The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential

摘要

The Leja method is a polynomial interpolation procedure that can be used tocompute matrix functions. In particular, computing the action of the matrixexponential on a given vector is a typical application. This quantity isrequired, e.g., in exponential integrators. The Leja method essentially depends on three parameters: the scalingparameter, the location of the interpolation points, and the degree ofinterpolation. We present here a backward error analysis that allows us todetermine these three parameters as a function of the prescribed accuracy.Additional aspects that are required for an efficient and reliableimplementation are discussed. Numerical examples that illustrate theperformance of our Matlab code are included.