[PDF] Top 20 Structured Quadraticization and Structure-Preserving Algorithm for Palindromic Polynomial Eigenvalue Problems

... a structured quadraticization to transform a (?, ε)-PPEP with the even degree into a (?, ...a structure-preserving algorithm for solving the transformed ...bounds and the ... See full document

... λ and 1/λ ? . Result on unstructured condition number for a nonzero simple eigenvalue of poly- nomial eigenvalue problem (PEP) have been investigated by Tisseur (Linear Algebra ...bers ... See full document

... Quadratic Palindromic Eigenvalue Problem (QPEP) [1, 2, 3]: find a scalar λ and an n-dimensional vector x such that (A T 1 λ 2 + A 0 λ + A 1 )x = 0, ...0 and A 1 are n × n (complex) matrices, A ... See full document

... BVD, and palindromic approaches to dis- crete-time control ...trains, palindromic eigenvalue problems and structure-preserving doubling ...error and ... See full document

... an eigenvalue λ and its reciprocal ...rail and the train, all 2n eigenvalues and their associated eigenvectors are ...form and compute its generalized Schur form (see ...symplectic ... See full document

... (a) and (b) of Figure 6.4, we show those RRes for frequency ω = 50 and ω = 2000, ...“∆” and “×” denote the results computed by Algorithms ...5.2 and 5.3 are terminated for Ω = ... See full document

... generalized structure-preserving doubling algorithm (g-SDA) is developed and analyzed in Sections 2 and ...generalized palindromic QEP is discussed in Section ...5 and the ... See full document

... a palindromic quadratization to transform a palin- dromic matrix polynomial of even degree into a palindromic quadratic pencil, instead of the palin- dromic linearization to a palindromic ... 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 ...Theory and is given to ... See full document

... block-rows and columns. Also H 0 is complex symmetric, i.e., H 0 T = H 0 . For future references, we will call PQEP ...Mehl, and Mehrmann [10, ...0 and ∞ and in fact, by examining A, we ... See full document

... A STRUCTURE-PRESERVING DOUBLING ALGORITHM CHUN-HUA GUO † AND WEN-WEI LIN ‡ ...a palindromic quadratic eigen- value problem (QEP) (λ 2 A T + λQ + A)z = 0, where A, Q ∈ C n×n and Q ... See full document

... A STRUCTURED QUADRATIC EIGENVALUE PROBLEM BY A STRUCTURE-PRESERVING DOUBLING ALGORITHM ∗ CHUN-HUA GUO † AND WEN-WEI LIN ‡ ...a palindromic quadratic eigen- value problem ... See full document

... The algorithm is efficient for small to medium size examples, as illustrated by numerical ...simulation. For large and structured problems, modifications to the SDA + Newton ... See full document

... highways and aircrafts made them practical for a greater portion of the population, especially in the ...Europe and Japan, emphasis was given to rebuilding the ...petroleum and environmental ... See full document

... proposed structured algorithms in Sections ...(ERS) and train suspension ...[22] and a procedure for designing an optimal ERS are proposed by ...frequency for such ...use ... See full document

... Þ for k ¼ 1; . . . ; 5 and takes a shift value s ¼ ...5;I and k 5;O ...in Algorithm 1, according to the relationship l ¼ k þ k 1 , the eigenvalue l of Kz ¼ l N z is far away from the ... See full document

... multiple eigenvalue of PEP whose largest Jordan block has size n 1 and let ω be a any positive ...Then for any positive number ε, sufficiently small, there is a matrix B 0 with kB 0 k ≤ ω such that ... See full document

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

... Inexact Structure-Preserving Arnoldi Methods (ISPAM) for solving Hermitian and skew-Hermitian eigenvalue problems, by which the solutions can preserve the desirable numerical ... See full document

... polynomials, palindromic linearizations, the anti-triangular canonical form [16–18] and the semi-Schur anti-triangular canonical form is investigated by means of the Bauer–Fike technique for ... See full document