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[M] In Exercises 19 and 20, find (a) the largest
Chapter 5, Problem 19E(choose chapter or problem)
[M] In Exercises 19 and 20, find (a) the largest eigenvalue and (b) the eigenvalue closest to zero. In each case, set x0 (1, 0, 0, 0) and carry out approximations until the approximating sequence seems accurate to four decimal places. Include the approximate eigenvector.
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QUESTION:
[M] In Exercises 19 and 20, find (a) the largest eigenvalue and (b) the eigenvalue closest to zero. In each case, set x0 (1, 0, 0, 0) and carry out approximations until the approximating sequence seems accurate to four decimal places. Include the approximate eigenvector.
ANSWER:Solution 19EStep 1 The objective is to find the largest eigenvalue and the eigenvalue closest to zero for the following matrix: Use MATLAB to find the list.Code in MATLAB:function[x,lambda]=powermat(A,x0,nit) x = x0; for n=1:nit xnew = A*x; lambda = norm(xnew,inf)/norm(x,inf); fprintf('n = %4d lambda = %g x = %g %g %g \n', n, lambda, x'); x=xnew; end x=x/norm(x);%normalise x fprintf('n = %4d normalised x = %g %g %g\n', n, x');