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

Convex Analysis

1970 • 9,645 citations

Theory of Functional Differential Equations

1977 • 6,764 citations

The Algebraic Eigenvalue Problem

1966 • 5,231 citations

Iterative Solution of Nonlinear Equations in Several Variables

1971 • 4,427 citations

Multi-level adaptive solutions to boundary-value problems

1977 • 3,170 citations

Linear Programming and Extensions

1963 • 2,647 citations

Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces

1976 • 1,888 citations

Some global results for nonlinear eigenvalue problems

1971 • 1,826 citations

Topology from the Differentiable Viewpoint.

1967 • 1,474 citations

Equilibrium Points of Bimatrix Games

1964 • 1,252 citations

A generalization of Brouwer’s fixed point theorem

1941 • 1,181 citations

Introduction to Piecewise-Linear Topology

1972 • 1,128 citations

Bimatrix Equilibrium Points and Mathematical Programming

1965 • 1,020 citations

Solution of Equations and Systems of Equations

1967 • 963 citations

Convexity and Optimization in Finite Dimensions I

1970 • 885 citations

The Computation of Economic Equilibria.

1974 • 873 citations

Transversal mappings and flows

2008 • 840 citations

Topologie et équations fonctionnelles

1934 • 757 citations

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

1972 • 738 citations

The Core of an N Person Game

1967 • 704 citations

TOPOLOGICAL METHODS IN THE THEORY OF NON-LINEAR INTEGRAL EQUATIONS

1966 • 619 citations

Nonlinear Functional Analysis

1970 • 538 citations

The measure of the critical values of differentiable maps

1942 • 528 citations

Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe

1929 • 521 citations

�ber Abbildung von Mannigfaltigkeiten

1911 • 508 citations

Extensions of two fixed point theorems of F. E. Browder

1969 • 468 citations

Topics in nonlinear functional analysis, 1973-1974

1974 • 465 citations

Functional Differential Equations and Approximation of Fixed Points

1979 • 443 citations

A convergent process of price adjustment and global newton methods

1976 • 420 citations

The Computation of Fixed Points and Applications

1976 • 416 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

On the basic theorem of complementarity

1971 • 351 citations

Computer Solution of Ordinary Differential Equations

1976 • 345 citations

Homotopies for computation of fixed points

1972 • 327 citations

Fixed Points and Topological Degree in Nonlinear Analysis

1995 • 320 citations

Neuer beweis für die invarianz der dimensionszahl und des gebietes

1928 • 292 citations

On the number of solutions to the complementarity problem and spanning properties of complementary cones

1972 • 251 citations

Piecewise linear topology

1993 • 251 citations

The complementarity problem

1972 • 249 citations

Homotopies for computation of fixed points on unbounded regions

1972 • 214 citations

Accurate Difference Methods for Nonlinear Two-Point Boundary Value Problems

1974 • 211 citations

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

1976 • 204 citations

Some Combinatorial Lemmas in Topology

1960 • 198 citations

A generalization of the linear complementarity problem

1970 • 193 citations

SIMPLICIAL APPROXIMATION OF FIXED POINTS

1968 • 187 citations

The Solution of Systems of Piecewise Linear Equations

1976 • 177 citations

Some Efficient Algorithms for Solving Systems of Nonlinear Equations

1973 • 172 citations

Vektorfelder inn-dimensionalen Mannigfaltigkeiten

1927 • 168 citations

Nonlinear Programs with Positively Bounded Jacobians

1966 • 166 citations

A globally convergent algorithm for computing fixed points of C2 maps

1979 • 160 citations

A note on the Lemke-Howson algorithm

1974 • 156 citations

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

1976 • 149 citations

Coercivity Conditions in Nonlinear Complementarity Problems

1974 • 149 citations

The homotopy continuation method: numerically implementable topological procedures

1978 • 146 citations

Simplizialzerlegungen von Beschrankter Flachheit

1942 • 130 citations

On Solving Nonlinear Equations with a One-Parameter Operator Imbedding

1968 • 123 citations

Solving the Nonlinear Complementarity Problem by a Homotopy Method

1979 • 122 citations

Classes of functions and feasibility conditions in nonlinear complementarity problems

