1.1 - 8.10 - Power Iteration - Teradata Vantage

Teradata Vantage™ - Machine Learning Engine Analytic Function Reference

Product
Teradata Vantage
Release Number
1.1
8.10
Release Date
October 2019
Content Type
Programming Reference
Publication ID
B700-4003-079K
Language
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, you can use it 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. This iteration describes the method:

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.