International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 2, Pages 299-308

Modifications of the continuation method for the solution of systems of nonlinear equations

G. R. Lindfield and D. C. Simpson

Computer Centre, The University of Aston in Birmingham, 15 Coleshill Street, Birmingham B4 7PA, United Kingdom

Received 20 September 1978

Copyright © 1979 G. R. Lindfield and D. C. Simpson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Modifications are proposed to the Davidenko-Broyden algorithm for the solution of a system of nonlinear equations. The aim of the modifications is to reduce the overall number of function evaluations by limiting the number of function evaluations for any one subproblem. To do this alterations are made to the strategy used in determining the subproblems to be solved. The modifications are compared with other methods for a wide range of test problems, and are shown to significantly reduce the number of function evaluations for the difficult problems. For the easier problems the modified method is equivalent to the Davidenko-Broyden algorithm.