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

The Leja method is a polynomial interpolation procedure that can be used to computematrix functions. In particular, computing the action of the matrix exponential on a given vector isa typical application. This quantity is required, e.g., in exponential integrators.The Leja method essentially depends on three parameters: the scaling parameter, the location ofthe interpolation points, and the degree of interpolation. We present here a backward error analysisthat allows us to determine these three parameters as a function of the prescribed accuracy. Addi-tional aspects that are required for an efficient and reliable implementation are discussed. Numericalexamples illustrating the performance of our Matlab code are included.