[PDF] Top 20 Solving a Structured Quadratic Eigenvalue Problem by a Structure-Preserving Doubling Algorithm

... solved a structured quadratic eigenvalue problem effi- ciently and accurately, by using a structure-preserving doubling algorithm in the sol- ... See full document

... SOLVING A STRUCTURED QUADRATIC EIGENVALUE PROBLEM BY A STRUCTURE-PRESERVING DOUBLING ALGORITHM ∗ CHUN-HUA GUO † AND WEN-WEI LIN ‡ ... See full document

... SDA algorithm for solving the ε ...develop a deflation technique for finding all unimodular eigenvalues in Section ...4. A structured backward error analysis for PCP_PQEPs is presented ... See full document

... This paper is organized as follows. The generalized structure-preserving doubling algorithm (g-SDA) is developed and analyzed in Sections 2 and 3. Application of the g-SDA to several ... See full document

... To compute the minimal positive solution of the NARE (1.1) under certain assumptions, Guo and Laub [16] recently proposed a Newton iteration method and a fixed-point iteration method. However, either the ... See full document

... the structure-preserving doubling algorithm will be adapted, with the iterates for A not explicitly computed but in the recursive form A k = A 2 k−1 = A 2 k ... See full document

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

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

... the problem to a single cell domain with one IDT by assuming that the wave w is quasi-periodic of the form wðx 1 ; x 2 Þ ¼ w p ðx 1 ; x 2 Þe ð a þibÞx 1 , where x 1 is the wave propagation ... See full document

... have a ‘symplectic’ property, that is, they are symmetrically placed with respect to the unit circle, containing both an eigenvalue λ and its reciprocal ...desired. A standard approach of finding all ... See full document

... matrices A 1 and A 0 in ...in a specified region are ...Arnoldi algorithm [6, 7, 14, 16] is widely used for the large sparse matrix pencil M − ...to a Hessenberg form which no longer ... See full document

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

... (1.3) a fast train PQEP. This fast train PQEP was first raised in a study in Germany by Hilliges, Mehl, and Mehrmann [10, ...in solving it: (1) most eigenvalues are 0 and ∞ and in fact, ... See full document

... (LR) algorithm which solves the QBD problem (positive recurrent and transient) with high efficiency, low cost and quadratic convergence ...LR algorithm and SDA algorithm, respectively, ... See full document

... for solving the NME based on the SDA algorithm [9] is shown to be linearly convergent if the unimodular eigenvalues of Z −1 + A have half of the partial multiplicity of the associated unimodular ... See full document

... Qian, Structure-preserving algorithms for palindromic quadratic eigenvalue problems arising from vibration of fast trains, SIAM ...Wu, Structure-preserving Arnoldi-type ... See full document

... the quadratic inverse eigenvalue problem (QIEP) of dimension ...is a constructible nonsingular symmetric quadratic pencil solution Q(λ) ≡ λ 2 M +λC +K to the QIEP such that Q(λ j )x j = ... See full document

... of doubling algorithms, espe ially the stru ture-preserving properties and eÆ ien y of the SDA [24℄, give this old approa h a new lease of ...optimally. A Fibona i sear h for hoosing was ... See full document

... FOR SOLVING QUADRATIC EIGENVALUE PROBLEMS MOODY ...for solving large-scale quadratic eigen- value problems for which a set of eigenvalues closest to a fixed target and the ... See full document

... E −1 F = ¯ F ¯ E −1 , (18) Here the inverses of E or ¯ E are merely notational — they do not have to be constructed explicitly unless required by the particular circumstances. For the G-SDA, we first assume, ... See full document