engleski

A hybrid m-Hessenberg reduction algorithm

The m-Hessenberg form (also known as banded Hessenberg form with lower bandwidth m) of a given matrix A is a matrix H orthogonally similar to A such that H(i, j) = 0 for all i, j such that i > j + m. The need for reducing a matrix to an m-Hessenberg form occurs e.g. in control theory as the reduction to the controller Hessenberg form and also in some implementations of the block Arnoldi algorithm for computing the eigenvalues of a large sparse matrix. In this talk we analyze and improve the implementation of this reduction. The improvement introduces blocking with a sophisticated performance boost for larger values of m. We also incorporate a hybrid CPU+GPU and analyze the performance benefits.

Hessenberg form; hybrid algorithm

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