('3-D plot for understanding about BI-SECTION method')

figure(2)

z=[F;Xin;err];

surf(z)

grid on

xlabel('Function Value');

ylabel('Xinput');

zlabel('Tolerance');

title('3-D plot for understanding about NR method')

Function files which required for running above code

NR Method:

function [Xin,F,F_d,err,t_NRmethod]=NRmethod(a,tolerance)

%% initialization part

syms x % symbol representation

tic;

b0=a;

x0=b0;

for i=1:1/eps

syms f1 f2 x

f1= x.^3-x-2;

f2=diff(x.^3-x-2);

x=x0;

F(i)= eval(f1);

act=F(i);

F_d(i)=eval(f2);

dif=F_d(i);

Xin(i)=x;

Xn(i)=x-(act./dif);

X=Xn(i);

x0=X;

err(i)=abs(Xn(i)-x);

if (err(i) < tolerance), break; end

end

t_NRmethod=toc;

end

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