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Question: How to approximate the most dominant eigenvalue of the matrix using Symmetric Power Method in maple

Question:How to approximate the most dominant eigenvalue of the matrix using Symmetric Power Method in maple

peace951 15 Maple
linear-algebra homework eigenvalues symmetric power
April 05 2021
0

 

Use the Symmetric Power method to approximate the most dominant eigenvalue of the matrix A=Matrix([[4, 2, -1], [2, 0, 2], [-1, 2, 0]]) , Use x_0 = (-1,0, 1)^t.  Iterate until a tolerance of 10^-4 is achieved or until the number of iterations exceeds 25. 

I tried but failed to get full evaluation (numbers only).

with(LinearAlgebra);

A := Matrix([[4, 2, -1], [2, 0, 2], [-1, 2, 0]]);
x_0 := <-1, 0, 1>;
Tol := 0.0001;
k := 15;
y_k := evalf(A*x[k - 1]);
mu_k := evalf(Transpose(x_k - 1)*y_k);
x_k = y_k/Norm(y_k, 2);
 

Q5_Ch_9.3.pdf

 
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