1974 • 114 citations

Extension of the Generalized Complementarity Problem

1976 • 109 citations

Foundations of Combinatorial Topology

1952 • 107 citations

Combinatorial topology

1991 • 102 citations

Numerical Solutions by the Continuation Method

1973 • 101 citations

The nonlinear complementarity problem with applications, part 2

1969 • 101 citations

An observation on the structure of production sets with indivisibilities

1977 • 99 citations

AN ALGORITHM FOR EQUILIBRIUM POINTS IN BIMATRIX GAMES

1961 • 97 citations

The Solution of Nonlinear Systems of Equations by A-Stable Integration Techniques

1971 • 94 citations

Computing the topological degree of a mapping inR n

1975 • 88 citations

Recent Results on Complementarity Problems

1970 • 87 citations

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

1979 • 84 citations

Deflation techniques for the calculation of further solutions of a nonlinear system

1971 • 83 citations

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

1977 • 82 citations

The continuation method for functional equations

1951 • 79 citations

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

1961 • 78 citations

Sandwich method for finding fixed points

1975 • 77 citations

Iterated deferred corrections for nonlinear boundary value problems

1968 • 76 citations

On the Convergence Rate of Algorithms for Solving Equations that are Based on Methods of Complementary Pivoting

1977 • 74 citations

Squeezing of a viscous fluid between elliptic plates

1979 • 70 citations

Computing Kakutani Fixed Points

1971 • 70 citations

Orientation in Complementary Pivot Algorithms

1976 • 68 citations

On the Computation of Fixed Points in the Product Space of Unit Simplices and an Application to Noncooperative N Person Games

1982 • 63 citations

Simplicial maps from an orientable n-pseudomanifold into Sm with the octahedral triangulation

1967 • 61 citations

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

1978 • 60 citations

On the Sperner lemma

1967 • 59 citations

On the existence and uniqueness of solutions in nonlinear complementarity theory

1977 • 57 citations

Union Jack Triangulations

1977 • 57 citations

Applied Combinatorial Mathematics

1965 • 57 citations

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

1966 • 56 citations

On triangulations for computing fixed points

1976 • 55 citations

A unification of the existence theorems of the nonlinear complementarity problem

1975 • 52 citations

Zeros of Nonlinear Functions

1961 • 49 citations

Improving the convergence of fixed-point algorithms

1978 • 49 citations

A new proof of the fundamental theorem of algebra

1974 • 48 citations

Untitled

1970 • 47 citations

Efficient Acceleration Techniques for Fixed Point Algorithms

1978 • 47 citations

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

1980 • 44 citations

Continuation of Newton’s Method Through Bifurcation Points

1969 • 43 citations

Fluid Dynamics of the Elliptic Porous Slider

1978 • 42 citations

The Computation of Equilibrium Prices

1978 • 41 citations

Optimum Quantizer Design Using a Fixed-Point Algorithm

1976 • 37 citations

A unified approach to complementarity in optimization

1974 • 37 citations

Fixed points of C2 maps

1979 • 35 citations

Generic properties of the complementarity problem

1973 • 35 citations

A Theorem on Homotopy Paths

1978 • 35 citations

On the homotopic approach to systems of equations with separable mappings

1978 • 32 citations

Mathematical programming study 2

1975 • 32 citations

On Paths Generated by Fixed Point Algorithms

1976 • 31 citations

An improvement of fixed point algorithms by using a good triangulation

1980 • 30 citations

Fluid Dynamics of the Circular Porous Slider

1974 • 30 citations

A complementary variant of Lemke's method for the linear complementary problem

1974 • 30 citations

A simplicial algorithm for the nonlinear complementarity problem

1974 • 30 citations

Simplicial Approximation of an Equilibrium Point for Non-Cooperative N-Person Games

1973 • 28 citations

Komplementaritäts- und Fixpunktalgorithmen in der mathematischen Programmierung, Spieltheorie und Ökonomie

