Lanczos Method
During the procedure of applying the power method, while getting the ultimate eigenvector, we also got a series of vectors which were eventually discarded. As is often taken to be quite large, this can result in a large amount of disregarded information. More advanced algorithms, such as Arnoldi's algorithm and the Lanczos algorithm, save this information and use the Gram–Schmidt process or Householder algorithm to reorthogonalize them into a basis spanning the Krylov subspace corresponding to the matrix .
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