This is reprinted, with permission from the author and the publisher, from the original paper published in Research Association of Applied Geometry (RAAG) Memoirs, Vol. 2 (1958) pp. 29-46, published by Gakujutsu Bunken Fukyu-kai, Tokyo, Japan.
"Theory of an interval algebra and its application to numerical analysis [Reprint of Res. Assoc. Appl. Geom. Mem. 2 (1958), 29–46]." Japan J. Indust. Appl. Math. 26 (2-3) 125 - 143, October 2009.