[PDF] Top 20 PERTURBATION RESULTS RELATED TO PALINDROMIC EIGENVALUE PROBLEMS

... the perturbation of eigenvalues in terms of general matrix polynomials, palindromic linearizations, the anti-triangular canonical form [16–18] and the semi-Schur anti-triangular canonical form is ... See full document

... general perturbation of eigenvalues for polynomial eigenvalue problems, see [1, ...On results for general matrix polynomials, see the mas- terpiece ...the perturbation of ... See full document

... easy to see that the eigenvalues of a ?-PPEP contain both eigenvalues λ and 1/λ ? ...simple eigenvalue of poly- nomial eigenvalue problem (PEP) have been investigated by Tisseur (Linear Algebra ...of ... See full document

... Her results do not apply to PPEP’s structured backward error analysis, ...kinds. To present these PPEP compactly, we let the superscript “ · X ” be either “ · T ” or “ · H ” which takes complex ... See full document

... impossible to verify when the approximate eigenpair is so accurate in the working precision that r may have no correct significant ...numerical results presented in ...μ to μ(1 + 10 −8 )) to ... See full document

... the eigenvalue problem for matrix pencil λH 1 T + Φ ...an eigenvalue of λ b Φ + H 1 , then 1/µ is an eigenvalue of λH 1 T + b Φ and vice ...are related, ... See full document

... quadratic eigenvalue problem (QEP) Q(λ)x ≡ (λ 2 B + λC + A)x = 0, (1) where A, B, C ∈ C n×n , λ ∈ C, x 6= 0 ∈ C n ...that results in certain symmetry in the ...the palindromic QEP with the property ... See full document

... quadraticization to transform a (?, ε)-PPEP with the even degree into a (?, ...numerical results computed by PQEP, PGEP and the standard GEP are presented in Section ... See full document

... respect to the unit circle, containing both an eigenvalue λ and its reciprocal ...Practically, to optimize the design of the rail and the train, all 2n eigenvalues and their associated eigenvectors ... See full document

... the results computed by Algorithms ...these results, we see that the reciprocity properties of eigenvalues are preserved in all three algorithms, but the accuracy of the eigenpairs computed by Algorithm ... See full document

... numerical results of the vibration of fast trains to illustrate the perfor- mance of proposed structured algorithms in Sections ...contributes to the safety of operations of high-speed trains as well ... See full document

... preserving doubling algorithms on the quadratic palindromic eigenvalue prob- lem. The problem is difficult, far from being solved (see the concluding com- ments in Section 7). Our numerical results ... See full document

... quadratic eigenvalue problems (TPQEP) arising from modeling leaky surface waves propagation in a acoustic resonator with in- finitely many periodically arranged interdigital ...given to reduce the ... See full document

... some results in [1] on how to solve the QEP by the solvent approach, and the SDA algorithm and the related convergence analysis in [10, ...4 to illustrate the efficiency of our ... See full document

... those results above, we get considerably more information than those obtained in ...largest eigenvalue ␭ 1 共 ␣ , 1兲 is further away from 0, and, hence, gives even smaller critical ...corresponds to ... See full document

... multiple eigenvalue of PEP whose largest Jordan block has size n 1 and let ω be a any positive ...a eigenvalue of e P (λ) := P (λ) + εB 0 and c > 0 is independent of ... See full document

... Here x is an unknown vector and λ an unknown scalar. Our task is to determine x’s and λ’s that satisfy (1). Ge ometrically, we are looking for vectors x for which the multiplication by A has the same effect as the ... See full document

... provided to yield better performance. All numerical results are generated by using a semiconductor quantum dot model which exhibits both non-linear and large-scale properties in the resulting ... See full document

... The possibility of normalizing any eigenvector is mentioned in connection with Theorem 2, but this will be of greater interest to us only in connection with orthonormal or unitary systems (Secs. 8.4 and 8.5). In ... See full document

... allows errors in the computation, and can work on an appropriate initial subspace. • With shift-invert enhancement, residual Arnoldi[r] ... See full document