BHESS uses Gaussian similarity transformations to reduce a general real square matrix to similar upper Hessenberg form. Multipliers are bounded in root mean square by a user-supplied parameter. If the input matrix is not highly nonnormal and the user-supplied tolerance on multipliers is of a size greater than ten, the returned matrix usually has small upper bandwidth. In such a case, eigenvalues of the returned matrix can be determined by the bulge-chasing BR iteration or by Rayleigh quotient iteration. BHESS followed by BR iteration determines a complete spectrum in about one-fifth the time required for orthogonal reduction to Hessenberg form followed by QR iterations. The FORTRAN 77 code provided for BHESS runs efficiently on a cache-based architecture. (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 1 article , 1 standard article )

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  1. Howell, Gary W.; Diaa, Nadia: Algorithm 841: BHESS: Gaussian reduction to a similar banded Hessenberg form (2005)