论文标题
Krylov子空间评估$φ$矩阵函数的剩余概念
A residual concept for Krylov subspace evaluation of the $φ$ matrix function
论文作者
论文摘要
提出了一种用于计算大型矩阵$φ$矩阵函数的计算操作的高效Krylov子空间算法。该矩阵函数广泛用于指数时间集成，马尔可夫链和网络分析以及许多其他应用程序。我们的算法基于可靠的基于残差的停止标准和新的有效重新启动程序。对于在稳定的复合半平面中具有数值范围的矩阵，我们分析了残差收敛，并证明重新启动的方法可以为任何Krylov子空间维度收敛。数值测试表明，我们解决了由于在时空依赖性PDE中离散的大规模演变问题的效率，尤其是扩散和对流扩散问题。
An efficient Krylov subspace algorithm for computing actions of the $φ$ matrix function for large matrices is proposed. This matrix function is widely used in exponential time integration, Markov chains and network analysis and many other applications. Our algorithm is based on a reliable residual based stopping criterion and a new efficient restarting procedure. For matrices with numerical range in the stable complex half plane, we analyze residual convergence and prove that the restarted method is guaranteed to converge for any Krylov subspace dimension. Numerical tests demonstrate efficiency of our approach for solving large scale evolution problems resulting from discretized in space time-dependent PDEs, in particular, diffusion and convection-diffusion problems.
