System of equations: (Gauss Elimination Method) Root of equations: Newtons MethodInterpolation:...

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System of equations: (Gauss Elimination Method)
Root of equations: Newtons Method
Interpolation: (cubic Spline Interpolation)
Numerical Integration (Trapezoidal Rule)
Optimization: (Golden section Search)

005_x1sxazo-kah2vcnw.docx

David · Accepted Answer

System of equations: (Gauss Elimination Method)  
Program 
function [x] = GaussianEliminate(A, b)  
%work out the number of equations  
N = length(b)  
%Gaussian elimination  
for column=1:(N-1)  
%work on all the rows below the diagonal element  
for row = (column+1):N  
%work out the value of d  
d = A(row,column)/A(column,column);  
%do the row operation  
A(row,:) = A(row,:)-d*A(column,:)  
b(row) = b(row)-d*b(column)  
end%loop through rows  
end %loop through columns  
%back substitution  
for row=N:-1:1  
x(row) = b(row);  
for i=(row+1):N  
x(row) = x(row)-A(row,i)*x(i);  
end  
x(row) = x(row)/A(row,row);  
end  
%return the answer  
x = x’;  
return 
As we have             and          
         and      
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]  [
  
  
  
] 
By using above equalities 
[
       
      
       
] [
  
  
  
]  [
  
 
  
] 
By Gaussian elimination method 
[
       
      
       
|
  
 
  
] 
R2 = 6*R2+R1,

System of equations: (Gauss Elimination Method) Root of equations: Newtons Method Interpolation: (cubic Spline Interpolation) Numerical Integration (Trapezoidal Rule) Optimization: (Golden section...

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