Steps

starts with 𝐴1=𝐴 and repeat for 𝑘=1,2,
𝑄𝑘𝑅𝑘=𝐴𝑘 by QR factorization
𝐴𝑘+1=𝑅𝑘𝑄𝑘
when 𝐴𝑘+1𝐴𝑘<𝑡𝑜𝑙, stop

after convergence,
The diagonal entries of 𝐴 are the corresponding eigenvalues.
Eigenvectors are the columns of matrix 𝑄=𝑘𝑗𝑄𝑗.

Cost

  • Symmetric
    • 43𝑛3 for only eigenvalues
    • 9𝑛3 for both eigenvalues and eigenvectors
  • General
    • 10𝑛3 for eigenvalues only
    • 25𝑛3 for both