Free Access
Volume 26, Number 2, 1992
Page(s) 309 - 330
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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you