Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian
HTML articles powered by AMS MathViewer
- by L. K. Schubert PDF
- Math. Comp. 24 (1970), 27-30 Request permission
Abstract:
For solving large systems of nonlinear equations by quasi-Newton methods it may often be preferable to store an approximation to the Jacobian rather than an approximation to the inverse Jacobian. The main reason is that when the Jacobian is sparse and the locations of the zeroes are known, the updating procedure can be made more efficient for the approximate Jacobian than for the approximate inverse Jacobian.References
- C. G. Broyden, A class of methods for solving nonlinear simultaneous equations, Math. Comp. 19 (1965), 577–593. MR 198670, DOI 10.1090/S0025-5718-1965-0198670-6 E. M. Rosen, "A Review of Quasi-Newton Methods in Nonlinear Equation Solving and Unconstrained Optimization," Proc. Twenty-first Nat. Conf. ACM, Thompson, Washington, D. C., 1966, pp. 37–41.
- Frank J. Zeleznik, Quasi-Newton methods for nonlinear equations, J. Assoc. Comput. Mach. 15 (1968), 265–271. MR 237094, DOI 10.1145/321450.321458
- J. G. P. Barnes, An algorithm for solving non-linear equations based on the secant method, Comput. J. 8 (1965), 66–72. MR 181101, DOI 10.1093/comjnl/8.2.113
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Math. Comp. 24 (1970), 27-30
- MSC: Primary 65.50
- DOI: https://doi.org/10.1090/S0025-5718-1970-0258276-9
- MathSciNet review: 0258276