In this paper the construction of diagonal matrices, in some sense approximating the inverse of a given square matrix, is described. The matrices are constructed using the well-known computer algebra system Maple. The techniques we show are applicable to square matrices in general. Results are given for use in Parallel diagonal-implicit Runge-Kutta (PDIRK) methods. For an s-stage Radau IIA corrector we conjecture $s!$ possibilities for the diagonal matrices.

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Department of Numerical Mathematics [NM]

Lioen, W.M. (1995). On the diagonal approximation of full matrices. Department of Numerical Mathematics [NM]. CWI.