Adaptive rational Krylov subspaces for large-scale dynamical systems

2011 ◽  
Vol 60 (8) ◽  
pp. 546-560 ◽  
Author(s):  
V. Druskin ◽  
V. Simoncini
Keyword(s):  
Dynamical Systems ◽  
Large Scale ◽  
Krylov Subspaces ◽  
Rational Krylov Subspaces

Solution of Large Scale Evolutionary Problems Using Rational Krylov Subspaces with Optimized Shifts

2009 ◽  
Vol 31 (5) ◽  
pp. 3760-3780 ◽  
Author(s):  
Vladimir Druskin ◽  
Leonid Knizhnerman ◽  
Mikhail Zaslavsky
Keyword(s):  
Large Scale ◽  
Krylov Subspaces ◽  
Rational Krylov Subspaces

Reduction of large-scale dynamical systems by the Krylov subspaces method: Analysis of approaches

2015 ◽  
Vol 54 (2) ◽  
pp. 165-183 ◽  
Author(s):  
N. E. Zubov ◽  
E. A. Mikrin ◽  
M. Sh. Misrikhanov ◽  
A. V. Proletarskii ◽  
V. N. Ryabchenko
Keyword(s):  
Dynamical Systems ◽  
Large Scale ◽  
Krylov Subspaces ◽  
Method Analysis

scholarly journals Compressing Large-Scale Wave Propagation Models via Phase-Preconditioned Rational Krylov Subspaces

2018 ◽  
Vol 16 (4) ◽  
pp. 1486-1518 ◽  
Author(s):  
Vladimir Druskin ◽  
Rob F. Remis ◽  
Mikhail Zaslavsky ◽  
Jörn T. Zimmerling
Keyword(s):  
Wave Propagation ◽  
Large Scale ◽  
Krylov Subspaces ◽  
Propagation Models ◽  
Rational Krylov Subspaces

scholarly journals Model reduction methods based on Krylov subspaces

Acta Numerica ◽  
2003 ◽  
Vol 12 ◽  
pp. 267-319 ◽  
Author(s):  
Roland W. Freund
Keyword(s):  
Large Scale ◽  
Krylov Subspace ◽  
Circuit Simulation ◽  
Krylov Subspaces ◽  
Lanczos Algorithm ◽  
Linear Dynamical Systems ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Reduction Methods ◽  
Modelling Techniques

In recent years, reduced-order modelling techniques based on Krylov-subspace iterations, especially the Lanczos algorithm and the Arnoldi process, have become popular tools for tackling the large-scale time-invariant linear dynamical systems that arise in the simulation of electronic circuits. This paper reviews the main ideas of reduced-order modelling techniques based on Krylov subspaces and describes some applications of reduced-order modelling in circuit simulation.

ON THE LOCATION AND CONTINUATION OF HOPF BIFURCATIONS IN LARGE-SCALE PROBLEMS

2008 ◽  
Vol 18 (05) ◽  
pp. 1589-1597 ◽  
Author(s):  
M. FRIEDMAN ◽  
W. QIU
Keyword(s):  
Dynamical Systems ◽  
Large Scale ◽  
Orthonormal Basis ◽  
Invariant Subspaces ◽  
Hopf Bifurcations ◽  
Augmented System ◽  
Large Scale Problems ◽  
System Technique ◽  
Matlab Package ◽  
Parameter Dependent

CL_MATCONT is a MATLAB package for the study of dynamical systems and their bifurcations. It uses a minimally augmented system for continuation of the Hopf curve. The Continuation of Invariant Subspaces (CIS) algorithm produces a smooth orthonormal basis for an invariant subspace [Formula: see text] of a parameter-dependent matrix A(s). We extend a minimally augmented system technique for location and continuation of Hopf bifurcations to large-scale problems using the CIS algorithm, which has been incorporated into CL_MATCONT. We compare this approach with using a standard augmented system and show that a minimally augmented system technique is more suitable for large-scale problems. We also suggest an improvement of a minimally augmented system technique for the case of the torus continuation.

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