1976/10/01 by Gene H. Golub, J. H. Wilkinson · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research #Electromagnetic Scattering and Analysis #Jordan matrix #Rounding #Canonical form #Eigenvalues and eigenvectors #Mathematics #Linear subspace #Computation #Invariant (physics) #Defective matrix #Matrix (chemical analysis) #Algebra over a field #Applied mathematics #Pure mathematics #Symmetric matrix #Computer science #Algorithm #Diagonalizable matrix #Mathematical physics
paper · doi:10.1137/1018113
openalex publication_date 1976/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
The solution of the complete eigenvalue problem for a nonnormal matrix A presents severe practical difficulties when A is defective or close to a defective matrix. Moreover, in the presence of rounding errors, one cannot even determine whether or not a matrix is defective. Several of the more stable methods for computing the Jordan canonical form are discussed, together with the alternative approach of computing well-defined bases (usually orthogonal) of the relevant invariant subspaces.