On the diagonal approximation of full matrices
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.