Fractional-rational regularization of a system of linear equations over the skew-field of quaternions

We generalize the Padé approximation method of transforming a power series into a rational function for systems of linear equations over the skew-field of quaternions. We carry out a regularization of the solution for the case when the operator equation is ill-posed. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 89–95.