Numerical Solution of Nonlinear Equations

ACM Transactions on Mathematical Software (TOMS)

Volumn 5, Issue 1, 1979, Pages 64-85

  Moré, Jorge J ^a   Cosnard, Michel Y ^b  

^a ARGONNE NATIONAL LABORATORY   (United States)

^b Universite de Grenoble   (France)

Author keywords

Brent's method; Brown's method; Newton's method; nonlmear equations; numerical solution

Indexed keywords

EID: 84976787118     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/355815.355820     Document Type: Article

References (9)

1. Brent, R.P. Some efficient algorithms for solving systems of nonlinear equations. SIAM J Numer Anal. 10 (1973), 327-344.
2. Brown, K.M. A quadratically convergent method for solving simultaneous nonlinear equations. Ph.D. Diss., Purdue U, Lafayette, Ind., 1966.
3. Brown, K.M., And Dennis, J.E. On the second order convergence of Brown's derivative-free method for solving simultaneous nonlinear equations. Tech. Rep. 71-7, Dept. Comptr Sci., Yale U, New Haven, Conn., 1971
4. Cosnard, M Y. A Comparison of four methods for solving systems of nonlinear equations. Tech. Rep. 75-248, Dept. Comptr Sci., Cornell U., Ithaca, 1975.
5. Curtis, A R., Powell, M.J.D., And Reid, J K. On the estimation of sparse Jacobian matrices. J Inst. Math Applic. 13 (1974), 117-119.
6. Gay, D.M., Brown's Method And Some Generalizations, With Applications To Minimization Problems. Ph.D Diss., Cornell U, Ithaca, N Y, 1975.
7. Gay, D.M., Implementing Brown's method. Rep. CNA-109, Ctr. Numer. Anal., The U. of Texas at Austin, 1975.
8. Martinez, J.M. Generalizations of the methods of Brent and Brown for solving nonlinear simultaneous equations Ph.D. Diss., U of Río de Janeiro, Brazil, 1977.
9. Shampine, L F., And Gordon, M K. Solving systems of nonlinear equations. Tech Rep. SAND-75-0450, Sandia Labs, Albuquerque, N. Mex, 1975.