A residual based error estimate for Leja interpolation of matrix functions

作者：Kandolf Peter^*; Ostermann Alexander; Rainer Stefan

来源：Linear Algebra and Its Applications, 2014, 456: 157-173.

DOI：10.1016/j.laa.2014.04.023

• Leja interpolation
• Action of matrix exponential
• Exponential integrators
• Matrix residual
• phi functions

Recent applications in science and engineering require a reliable implementation of the action of the matrix exponential and related phi functions. For possibly large matrices an approximation up to a certain tolerance needs to be obtained in a robust and efficient way. In this work we consider Leja interpolation for performing this task. Our focus lies on a new a posteriori error estimate for the method. We introduce the notion of a residual based estimate, where the residual is obtained from differential equations defining the phi functions. The properties of this new error estimate are investigated and compared to an existing one. Further, a numerical investigation is performed based on test examples originating from spatial discretization of time dependent partial differential equations in two and three space dimensions. The experiments show that this new approach is robust for various types of matrices and applications.

• 出版日期2014-9-1