On convergence of Krylov subspace approximations of time-invariant self-adjoint dynamical systems
On convergence of Krylov subspace approximations of time-invariant self-adjoint dynamical systems
复制标题
时不变自伴动力系统Krylov子空间近似的收敛性
DOI：
10.1016/j.laa.2011.02.039
复制
发表时间：
2012
影响因子：
1.1
通讯作者：
M. Zaslavsky
中科院分区：
文献类型：
--
作者：
V. Druskin;M. Zaslavsky
本文将有理Krylov子空间算法从矩阵指数作用量的计算推广到稳定动力系统的求解，其中m∈N 0，u（t），B（t）∈RN，B| t<0=0（不假设B（t）的演化由RN的低维子空间描述）。我们证明了约化方程是稳定的，并通过有理逼近的非线性数值范围的边界上的指数，获得了一个先验的误差界。我们还描述了该数值范围的简单且易于计算的外部界限。所得结果被应用到色散麦克斯韦系统的解决方案中所产生的无限阶问题。
We extend the rational Krylov subspace algorithm from the computation of the action of the matrix exponential to the solution of stable dynamical systemswhere m∈N∪{∞}, Ai=Ai∗∈RN×N,s⩽0, and u(t),b(t)∈RN,b|t<0=0 (not assuming that evolution of b(t) is described by a low-dimensional subspace of RN). We show that the reduced equation is stable and derive an a priori error bound via rational approximation of the exponential on the boundary of the nonlinear numerical range of A˜. We also describe a simple and easily computable external bound of this numerical range. The obtained results are applied to the infinite order problem arising in the solution of the dispersive Maxwell’s system.