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.

Approximation (acm G.1.2), Roots of Nonlinear Equations (acm G.1.5), Ordinary Differential Equations (acm G.1.7), Applications (acm I.1.4)
Systems of equations (msc 65H10), None of the above, but in MSC2010 section 65Dxx (msc 65D99), Matrix norms, conditioning, scaling (msc 65F35)
Department of Numerical Mathematics [NM]

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