Proceedings of the 2006 international symposium on Physical design
On a quadratic eigenproblem occurring in regularized total least squares
Computational Statistics & Data Analysis
Critical delays and polynomial eigenvalue problems
Journal of Computational and Applied Mathematics
Continuation of Invariant Subspaces for Parameterized Quadratic Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
Efficient Arnoldi-type algorithms for rational eigenvalue problems arising in fluid-solid systems
Journal of Computational Physics
A Krylov Method for the Delay Eigenvalue Problem
SIAM Journal on Scientific Computing
Model reduction for RF MEMS simulation
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Structure-preserving model reduction
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Computing eigenpairs of quadratic eigensystems
Mathematical and Computer Modelling: An International Journal
Efficient determination of the hyperparameter in regularized total least squares problems
Applied Numerical Mathematics
Structure preserving model-order reductions of MIMO second-order systems using Arnoldi methods
Mathematical and Computer Modelling: An International Journal
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We first introduce a second-order Krylov subspace $\mathcal{G}_n$(A,B;u) based on a pair of square matrices A and B and a vector u. The subspace is spanned by a sequence of vectors defined via a second-order linear homogeneous recurrence relation with coefficient matrices A and B and an initial vector u. It generalizes the well-known Krylov subspace $\mathcal{K}_n$(A;v), which is spanned by a sequence of vectors defined via a first-order linear homogeneous recurrence relation with a single coefficient matrix A and an initial vector v. Then we present a second-order Arnoldi (SOAR) procedure for generating an orthonormal basis of $\mathcal{G}_n$(A,B;u). By applying the standard Rayleigh--Ritz orthogonal projection technique, we derive an SOAR method for solving a large-scale quadratic eigenvalue problem (QEP). This method is applied to the QEP directly. Hence it preserves essential structures and properties of the QEP. Numerical examples demonstrate that the SOAR method outperforms convergence behaviors of the Krylov subspace--based Arnoldi method applied to the linearized QEP.