Document Zbl 0385.65027

On the convergence of a quasi-Newton method for sparse nonlinear systems. (English) Zbl 0385.65027

Math. Comput. 32, 447-451 (1978).

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MSC:

65H10	Numerical computation of solutions to systems of equations
65K05	Numerical mathematical programming methods

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References:

[1]	C. G. Broyden, A class of methods for solving nonlinear simultaneous equations, Math. Comp. 19 (1965), 577 – 593. · Zbl 0131.13905
[2]	C. G. Broyden, The convergence of single-rank quasi-Newton methods, Math. Comp. 24 (1970), 365 – 382. · Zbl 0208.18403
[3]	C. G. Broyden, The convergence of an algorithm for solving sparse nonlinear systems, Math. Comp. 25 (1971), 285 – 294. · Zbl 0227.65038
[4]	C. G. Broyden, J. E. Dennis Jr., and Jorge J. Moré, On the local and superlinear convergence of quasi-Newton methods, J. Inst. Math. Appl. 12 (1973), 223 – 245. · Zbl 0282.65041
[5]	J. E. Dennis Jr. and Jorge J. Moré, A characterization of superlinear convergence and its application to quasi-Newton methods, Math. Comp. 28 (1974), 549 – 560. · Zbl 0282.65042
[6]	L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, Translated from the Russian by D. E. Brown. Edited by A. P. Robertson. International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Co., New York, 1964. · Zbl 0127.06104
[7]	L. K. Schubert, Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian, Math. Comp. 24 (1970), 27 – 30. · Zbl 0198.49402

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