# 7.00.02 - Power Iteration - Aster Analytics

## Teradata Aster® Analytics Foundation User GuideUpdate 2

Product
Aster Analytics
Release Number
7.00.02
Release Date
September 2017
Content Type
Programming Reference
User Guide
Publication ID
B700-1022-700K
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, 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.