CALCULATIONS OF PHOTOIONIZATION CROSS SECTIONS USING THE COMPLEX CORDINATE METHOD AND THE LANCZOS ALGORITHM Hiroya Suno$^\S$, Lidija Andric$^\S$, Tasko P. Grozdanov$^\S$$^\P$ and Ronald McCarroll$^\S$ $^\S$Laboratoire de Dynamique des Ions, Atomes et Mol=E9cules (ESA 7066 du CNRS), Universit=E9 Pierre et Marie Curie, 4 place Jussieu, 75252-Paris Cedex 05, France $^\P$Institute of Physics, P.O. Box, 11001 Belgrade, Yugoslavia A new method, using complex coordinates, is proposed to determine photoionization cross sections of atoms without the need to calculate explicitly the continuum wave functions. Key elements in the calculations are the use of a discrete variable representation together with a variant of the Lanczos iterative diagonalization procedure.