Untitled

adityass

Jun 26th, 2024

150

Never

Add comment

Not a member of Pastebin yet? Sign Up, it unlocks many cool features!

MatLab 2.23 KB | None | 0 0

raw download clone embed print report

%% GAUSS elimination
A = input("Enter matrix") ;
B = input("Enter source vector");
N = length(B);
X = zeros(N,1);
Aug = [A B];
for j = 1:N-1
for i = j+1:N
m = Aug(i,j)/Aug(j,j);
Aug(i,:) = Aug(i,:) - m*Aug(j,:);
end
end
Aug
X(N) = Aug(N, N+1)/Aug(N,N) ;
for k = N-1:-1:1
X(k) = (Aug(k , N+1) - Aug(k, k+1:N)*X(k+1:N))/ Aug(k,k);
end
X
%% GAUSS SEIDEL
A = input("Enter matrix") ;
B = input("Enter source vector");
N = length(B);
X = zeros(N,1);
n = 10 ;
Y = zeros(N,1);
P = input('initial giess vector ');
e = 0.0001;
for j = 1:n
for i = 1:N
X(i) = (B(i)/A(i,i)) - (A(i, [1:i-1, i+1:N]) * P([1:i-1, i+1:N])) / A(i,i);
P(i) = X(i);
end
if abs(Y-X)<e
break
end
Y=X;
end
X
%% POWER METHOD
A = input("Enter matrix") ;
v = input("Enter guess");
n = 30 ;
e = 0.001 ;
M = 0 ;
vO = v ;
for j = 1 :n
v = A*vO ;
M = max(v);
v = v/M ;
if abs(v-vO)<e
break
end
vO = v ;
end
B
%% NEWTON
clc
clear all
f = @(x) 2^x - 5*x + 2 ;
df = @(x) log(2)*(2^x) - 5 ;
e = 0.00000000000001 ;
xO = 0 ;
n = 10 ;
for i = 1:n
x1 = xO - f(xO)/df(xO);
if abs(x1-xO) < e
break ;
end
xO = x1 ;
disp(xO)
end
%% SECANT
f = @(x) x - 5*x^2 + 2 ;
e =0.000000000000000000001 ;
x0 = 0 ;
x1 = 1 ;
x2 = 0 ;
n = 10 ;
for i = 1:n
x2 = (x0*f(x1) - x1*f(x0))/(f(x1) - f(x0));
if abs(x2-x1)<e
break
end
disp(x2)
x1 = x2;
x0 = x1;
end
%% FIXED POINT
f = @(x) 2^x -5*x + 2 ;
g = @(x) (2^x + 2 )/5 ;
e = 0.00001 ;
xO = 0 ;
n = 10 ;
x1 = 0 ;
for i = 1:n
x1 = g(xO);
if abs(xO-x1)<e
disp(x1)
break
end
xO = x1 ;
end
%%BISECTION
clc
clear ALL
f = @(x) 2^x - 5*x + 2 ;
a = 0 ;
b =1 ;
n = 30 ;
e =0.0001 ;
c = 0 ;
if f(a)*f(b)<0
for i=1:n
c = (a+b)/2 ;
if abs(c-b) < e || abs(c-a) <e
disp(i)
break;
end
if f(a)*f(c)<0
b = c ;
elseif f(b)*f(c)<0
a = c ;
end
end
else
disp('no') ;
end
disp(c)

Add Comment

Please, Sign In to add comment