Free Access
Issue
ESAIM: M2AN
Volume 26, Number 2, 1992
Page(s) 309 - 330
DOI https://doi.org/10.1051/m2an/1992260203091
Published online 31 January 2017
  1. R. H. BARTELS and G. H. GOLUB, The Simplex Method of Linear Programming using LU decomposition, Comm. ACM12 (1969) 266-268. [Zbl: 0181.19104]
  2. C. G. BROYDEN, A class of methods for solving nonlinear simultaneous equations, Math. Comp. 19 1965) 577-593. [MR: 198670] [Zbl: 0131.13905]
  3. C. G. BROYDEN, The convergence of an algorithm for solving sparse nonlinear Systems, Math. Comp. 25 (1971) 285-294. [MR: 297122] [Zbl: 0227.65038]
  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: 341853] [Zbl: 0282.65041]
  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: 278556] [Zbl: 0276.65029]
  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: 343581] [Zbl: 0282.65042]
  7. J. E. DENNIS and R. B. SCHNABEL, Numerical methods for unconstrained optimization and nonlinear equations, Prentice Hall, Englewood Cliffs, New Jersey, 1983. [MR: 702023] [Zbl: 0579.65058]
  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: 1105100]
  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: 638993] [Zbl: 0527.65032]
  10. I. S. DUFF, A. M. ERISMAN and J. K. REID, Direct methods for sparse matrices, Clarendon Press, Oxford, 1986. [MR: 892734] [Zbl: 0604.65011]
  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: 911061] [Zbl: 0632.65021]
  12. G. H. GOLUB and Ch. F. VAN LOAN, Matrix Computations, John Hopkins, Baltimore, 1983. [MR: 733103] [Zbl: 0559.65011]
  13. W. A. GRUVER and E. SACHS, algorithmic methods in optimal control, Pitman, Boston, London, Melbourne, 1981. [MR: 604361] [Zbl: 0456.49001]
  14. L. V. KANTOROVICH and G. P. AKILOV, Functional analysis in normed spaces, MacMillan, New York, 1964. [MR: 213845] [Zbl: 0127.06104]
  15. T. KATO, Perturbation theory for linear operators, Springer Verlag, New York, 1966. [MR: 203473] [Zbl: 0148.12601]
  16. A. KOLMOGOROFF and S. FOMIN, Elements of the Theory of Functions and Functional Analysis, Izdat. Moscow Univ., Moscow, 1954. [Zbl: 0501.46001]
  17. J. M. MARTINEZ, A quasi-Newton method with modification of one column periteration, Computing 33 (1984), 353-362. [MR: 773934] [Zbl: 0546.90102]
  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: 1051122] [Zbl: 0702.65053]
  19. E. S. MARWIL, Convergence results for Schubert's method for solving sparse nonlinear equations, SIAM J. Numer. Anal. 16 (1979), 588-604. [MR: 537273] [Zbl: 0453.65033]
  20. H. MATTHIES and G. STRANG, The solution of nonlinear finite element equations, Internat. J. Numer. Methods in Engrg. 14 (1979), 1613-1626. [MR: 551801] [Zbl: 0419.65070]
  21. J. M. ORTEGA and W. C. RHEINBOLDT, Iterative solution of nonlinear equations in several variables, Academic Press, New York, 1970. [MR: 273810] [Zbl: 0241.65046]
  22. E. SACHS, Convergence rates of quasi-Newton algorithms for some nonsmooth optimization problems, SIAM J. Control Optim. 23 (1985), 401-418. [MR: 784577] [Zbl: 0571.90083]
  23. E. SACHS, Broyden's method in Hilbert space, Math. Programming 35 (1986), 71-82. [MR: 842635] [Zbl: 0598.90080]
  24. L. K. SCHUBERT, Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian, Math. Comp. 24 (1970), 27-30. [MR: 258276] [Zbl: 0198.49402]
  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: 740859] [Zbl: 0539.65076]
  26. H. SCHWETLICK, Numerische Lösung nichtlinearer Gleichungen, Berlin : Deutscher Verlag der Wissenschaften, 1978. [MR: 519682] [Zbl: 0402.65028]
  27. Ph. L. TOINT, Numerical solution of large sets of algebraic nonlinear equations, Math. Comp. 16 (1986), 175-189. [MR: 815839] [Zbl: 0614.65058]

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