Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian

Author:
L. K. Schubert

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

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**C. G. Broyden, "A class of methods for solving nonlinear simultaneous equations,"*Math. Comp.*, v. 19, 1965, pp. 577-593. MR**33**#6825. MR**0198670 (33:6825)****[2]**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.**[3]**F. J. Zeleznik, "Quasi-Newton methods for nonlinear equations,"*J. Assoc. Comput. Mach.*, v. 15, 1968, pp. 265-271. MR**0237094 (38:5387)****[4]**J. G. P. Barnes, "An algorithm for solving nonlinear equations based on the secant method,"*Comput. J.*, v. 8, 1965, pp. 66-72. MR**31**#5330. MR**0181101 (31:5330)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0258276-9

Keywords:
Quasi-Newton method,
nonlinear simultaneous equations,
approximation to Jacobian,
nonlinear differential equations

Article copyright:
© Copyright 1970
American Mathematical Society