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An efficient numerical method is developed for evaluating φ(A), where A is a symmetric matrix and φ is the function defined by φ(x)=(e x -1)/x=1+x/2+x 2 /6+.... This matrix function is useful in the so-called exponential integrators for differential equations. In particular, it is related to the exact solution of the ODE system dy/dt=Ay+b, where A and b are t-independent. Our method...
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