Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics
SIAM Journal on Scientific Computing
Function Value Recovery and Its Application in Eigenvalue Problems
SIAM Journal on Numerical Analysis
Krylov-Based Model Order Reduction of Time-delay Systems
SIAM Journal on Matrix Analysis and Applications
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We introduce new two-sided Arnoldi recursions and use them to define a model reduction procedure for large, linear, time-invariant, multi-input/multi-output differential algebraic systems. We prove that this procedure has desirable moment matching properties. We define a corresponding model reduction procedure which is based on a band nonsymmetric Lanczos recursion and prove that if the deflation is exact and there are no breakdowns in the recursions, then these two model reduction procedures generate identical reduced-order systems. We prove similar equivalences for corresponding eigenelement procedures. We concentrate on the theoretical properties of the new algorithms.