A survey of homotopy methods for smooth mappings

Iterative Solution of Nonlinear Equations in Several Variables

2000 • 6,865 citations

Bifurcation from simple eigenvalues

1971 • 1,902 citations

Some global results for nonlinear eigenvalue problems

1971 • 1,826 citations

Topology from the Differentiable Viewpoint.

1967 • 1,474 citations

Computer solution of ordinary differential equations : the initial value problem

1975 • 1,324 citations

NUMERICAL SOLUTION OF BIFURCATION AND NONLINEAR EIGENVALUE PROBLEMS.

1977 • 1,051 citations

Transversal mappings and flows

2008 • 840 citations

The Application of Newton’s Method to the Problem of Elastic Stability

1972 • 738 citations

Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations

1980 • 437 citations

A convergent process of price adjustment and global newton methods

1976 • 420 citations

Widely Convergent Method for Finding Multiple Solutions of Simultaneous Nonlinear Equations

1972 • 377 citations

Finding zeroes of maps: homotopy methods that are constructive with probability one

1978 • 370 citations

A Constructive Proof of the Brouwer Fixed-Point Theorem and Computational Results

1976 • 204 citations

A globally convergent algorithm for computing fixed points of C2 maps

1979 • 160 citations

Solution Fields of Nonlinear Equations and Continuation Methods

1980 • 154 citations

A switching‐parameter algorithm for finding multiple solutions of nonlinear resistive circuits

1976 • 149 citations

The homotopy continuation method: numerically implementable topological procedures

1978 • 146 citations

On Algorithms for Solving f(x)=0

1979 • 128 citations

Global Homotopies and Newton Methods

1978 • 127 citations

On Solving Nonlinear Equations with a One-Parameter Operator Imbedding

1968 • 123 citations

Perturbed bifurcation theory

1973 • 121 citations

Global analysis and economics VI

1976 • 106 citations

Numerical Solutions by the Continuation Method

1973 • 101 citations

Numerical Methods for a Class of Finite Dimensional Bifurcation Problems

1978 • 99 citations

A stepsize control for continuation methods and its special application to multiple shooting techniques

1979 • 95 citations

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 • 87 citations

An Algorithm That is Globally Convergent with Probability One for a Class of Nonlinear Two-Point Boundary Value Problems

1979 • 84 citations

Eine Methode zur berechnung s�mtlicher L�sungen von Polynomgleichungssystemen

1977 • 82 citations

The Solution of Non-Linear Equations and of Differential Equations with Two-Point Boundary Conditions

1961 • 78 citations

Difference Equations Associated with Boundary Value Problems for Second Order Nonlinear Ordinary Differential Equations

1974 • 77 citations

Recent Advances in Numerical Analysis.

1982 • 76 citations

Algorithm 555: Chow-Yorke Algorithm for Fixed Points or Zeros of C ² Maps [C5]

1980 • 60 citations

Zur L�sung parameterabh�ngiger nichtlinearer Gleichungen mit singul�ren Jacobi-Matrizen

1978 • 60 citations

On Tracing an Implicitly Defined Curve by Quasi-Newton Steps and Calculating Bifurcation by Local Perturbations

1981 • 59 citations

An extension of the Newton-Kantorovič method for solving nonlinear equations with an application to elasticity

1966 • 56 citations

A modified continuation method for the numerical solution of nonlinear two-point boundary value problems by shooting techniques

1976 • 55 citations

Global Continuation Methods for Finding all Solutions to Polynomial Systems of Equations in N Variables

1980 • 44 citations

Numerical solution of bifurcation problems for ordinary differential equations

1977 • 43 citations

Nonlinear elliptic boundary value problems versus their finite difference approximations: numerically irrelevant solutions.

1981 • 43 citations

Continuation of Newton’s Method Through Bifurcation Points

1969 • 43 citations

Adaptive step size selection for use with the continuation method

1978 • 39 citations

The Leray-Schauder continuation method is a constructive element in the numerical study of nonlinear eigenvalue and bifurcation problems

1979 • 36 citations

Une méthode de résolution d'une catégorie d'équations transcendantes

1934 • 33 citations

Topological Perturbations in the Numerical Study of Nonlinear Eigenvalue and Bifurcation Problems

1980 • 30 citations

Numerische Behandlung von Verzweigungsproblemen bei gew�hnlichen Differentialgleichungen

1979 • 27 citations

Numerical integration of the Davidenko equation

1981 • 24 citations

On the bifurcation diagram of discrete analogues for ordinary bifurcation problems

1979 • 17 citations

A derivative-free arc continuation method and a bifurcation technique

1981 • 12 citations

Über einen Ordnungsbegriff bei Einbettungsalgorithmen zur Lösung nichtlinearer Gleichungen

1976 • 11 citations

Ein Iterationsverfahren zur Lösung spezieller nichtlinearer Randwertprobleme

1972 • 11 citations

Discrete correction methods for operator equations

1981 • 10 citations

Chord techniques and Newton's method for discrete bifurcation problems

1980 • 7 citations

On a Discretization of y″ + λ yk = 0

1975 • 7 citations

Ein implementierbarer Algorithmus zur Lösung nichtlinearer Gleichungssysteme bei schwach singulärer Einbettung

1980 • 2 citations