On condition numbers and the distance to the nearest III-posted problem
Numerische Mathematik
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Iterative solution of the Lyapunov matrix equation
Applied Mathematics Letters
Average-case stability of Gaussian elimination
SIAM Journal on Matrix Analysis and Applications
Functional stability analysis of numerical algorithms
Functional stability analysis of numerical algorithms
Reduction of a general matrix to tridiagonal form
SIAM Journal on Matrix Analysis and Applications
Alternating direction implicit iteration for systems with complex spectra
SIAM Journal on Numerical Analysis
Algorithm 694: a collection of test matrices in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Algorithm 696: an inverse rayleigh iteration for complex band matrices
ACM Transactions on Mathematical Software (TOMS)
Reduction to tridiagonal form and minimal realizations
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices
SIAM Journal on Scientific Computing
A breakdown-free variation of the nonsymmetric Lanczos algorithms
Mathematics of Computation
Error analysis of the Lanczos algorithm for the nonsymmetric eigenvalue problem
Mathematics of Computation
Efficient computation of eigenvalues of randomly generated matrices
Applied Mathematics and Computation
Expected conditioning for eigenvalues of randomly generated matrices
Neural, Parallel & Scientific Computations
SIAM Journal on Matrix Analysis and Applications
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
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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.