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On the convergence of a quasi-Newton method for sparse nonlinear systems
Author:
Binh Lam
Journal:
Math. Comp. 32 (1978), 447-451
MSC:
Primary 65H10
MathSciNet review:
0483389
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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.
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C.
G. Broyden, A class of methods for solving
nonlinear simultaneous equations, Math.
Comp. 19 (1965),
577–593. MR 0198670
(33 #6825), http://dx.doi.org/10.1090/S0025-5718-1965-0198670-6
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C.
G. Broyden, The convergence of single-rank
quasi-Newton methods, Math. Comp. 24 (1970), 365–382. MR 0279993
(43 #5714), http://dx.doi.org/10.1090/S0025-5718-1970-0279993-0
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C.
G. Broyden, The convergence of an algorithm for
solving sparse nonlinear systems, Math.
Comp. 25 (1971),
285–294. MR 0297122
(45 #6180), http://dx.doi.org/10.1090/S0025-5718-1971-0297122-5
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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 0341853
(49 #6599)
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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 0343581
(49 #8322), http://dx.doi.org/10.1090/S0025-5718-1974-0343581-1
- [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
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(35 #4699)
- [7]
L.
K. Schubert, Modification of a quasi-Newton method
for nonlinear equations with a sparse Jacobian, Math. Comp. 24 (1970), 27–30. MR 0258276
(41 #2923), http://dx.doi.org/10.1090/S0025-5718-1970-0258276-9
- [1]
- C. G. BROYDEN, "A class of methods for solving nonlinear simultaneous equations," Math. Comp., v. 19, 1965, pp. 577-593. MR 0198670 (33:6825)
- [2]
- C. G. BROYDEN, "The convergence of single-rank quasi-Newton methods," Math. Comp., v. 24, 1970, pp. 365-382. MR 0279993 (43:5714)
- [3]
- C. G. BROYDEN, "The convergence of an algorithm for solving sparse nonlinear systems," Math. Comp., v. 25, 1971, pp. 285-294. MR 0297122 (45:6180)
- [4]
- C. G. BROYDEN, J. E. DENNIS & J. J. MORÉ, "On the local and superlinear convergence of quasi-Newton methods," J. Inst. Math. Appl., v. 12, 1973, pp. 223-246. MR 0341853 (49:6599)
- [5]
- J. E. DENNIS & J. J. MORÉ, "A characterization of superlinear convergence and its application to quasi-Newton methods," Math. Comp., v. 28, 1974, pp. 549-560. MR 0343581 (49:8322)
- [6]
- L. V. KANTOROVIC & G. P. AKILOV, Functional Analysis in Normed Spaces, English transl., Pergamon Press, 1964. MR 0213845 (35:4699)
- [7]
- L. K. SCHUBERT, "Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian," Math. Comp., v. 24, 1970, pp. 27-30. MR 0258276 (41:2923)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1978-0483389-3
PII:
S 0025-5718(1978)0483389-3
Article copyright:
© Copyright 1978 American Mathematical Society
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