[PDF] Top 20 The Palindromic Generalized Eigenvalue Problem A*x =Ax: Numerical Solution and Applications
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The Palindromic Generalized Eigenvalue Problem A*x =Ax: Numerical Solution and Applications
... develop the palindromic doubling algorithm (PDA) for solving ...establish the convergence theory for the PDA. In Section 4 we use the PDA to compute numerical solutions ... See full document
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The palindromic generalized eigenvalue problem A*x = lambda Ax: Numerical solution and applications
... knowledge, the associated generalized discrete-time algebraic Riccati equation (GDARE) has not been solved successfully in a structure-preserving ...develop the palindromic doubling ... See full document
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On a General Solution of Partially Described Inverse Quadratic Eigenvalue Problems and Its Applications
... Introduction. The problem of finding scalars λ ∈ C and nontrivial vectors x ∈ C n such that Q(λ)x ≡ (λ 2 M + λC + K)x = 0, ...C and K are given n × n real matrices, is ... See full document
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A FAST ALGORITHM FOR FAST TRAIN PALINDROMIC QUADRATIC EIGENVALUE PROBLEMS
... examining A, but it is its remaining 2k eigenvalues, usually nonzero and finite but with an extreme wide range in magnitude, that are of ...interest. The problem is notoriously difficult ...0 ... See full document
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A Semiorthogonal Generalized Arnoldi Method and Its Variations for Quadratic Eigenvalue Problems
... with the computation of a few eigenpairs with smallest eigenvalues in absolute value of quadratic eigenvalue ...develop a semiorthogonal generalized Arnoldi method where the name ... See full document
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A semiorthogonal generalized Arnoldi method and its variations for quadratic eigenvalue problems
... on the quadratic eigenvalue ...preserves the spectral properties of the original quadratic eigenvalue ...propose a refinement scheme to improve the accuracy of the ... See full document
22
Structured Condition Number for Palindromic Polynomial Eigenvalue Problems
... numbers and backward errors play an important role in numerical linear ...measure the sensitivity of solution of a problem to perturbations in the data and backward ... See full document
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Solutions to a quadratic inverse eigenvalue problem
... inverse eigenvalue problems for some partially prescribed eigen-information is a challenging task in many ...theoretical and computational. Thus far, the results are somewhat ...of the ... See full document
19
Vibration of Fast Trains, Palindromic Eigenvalue Problems and Structure-Preserving Doubling Algorithms
... study the resonance phenomena of the track under high frequent excitation ...to the safety of the operations of high-speed trains but also new designs of train bridges, embedded rail ... See full document
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A Numerical Method for Quadratic Eigenvalue Problems of Gyroscopic Systems
... Solving the QEP As described in Section 1, the classical approach for finding all 2n eigenpairs of the QEP is to use linearizations and solve the resulting 2n × 2n standard or ... See full document
15
Structured doubling algorithms for solving g-palindromic quadratic eigenvalue problems
... follows. The generalized structure-preserving doubling algorithm (g-SDA) is developed and analyzed in Sections 2 and ...of the g-SDA to several generalized palindromic QEP ... See full document
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Numerically Stable, Structure-preserving Algorithms for Palindromic Quadratic Eigenvalue Problems
... that the eigenvalues of (1.1) have a ‘symplectic’ property, that is, they are symmetrically placed with respect to the unit circle, containing both an eigenvalue λ and its reciprocal ... See full document
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STRUCTURE-PRESERVING ARNOLDI-TYPE ALGORITHMS FOR PALINDROMIC QUADRATIC EIGENVALUE PROBLEMS
... In applications, the matrices A 1 and A 0 in ...large and sparse, and all eigenvalues in a specified region are ...this, the shift-and- invert ... See full document
23
The Eigenvalue Shift Technique and Its Eigenstructure Analysis of a Matrix
... Abstract The eigenvalue shift technique is the most well-known and fundamental tool for matrix ...computations. Applications include the search of eigeninformation, the ... See full document
21
Perturbation of Palindromic Eigenvalue Problems
... polynomial eigenvalue problems, see [1, ...see the mas- terpiece ...2–5, the perturbation of palindromic eigenvalues, in terms of general matrix polynomials, palindromic linearizations, ... See full document
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Numerical Solution to Generalized Lyapunov, Stein and Rational Riccati Equations in Stochastic Control
... GLEs and GSEs, because of the lack of a complete ...for the existence of nonnegative definite solutions, when L A + Π is ...to the efficiency and success of Algorithm 1, ... See full document
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PERTURBATION RESULTS RELATED TO PALINDROMIC EIGENVALUE PROBLEMS
... 2–5, 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 ... See full document
14
Structured Quadraticization and Structure-Preserving Algorithm for Palindromic Polynomial Eigenvalue Problems
... proposed a structured quadraticization to transform a (?, ε)-PPEP with the even degree into a (?, ...develop a structure-preserving algorithm for solving the transformed ... See full document
31
The Generalized Consensus Problem in a Cloud Computing Environment
... in the cloud computing environment where have to execute application services ...Therefore, the high fault-tolerant capability of a cloud computing environment needs to be ...However, the ... See full document
12
Structured Backward Error for Palindromic Polynomial Eigenvalue Problems
... arises the 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 ... See full document
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