1976 • 27 citations

Combinatorial properties of certain simplicial and cubical vertex maps

1960 • 27 citations

Finding Roots of Polynomials By Pivoting

1977 • 27 citations

A generalized complementary pivoting algorithm

1974 • 26 citations

Newton's method with mesh refinements for numerical solution of nonlinear two-point boundary value problems

1978 • 26 citations

An odd theorem

1970 • 24 citations

The Calculation of the Topological Degree by Quadrature

1975 • 24 citations

A Study of ${\text{PC}}^1 $ Homeomorphisms on Subdivided Polyhedrons

1979 • 23 citations

On generalizing shapley's index theory to labelled pseudomanifolds

1976 • 23 citations

Constructive proofs of theorems relating to:F(x) = y, with applications

1977 • 23 citations

A simplicial approximation of a solution for the nonlinear complementarity problem

1975 • 22 citations

Studies on Piecewise-Linear Approximations of Piecewise-C¹ Mappings in Fixed Points and Complementarity Theory

1978 • 22 citations

A Method of Continuation for Calculating a Brouwer Fixed Point

1977 • 22 citations

On Piecewise Linear Approximations to Smooth Mappings

1979 • 22 citations

Existence and error estimates for solutions of a discrete analog of nonlinear eigenvalue problems

1972 • 22 citations

A PL homotopy for finding all the roots of a polynomial

1979 • 21 citations

On the Approximation of Nash Equilibrium Points in an N-Person Noncooperative Game

1974 • 21 citations

Fluid Dynamics of a Long Porous Slider

1975 • 21 citations

Solving piecewise linear convex equations

1974 • 21 citations

A Covering Property of Simplexes.

1968 • 20 citations

On the Relationship Between Conditions that Insure a PL Mapping is a Homeomorphism

1980 • 20 citations

The fixed point approach to nonlinear programming

1979 • 19 citations

Computation of Solutions to Nonlinear Equations Under Homotopy Invariance

1977 • 18 citations

A general mesh independence principle for Newton's method applied to second order boundary value problems

1979 • 18 citations

The approximation of solutions of nonlinear elliptic boundary value problems having several solutions

1973 • 17 citations

Application of a Fixed Point Search Algorithm to Nonlinear Boundary Value Problems Having Several Solutions

1977 • 15 citations

Fixed Point Computing Methods

1976 • 14 citations

Triangulations by Reflections with Applications to Approximation

1978 • 14 citations

A combinatorial property of pseudomanifolds and covering properties of simplexes

1970 • 13 citations

Investigations Into the Efficiency of the Fixed Point Algorithms

1977 • 13 citations

A new and constructive proof of the Borsuk-Ulam theorem

1979 • 13 citations

A revised mesh refinement strategy for newton’s method applied to nonlinear two-point boundary value problems

1978 • 12 citations

Über einen Ordnungsbegriff bei Einbettungsalgorithmen zur Lösung nichtlinearer Gleichungen

1976 • 11 citations

A modification of todd's triangulationJ 3

1978 • 11 citations

Optimal Dissection of Simplices

1978 • 10 citations

Scalar labelings for homotopy paths

1979 • 10 citations

On the Jacobian of a Function at a Zero Computed by a Fixed Point Algorithm

1978 • 9 citations

A New Simplicial Approximation Algorithm With Restarts: Relations Between Convergence and Labelings

1977 • 8 citations

A fixed point theorem including the last theorem of Poincaré

1975 • 8 citations

Mathematical Programming in Use

1978 • 7 citations

A Computational Comparison of Fixed Point Algorithms Which Use Complementary Pivoting

1977 • 6 citations

Complementary Pivot Theory and Markovian Decision Chains

1977 • 5 citations

A property of matrices with positive determinants

1980 • 4 citations

Recent and Past Developments in the Simplicial Approximation Approach to Solving Nonlinear Equations—A Subjective View

1980 • 4 citations

Simplicial Methods for the Solution of Systems of Nonlinear Equations

1976 • 3 citations

Numerische Approximation von Lösungen nichtlinearer Randwertaufgaben mit mehreren Lösungen

1974 • 2 citations

Error Bounds for Approximate Fixed Points

1977 • 2 citations

Kombinatorik bewerteter Komplexe

1973 • 1 citations