GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Implementation of the GMRES method using householder transformations
SIAM Journal on Scientific and Statistical Computing - Telecommunication Programs at U.S. Universities
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Coping with RC(L) interconnect design headaches
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
Matrix computations (3rd ed.)
Matrix market: a web resource for test matrix collections
Proceedings of the IFIP TC2/WG2.5 working conference on Quality of numerical software: assessment and enhancement
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
On Stability Robustness of 2-D Systems Described by theFornasini–Marchesini Model
Multidimensional Systems and Signal Processing
Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
Applied Numerical Mathematics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Parameterized model order reduction via a two-directional Arnoldi process
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
PRIMA: passive reduced-order interconnect macromodeling algorithm
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Time-domain macromodels for VLSI interconnect analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
SIAM Journal on Scientific Computing
Parametric dominant pole algorithm for parametric model order reduction
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
We consider a two-directional Krylov subspace K"k(A"["j"],b"["j"]), where besides the dimensionality k of the subspace increases, the matrix A"["j"] and vector b"["j"] which induce the subspace may also augment. Specifically, we consider the case where the matrix A"["j"] and the vector b"["j"] are augmented by block triangular bordering. We present a two-directional Arnoldi process to efficiently generate a sequence of orthonormal bases Q"k^[^j^] of the Krylov subspaces. The concept of a two-directional Krylov subspace and an Arnoldi process is triggered by the need of a multiparameter moment-matching based model order reduction technique for parameterized linear dynamical systems. Numerical examples illustrate computational efficiency and flexibility of the proposed two-directional Arnoldi process.