Symmetric Power Method, Eigen Value-Numerical Analysis-MATLAB Code, Exercises of Mathematical Methods for Numerical Analysis and Optimization

% SYMMETRIC POWER METHOD ALGORITHM 9.2

%

% To approximate the dominant eigenvalue and an associated

% eigenvector of the n by n symmetric matrix A given a nonzero vector x:

%

% INPUT: Dimension n; matrix A; vector x; tolerance TOL;

% maximum number of iterations N.

%

% OUTPUT: Approximate eigenvalue MU; approximate eigenvector x or

fprintf(1,'This is the Symmetric Power Method.\n');

OK = FALSE;

fprintf(1,'The array will be input from a text file in the order:\n');

fprintf(1,'A(1,1), A(1,2), ..., A(1,n), \n');

fprintf(1,'A(2,1), A(2,2), ..., A(2,n),\n');

fprintf(1,'..., A(n,1), A(n,2), ..., A(n,n)\n\n');

fprintf(1,'Place as many entries as desired on each line, but separate

');

fprintf(1,'entries with\n');

fprintf(1,'at least one blank.\n');

fprintf(1,'for example: A:\\DATA.DTA\n');

NAME = input(' ','s');

INP = fopen(NAME,'rt');

OK = FALSE;

while OK == FALSE

fprintf(1,'Input the dimension n.\n');

N = input(' ');

if N > 0

A = zeros(N,N);

Y = zeros(1,N);

% The initial input is into Y and X is initialized at the zero vector.

for I = 1 : N

Y(I) = fscanf(INP, '%f',1);

end;

for I = 1 : N

X(I) = 0;

end;