The column-updating method for solving nonlinear equations in Hilbert space
ESAIM: Modélisation mathématique et analyse numérique, Tome 26 (1992) no. 2, pp. 309-330. 
@article{M2AN_1992__26_2_309_0,
     author = {Gomes-Ruggiero, M. A. and Mart{\'\i}nez, J. M.},
     title = {The column-updating method for solving nonlinear equations in {Hilbert} space},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {309--330},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {26},
     number = {2},
     year = {1992},
     mrnumber = {1153004},
     zbl = {0752.65047},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1992__26_2_309_0/}
}
TY  - JOUR
AU  - Gomes-Ruggiero, M. A.
AU  - Martínez, J. M.
TI  - The column-updating method for solving nonlinear equations in Hilbert space
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1992
SP  - 309
EP  - 330
VL  - 26
IS  - 2
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://archive.numdam.org/item/M2AN_1992__26_2_309_0/
LA  - en
ID  - M2AN_1992__26_2_309_0
ER  - 
%0 Journal Article
%A Gomes-Ruggiero, M. A.
%A Martínez, J. M.
%T The column-updating method for solving nonlinear equations in Hilbert space
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1992
%P 309-330
%V 26
%N 2
%I AFCET - Gauthier-Villars
%C Paris
%U http://archive.numdam.org/item/M2AN_1992__26_2_309_0/
%G en
%F M2AN_1992__26_2_309_0
Gomes-Ruggiero, M. A.; Martínez, J. M. The column-updating method for solving nonlinear equations in Hilbert space. ESAIM: Modélisation mathématique et analyse numérique, Tome 26 (1992) no. 2, pp. 309-330. http://archive.numdam.org/item/M2AN_1992__26_2_309_0/

[1] R. H. Bartels and G. H. Golub, The Simplex Method of Linear Programming using LU decomposition, Comm. ACM12 (1969) 266-268. | Zbl

[2] C. G. Broyden, A class of methods for solving nonlinear simultaneous equations, Math. Comp. 19 1965) 577-593. | MR | Zbl

[3] C. G. Broyden, The convergence of an algorithm for solving sparse nonlinear Systems, Math. Comp. 25 (1971) 285-294. | MR | Zbl

[4] C. G. Broyden, J. E. Dennis and J. J. Moré, On the local and superlinear convergence of quasi-Newton methods, J. Inst. Math. Appl. 12 (1973) 223-246. | MR | Zbl

[5] J. E. Dennis, Toward a unified convergence theory for Newton-like methods, in L. B. Rall, ed., Nonlinear functional analysis and applications, Academic Press, New York, London, 1971, pp. 425-472. | MR | Zbl

[6] J. E. Dennis and J. J. Moré, A charactenzation of superlinear convergence and its application to quasi-Newton methods, Math. Comp. 28 (1974) 543-560. | MR | Zbl

[7] J. E. Dennis and R. B. Schnabel, Numerical methods for unconstrained optimization and nonlinear equations, Prentice Hall, Englewood Cliffs, New Jersey, 1983. | MR | Zbl

[8] J. E. Dennis and R. B. Schnabel, A View of Unconstrained Optimization, to appear in Handbook m Operations Research and Management Science, Vol.1, Optimization, G. L. Nemhauser, AHG Rinnooy Kan, M. J. Tood, eds., North Holland, Amsterdam 1989. | MR

[9] J. E. Dennis and H. F. Walker, Convergence theorems for least-change secant update methods, SIAM J. Numer. Anal. 18 (1981), 949-987. | MR | Zbl

[10] I. S. Duff, A. M. Erisman and J. K. Reid, Direct methods for sparse matrices, Clarendon Press, Oxford, 1986. | MR | Zbl

[11] A. George and E. Ng, Symbolic factorization for sparse Gaussian elimination with partial pivoting, SIAM J. Sci. Statist. Comput. 8 (1987), 877-898. | MR | Zbl

[12] G. H. Golub and Ch. F. Van Loan, Matrix Computations, John Hopkins, Baltimore, 1983. | MR | Zbl

[13] W. A. Gruver and E. Sachs, algorithmic methods in optimal control, Pitman, Boston, London, Melbourne, 1981. | MR | Zbl

[14] L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, MacMillan, New York, 1964. | MR | Zbl

[15] T. Kato, Perturbation theory for linear operators, Springer Verlag, New York, 1966. | MR | Zbl

[16] A. Kolmogoroff and S. Fomin, Elements of the Theory of Functions and Functional Analysis, Izdat. Moscow Univ., Moscow, 1954. | Zbl

[17] J. M. Martinez, A quasi-Newton method with modification of one column periteration, Computing 33 (1984), 353-362. | MR | Zbl

[18] J. M. Martínez, A new family of quasi-Newton methods with direct secant updates of matrix factorizations, SIAM J. Numer. Anal. 27 (1990), 1034-1049. | MR | Zbl

[19] E. S. Marwil, Convergence results for Schubert's method for solving sparse nonlinear equations, SIAM J. Numer. Anal. 16 (1979), 588-604. | MR | Zbl

[20] H. Matthies and G. Strang, The solution of nonlinear finite element equations, Internat. J. Numer. Methods in Engrg. 14 (1979), 1613-1626. | MR | Zbl

[21] J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York, 1970. | MR | Zbl

[22] E. Sachs, Convergence rates of quasi-Newton algorithms for some nonsmooth optimization problems, SIAM J. Control Optim. 23 (1985), 401-418. | MR | Zbl

[23] E. Sachs, Broyden's method in Hilbert space, Math. Programming 35 (1986), 71-82. | MR | Zbl

[24] L. K. Schubert, Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian, Math. Comp. 24 (1970), 27-30. | MR | Zbl

[25] L. K. Schubert, An interval arithmetic approach for the construction of an almost globally convergence method for the solution of the nonlinear Poisson equation on the unit square, SIAM J. Sci. Statist. Comput. 5 (1984), 427-452. | MR | Zbl

[26] H. Schwetlick, Numerische Lösung nichtlinearer Gleichungen, Berlin : Deutscher Verlag der Wissenschaften, 1978. | MR | Zbl

[27] Ph. L. Toint, Numerical solution of large sets of algebraic nonlinear equations, Math. Comp. 16 (1986), 175-189. | MR | Zbl