Fixed points of C2 maps

✍ Scribed by Layne T. Watson

• Publisher: Elsevier Science
• Year: 1979
• Tongue: English
• Weight: 684 KB
• Volume: 5
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/0771-050x(79)90009-3

✦ Synopsis

S. N. Chow and J. A. Yorke have proposed in abstract terms an algorithm for computing fixed points of C 2 maps that is globally convergent with probability one. A numerical implementation of that algorithm is presented here, where careful attention has been paid to computational efficiency, accuracy, and robustness. Convergence proofs for the numerical algorithm require differential geometry, and are given elsewhere. FORTRAN subroutines are given and explained in detail, and some typical numerical results are presented. It is shown how to modify the subroutines to compute zeros and handle some large sparse problems.