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TW 231
G. De Samblanx, K. Meerbergen, and A. Bultheel
Rational approximations of exp(x) for the calculation of rightmost eigenvalues
Abstract
The article considers the finding of rightmost eigenvalues of a generalised eigenvalue problem Ax = λBx. A common technique is to apply Arnoldi's method or Subspace Iteration to the shift-invert transformation. This transformation implies the knowledge of a shift, which is in essence an approximation of the eigenvalue that is searched. To avoid the need for a shift, the article proposes the use of a rational approximation of the exponential function as a transformation for the problem matrices. This transformation has the advantage that it can enhance the convergence speed of the algorithms and that it is more robust compared to shift-invert with a possible inaccuratly chosen shift.
mailto: G. De Samblanx