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.

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

CALIARI, Marco;Ostermann, Alexander;
2016-01-01

Abstract

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.
Leja interpolation, backward error analysis, action of matrix exponential
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/945921
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