7.00.02 - Power Iteration - Aster Analytics

Teradata Aster® Analytics Foundation User GuideUpdate 2

Aster Analytics
Release Number
Release Date
September 2017
Content Type
Programming Reference
User Guide
Publication ID
English (United States)

Power iteration is an eigenvalue algorithm to find the largest eigenvalue and corresponding eigenvector. This algorithm does not compute a matrix decomposition; therefore, it can be used when Α is a very large sparse matrix.

The power iteration algorithm starts with a vector b 0, which can be an approximation to the dominant eigenvector or a random vector. The method is described by the following iteration:

b k+1 = A b k / || A b k ||

At every iteration, the vector b k is multiplied by matrix Α and normalized.

The sequence (b k ) does not necessarily converge. A subsequence of (b k ) converges to an eigenvector associated with the dominant eigenvalue under these conditions:

  • A has an eigenvalue that is strictly greater in magnitude than its other eigenvalues.
  • Starting vector b 0 has a nonzero component in the direction of an eigenvector associated with the dominant eigenvalue.