A class of methods for solving nonlinear simultaneous equations

Author:
C. G. Broyden

Journal:
Math. Comp. **19** (1965), 577-593

MSC:
Primary 65.50

DOI:
https://doi.org/10.1090/S0025-5718-1965-0198670-6

MathSciNet review:
0198670

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References | Similar Articles | Additional Information

**[1]**W. C. Davidon, "Variable metric method for minimization," A.E.C. Research and Development Report, ANL-5990 (Rev. TID-4500, 14th ed.), 1959. MR**1094786 (91k:90160)****[2]**R. Fletcher & M. J. D. Powell, "A rapidly convergent descent method for minimization,"*Comput. J.*, v. 6, 1963/64, pp. 163-168. MR**27**#2096. MR**0152116 (27:2096)****[3]**F. Freudenstein & B. Roth, "Numerical solutions of systems of nonlinear equations,"*J. Assoc. Comput. Mach.*, v. 10, 1963, pp. 550-556. MR**0164442 (29:1739)****[4]**A. S. Householder,*Principles of Numerical Analysis*, McGraw-Hill, New York, 1953, pp. 135-138. MR**15**, 470. MR**0059056 (15:470b)****[5]**W. Kizner, "A numerical method for finding solutions of nonlinear equations,"*J. Soc. Indust. Appl. Math.*, v. 12, 1964, pp. 424-428. MR**0168115 (29:5379)****[6]**M. J. D. Powell, "An efficient method for finding the minimum of a function of several variables without calculating derivatives,"*Comput. J.*, v. 7, 1964, pp. 155-162. MR**0187376 (32:4828)****[7]**M. J. D. Powell, "A method for minimizing a sum of squares of non-linear functions without calculating derivatives,"*Comput. J.*, v. 7, 1965, pp. 303-307. MR**0172456 (30:2675)****[8]**B. Randell, "The Whetstone KDF9 ALGOL Translator,"*Introduction to System Programming*, P. Wegner (Ed.), Academic Press, London, 1964, pp. 122-136.**[9]**R. S. Varga,*Matrix Iterative Analysis*, Prentice-Hall, Englewood Cliffs, N. J. and International, London, 1962, p. 9. MR**28**#1725. MR**0158502 (28:1725)****[10]**R. S. Varga, op. cit., p. 62.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1965-0198670-6

Article copyright:
© Copyright 1965
American Mathematical Society