We rigorously study a recent algorithm due to Davidchack and Lai (DL) [Davi
dchack RL, Lai Y-C. Phys Rev E 1999;60(5):6172-5] for efficiently locating
complete sets of hyperbolic periodic orbits for chaotic maps. We give theor
ems concerning sufficient conditions on convergence and also describing var
iable sized basins of attraction of initial seeds, thus pointing out a part
icularly attractive feature of the DL-algorithm. We also point out the true
role of involutary matrices which is different from that implied by Schmel
cher and Diakonos [Schmelcher P, Diakonos FK. Phys Rev E 1998;57(3):2739-46
] and propagated by Davidchack and Lai. (C) 2001 Elsevier Science Ltd. All
rights reserved.