SOLUTION OF LARGE SCALE EVOLUTIONARY PROBLEMS USING RATIONAL KRYLOV SUBSPACES WITH OPTIMIZED SHIFTS

作者：Druskin Vladimir^*; Knizhnerman Leonid; Zaslavsky Mikhail

来源：SIAM Journal on Scientific Computing, 2009, 31(5): 3760-3780.

DOI：10.1137/080742403

• matrix function
• matrix exponential
• Zolotaryov problem
• time-domain Maxwell's system
• rational approximation
• model reduction

We consider the computation of u(t) - exp(-tA)phi using rational Krylov subspace reduction for 0 <= t < infinity, where u(t),phi is an element of R-N and 0 < A = A* is an element of R-NxN. The objective of this work is the optimization of the shifts for the rational Krylov subspace (RKS). We consider this problem in the frequency domain and reduce it to a classical Zolotaryov problem. The latter yields an asymtotically optimal solution with real shifts. We also construct an infinite sequence of shifts yielding a nested sequence of the RKSs with the same (optimal) Cauchy-Hadamard convergence rate. The effectiveness of the developed approach is demonstrated on an example of the three-dimensional diffusion problem for Maxwell's equation arising in geophysical exploration.

• 出版日期2009