
An accurate restarting for shiftandinvert Krylov subspaces computing matrix exponential actions of nonsymmetric matrices
An accurate residual–time (AccuRT) restarting for computing matrix expon...
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ART: adaptive residualtime restarting for Krylov subspace matrix exponential evaluations
In this paper a new restarting method for Krylov subspace matrix exponen...
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Vector logic and counterfactuals
In this work we investigate the representation of counterfactual conditi...
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Monotone Difference Schemes for ConvectionDominated DiffusionReaction Equations Based on Quadratic Spline
A threepoint monotone difference scheme is proposed for solving a oned...
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Efficient and accurate computation to the φfunction and its action on a vector
In this paper, we develop efficient and accurate algorithms for evaluati...
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Semi matrixfree twogrid shifted Laplacian preconditioner for the Helmholtz equation with near optimal shifts
Due to its significance in terms of wave phenomena a considerable effort...
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Accelerating eigenvector and pseudospectra computation using blocked multishift triangular solves
Multishift triangular solves are basic linear algebra calculations with...
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Practical shift choice in the shiftandinvert Krylov subspace evaluations of the matrix exponential
We propose two methods to find a proper shift parameter in the shiftandinvert method for computing matrix exponential matrixvector products. These methods are useful in the case of matrix exponential action has to be computed for a number of vectors. The first method is based on the zeroorder optimization of the mean residual norm for a given number of initial vectors. The second method processes the vectors onebyone and estimates, for each vector, the derivative of the residual norm as a function of the shift parameter. The estimated derivative value is then used to update the shift value for the next vector. To demonstrate the performance of the proposed methods we perform numerical experiments for twodimensional nonstationary convectiondiffusion equation with discontinuous coefficients and twodimensional anisotropic diffusion equation.
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