A survey of homotopy methods for smooth mappings

[1]  J. Yorke,et al.  Finding zeroes of maps: homotopy methods that are constructive with probability one , 1978 .

[2]  G. A. Thurston.  Continuation of Newton’s Method Through Bifurcation Points , 1969 .

[3]  William F. Schmidt,et al.  Adaptive step size selection for use with the continuation method , 1978 .

[4]  M. Prüfer,et al.  The Leray-Schauder continuation method is a constructive element in the numerical study of nonlinear eigenvalue and bifurcation problems , 1979 .

[5]  G. Meyer.  On Solving Nonlinear Equations with a One-Parameter Operator Imbedding , 1968 .

[6]  P. Anselone,et al.  AN EXTENSION OF THE NEWTON-KANTOROVIC METHOD FOR SOLVING NONLINEAR EQUATIONS, , 1966 .

[7]  R. B. Kearfott.  A derivative-free arc continuation method and a bifurcation technique , 1981 .

[8]  Klaus Böhmer,et al.  Discrete correction methods for operator equations , 1981 .

[9]  R. Kellogg,et al.  A Constructive Proof of the Brouwer Fixed-Point Theorem and Computational Results , 1976 .

[10]  J. Yorke,et al.  The homotopy continuation method: numerically implementable topological procedures , 1978 .

[11]  P. Deuflhard.  A stepsize control for continuation methods and its special application to multiple shooting techniques , 1979 .

[12]  E. Bohl,et al.  On the bifurcation diagram of discrete analogues for ordinary bifurcation problems , 1979 .

[13]  F. H. Branin.  Widely convergent method for finding multiple solutions of simultaneous nonlinear equations , 1972 .

[14]  K. Georg.  On Tracing an Implicitly Defined Curve by Quasi-Newton Steps and Calculating Bifurcation by Local Perturbations , 1981 .

[15]  W. I. Zangwill,et al.  Global Continuation Methods for Finding all Solutions to Polynomial Systems of Equations in N Variables , 1980 .

[16]  J. Milnor.  Topology from the differentiable viewpoint , 1965 .

[17]  E. Riks.  The Application of Newton's Method to the Problem of Elastic Stability , 1972 .

[18]  Layne T. Watson,et al.  Algorithm 555: Chow-Yorke Algorithm for Fixed Points or Zeros of C2 Maps [C5] , 1980, TOMS.

[19]  Edmond Lahaye,et al.  Une méthode de résolution d'une catégorie d'équations transcendantes , 1934 .

[20]  H. B. Keller.  Global Homotopies and Newton Methods , 1978 .

[21]  Paul H. Rabinowitz,et al.  Some global results for nonlinear eigenvalue problems , 1971 .

[22]  Peter R. Turner,et al.  Topics in Numerical Analysis , 1982 .

[23]  H. Peitgen,et al.  Nonlinear elliptic boundary value problems versus their finite difference approximations: numerically irrelevant solutions. , 1981 .

[24]  P. Deuflhard,et al.  A modified continuation method for the numerical solution of nonlinear two-point boundary value problems by shooting techniques , 1976 .

[25]  K. Georg.  Numerical integration of the Davidenko equation , 1981 .

[26]  H. Weber.  Numerische Behandlung von Verzweigungsproblemen bei gewöhnlichen Differentialgleichungen , 1979 .

[27]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[28]  S. Smale.  Convergent process of price adjust-ment and global newton methods , 1976 .

[29]  E. Bohl.  Chord techniques and Newton's method for discrete bifurcation problems , 1980 .

[30]  E. L. Allgower.  On a Discretization of y ″ + λ y k = 0 , 1975 .

[31]  W. Gähler.  R. Abraham and J. Robbin, Transversal Mappings and Flows. X + 161 S. m. Fig. New York/Amsterdam 1967. W. A. Benjamin, Inc. Preis geb. $ 12,50 , 1969 .

[32]  C. D. Boor,et al.  Recent Advances in Numerical Analysis. , 1982 .

[33]  W. Rheinboldt.  Numerical methods for a class of nite dimensional bifur-cation problems , 1978 .

[34]  F. Drexler.  Eine Methode zur berechnung sämtlicher Lösungen von Polynomgleichungssystemen , 1977 .

[35]  R. Gaines,et al.  DIFFERENCE EQUATIONS ASSOCIATED WITH BOUNDARY VALUE PROBLEMS FOR SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS , 1974 .

[36]  L. Chua,et al.  A switching-parameter algorithm for finding multiple solutions of nonlinear resistive circuits , 1976 .

[37]  E. Allgower,et al.  Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations , 1980 .

[38]  L. Watson.  An Algorithm That is Globally Convergent with Probability One for a Class of Nonlinear Two-Point Boundary Value Problems , 1979 .

[39]  E. Wasserstrom.  Numerical Solutions by the Continuation Method , 1973 .

[40]  H. Schwetlick,et al.  Zur Lösung parameterabhängiger nichtlinearer Gleichungen mit singulären Jacobi-Matrizen , 1978 .

[41]  L. Shampine,et al.  Computer solution of ordinary differential equations : the initial value problem , 1975 .

[42]  W. Langford.  Numerical solution of bifurcation problems for ordinary differential equations , 1977 .

[43]  C. Haselgrove,et al.  The Solution of Non-Linear Equations and of Differential Equations with Two-Point Boundary Conditions , 1961, Comput. J..

[44]  L. Watson.  A globally convergent algorithm for computing fixed points of C2 maps , 1979 .

[45]  S. Smale.  Global analysis and economics VI: Geometric analysis of Pareto Optima and price equilibria under classical hypotheses , 1976 .

[46]  H. Keller,et al.  Perturbed bifurcation theory , 1973 .

[47]  H. Peitgen,et al.  Topological Perturbations in the Numerical Study of Nonlinear Eigenvalue and Bifurcation Problems , 1980 .

[48]  Werner C. Rheinboldt,et al.  Solution Fields of Nonlinear Equations and Continuation Methods , 1980 .

[49]  M. Crandall,et al.  Bifurcation from simple eigenvalues , 1971 .

[50]  M. Hirsch,et al.  On Algorithms for Solving f(x)=0 , 1979 .