Approximating the Matrix Exponential of an Advection-Diffusion Operator Using the Incomplete Orthogonalization Method

  • Antti KoskelaEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 103)


In this paper we give first results for the approximation of e A b, i.e. the matrix exponential times a vector, using the incomplete orthogonalization method. The benefits compared to the Arnoldi iteration are clear: shorter orthogonalization lengths make the algorithm faster and a large memory saving is also possible. For the case of three term orthogonalization recursions, simple error bounds are derived using the norm and the field of values of the projected operator. In addition, an a posteriori error estimate is given which in numerical examples is shown to work well for the approximation. In the numerical examples we particularly consider the case where the operator A arises from spatial discretization of an advection-diffusion operator.


Krylov Subspace Posteriori Error Estimate Matrix Exponential Exponential Integrator Hessenberg Matrix 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.KTH Royal Institute of TechnologyStockholmSweden

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