  The Lorentz Integral Transform (LIT) method is reformulated via the Lanczos
algorithm both for inclusive and exclusive reactions. The new technique is
tested for the total photoabsorption cross section of 3H and 4He. Due to the
rapid convergence of the algorithm one has a decrease in cpu time by two orders
of magnitude, but at the same time an excellent agreement with the results of a
conventional LIT calculation. The present work opens up the possibility of ab
initio calculations for inclusive and exclusive processes for A greater equal 6
with inclusion of complete final state interactions.
