On the convergence of block constrained nonlinear equation solvers Footnote^∗

This work is partially supported under NASA Lewis Grant NAG3-666

References

• Antman , S. and Keller , S. 1969 . Bifurcation Theory and Nonlinear Eigenvalue Problems , New York : W. A. Benjamin Inc. .
   Google Scholar
• Arechaga , T. and Padovan , J. 1982 . Formal numerical characteristics of elliptically constrained incremental Newton-Raphson algorithms . Int. J. Engineering Science , 20 : 1077 – 1097 .
   Google Scholar
• Bathe , K. J. 1984 . Finite Element Procedures in Engineering Analysis , New Jersey : Prentice Hall .
   Google Scholar
• Crisfield , M. A. 1981 . A fast incremental iterative procedure that handles snap through . Computer Structures , 13 : 55 – 62 .
   Web of Science ®Google Scholar
• Krishna , L. 1985 . Error bounds for the SSOR semi-iterative method . SIAM J. Alg. Dist. Methods , 6 : 245 – 250 .
   Google Scholar
• Moscarello , R. and Padovan , J. 1986 . Locally bound constrained Newton-Raphson solution algorithms . Computers and Structures , 23 : 181 – 197 .
   Google Scholar
• Ortega , J. M. and Rheinboldt , W. C. 1970 . Iterative Solutions on Nonlinear Equations in Several Variables , New York : Academic Press .
   Google Scholar
• Padovan , J. and Tovichakchaikal , S. 1982 . Self adaptive closed constrained solution algorithms for nonlinear conduction . Numerical Heat Transfer , 5 : 253 – 274 .
   Google Scholar
• Parter , S. and Steuerwalt , M. 1982 . Block iterative methods for elliptic and parabolic difference equations . SIAM J. Numerical Anal. , 19 : 1173 – 1195 .
   Web of Science ®Google Scholar
• Riks , E. 1979 . An incremental approach to the solution of snapping and buckling problems . Int. J. Solids Structures , 15 : 529 – 551 .
   Web of Science ®Google Scholar
• Wempner , G. 1971 . Discrete approximations related to nonlinear theories of solids . Int. J. Solids Structures , 7 : 1581 – 1591 .
   Google Scholar
• White , R. 1986 . Parallel algorithms for nonlinear problems . SIAM J. Alg. Disc. Methods , 7 : 137 – 148 .
   Google Scholar
• Varga , R. 1962 . Matrix Iterative Analysis , NJ : Prentice Hall .
   Google Scholar
• Zienkiewicz , O. 1982 . The Finite Element Method , New York : Mc Graw Hill .
   Google Scholar