On the convergence of a quasi-Newton method for sparse nonlinear systems

Lam, Binh

doi:10.1090/S0025-5718-1978-0483389-3

On the convergence of a quasi-Newton method for sparse nonlinear systems
HTML articles powered by AMS MathViewer

by Binh Lam PDF

Math. Comp. 32 (1978), 447-451 Request permission

Abstract:

It is shown that an algorithm for solving a system of nonlinear equations where the Jacobian is known to be sparse, converges locally and Q-superlinearly.

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
C. G. Broyden, The convergence of single-rank quasi-Newton methods, Math. Comp. 24 (1970), 365–382. MR 279993, DOI 10.1090/S0025-5718-1970-0279993-0
C. G. Broyden, The convergence of an algorithm for solving sparse nonlinear systems, Math. Comp. 25 (1971), 285–294. MR 297122, DOI 10.1090/S0025-5718-1971-0297122-5
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. MR 341853
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. MR 343581, DOI 10.1090/S0025-5718-1974-0343581-1
L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Company, New York, 1964. Translated from the Russian by D. E. Brown; Edited by A. P. Robertson. MR 0213845
L. K. Schubert, Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian, Math. Comp. 24 (1970), 27–30. MR 258276, DOI 10.1090/S0025-5718-1970-0258276-9