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## QR-Iteration |

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |

The QR-iteration approximates an eigenvalue of a matrix in Hessenberg form with the aid of a sequence of orthogonal similarity transformations

Moreover, zero diagonals of the Hessenberg form are preserved. In particular, for syymetric , all matrices are tridiagonal.

As , the off-diagonal entry converges to zero and, as a consequence, approaches an eigenvalue of . Moreover, for symmetric the convergence is locally cubic.

If the iteration has converged, i. e., if the last off-diagonal entry of is zero within tolerance, the process is applied to the submatrix . Thus, eventually, all eigenvalues are computed.

(Authors: Höllig/Pfeil/Walter)

automatically generated 4/24/2007 |