Matrix analysis
Computation of transfer function matrices of linear multivariable systems
Automatica (Journal of IFAC)
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Remark on algorithms to find roots of polynomials
SIAM Journal on Scientific Computing
The Laguerre iteration in solving the symmetric tridiagonal eigenproblem, revisited
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Matrix algorithms
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Introduction to Numerical Methods for Parallel Computers
Introduction to Numerical Methods for Parallel Computers
QD-method with Newton shift
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
Perturbation bounds for polynomials
Numerische Mathematik
Perturbations of invariant subspaces of unreduced Hessenberg matrices
Computers & Mathematics with Applications
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The QR algorithm is considered one of the most reliable methods for computing matrix eigenpairs. However, it is unable to detect multiple eigenvalues and Jordan blocks. Matlab's eigensolver returns heavily perturbed eigenvalues and eigenvectors in such cases and there is no hint for possible principal vectors. This paper calls attention to Hyman's method as it is applicable for computing principal vectors and higher derivatives of the characteristic polynomial that may help to estimate multiplicity, an important information for more reliable computation. We suggest a test matrix collection for Jordan blocks. The first numerical tests with these matrices reveal that the computational problems are deeper than expected at the beginning of this work.