
Exponential of tridiagonal Toeplitz matrices: applications and generalization
In this paper, an approximate method is presented for computing exponent...
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The FaddeevLeVerrier algorithm and the Pfaffian
We adapt the FaddeevLeVerrier algorithm for the computation of characte...
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Computing the matrix sine and cosine simultaneously with a reduced number of products
A new procedure is presented for computing the matrix cosine and sine si...
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ParaExp using Leapfrog as Integrator for HighFrequency Electromagnetic Simulations
Recently, ParaExp was proposed for the time integration of linear hyperb...
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Exponential Integrators for MHD: Matrixfree Leja interpolation and efficient adaptive time stepping
We propose a novel algorithm for the temporal integration of the magneto...
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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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Computational graphs for matrix functions
Many numerical methods for evaluating matrix functions can be naturally ...
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An efficient algorithm to compute the exponential of skewHermitian matrices for the time integration of the Schrödinger equation
We present a practical algorithm to approximate the exponential of skewHermitian matrices based on an efficient computation of Chebyshev polynomials of matrices and the corresponding error analysis. It is based on Chebyshev polynomials of degrees 2, 4, 8, 12 and 18 which are computed with only 1, 2, 3, 4 and 5 matrixmatrix products, respectively. For problems of the form exp(iA), with A a real and symmetric matrix, an improved version is presented that computes the sine and cosine of A with a reduced computational cost. The theoretical analysis, supported by numerical experiments, indicates that the new methods are more efficient than is not very large, and also than other schemes based on rational Padé approximants and Taylor polynomials for all tolerances and time interval lengths. The new procedure is particularly recommended to be used in conjunction with exponential integrators for the numerical time integration of the Schrödinger equation.
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