Numerical Continuation Methods

[1]  Shinji Mizuno,et al.  An $$O(\sqrt n L)$$ iteration potential reduction algorithm for linear complementarity problems , 1991, Math. Program..

[2]  Xian-He Sun,et al.  Parallel Homotopy Algorithm for the Symmetric Tridiagonal Eigenvalue Problem , 1991, SIAM J. Sci. Comput..

[3]  Aubrey B. Poore,et al.  Variable Order Adams-Bashforth Predictors with an Error-Stepsize Control for Continuation Methods , 1991, SIAM J. Sci. Comput..

[4]  A. Morgan,et al.  Computing singular solutions to nonlinear analytic systems , 1990 .

[5]  Shinji Mizuno,et al.  Limiting Behavior of Trajectories Generated by a Continuation Method for Monotone Complementarity Problems , 1990, Math. Oper. Res..

[6]  H. Walker,et al.  Least-change secant update methods for undetermined systems , 1990 .

[7]  D. S. Riley,et al.  A numerical bifurcation study of natural convection in a tilted two-dimensional porous cavity , 1990, Journal of Fluid Mechanics.

[8]  A. Morgan,et al.  Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics , 1990 .

[9]  E. Miersemann,et al.  Extension of Beckert's Continuation Method to Variational Inequalities , 1990 .

[10]  D. Roose,et al.  Continuation Techniques and Bifurcation Problems , 1990 .

[11]  J. Stoer,et al.  Global ellipsoidal approximations and homotopy methods for solving convex analytic programs , 1990 .

[12]  J. Yorke,et al.  The cheater's homotopy: an efficient procedure for solving systems of polynomial equations , 1989 .

[13]  L. Watson,et al.  Modern homotopy methods in optimization , 1989 .

[14]  N. Megiddo.  Pathways to the optimal set in linear programming , 1989 .

[15]  Dolf Talman,et al.  A Simplicial Algorithm for Stationary Point Problems on Polytopes , 1989, Math. Oper. Res..

[16]  K. H. Winters,et al.  Modal exchange mechanisms in Lapwood convection , 1989, Journal of Fluid Mechanics.

[17]  Shinji Mizuno,et al.  A polynomial-time algorithm for a class of linear complementarity problems , 1989, Math. Program..

[18]  G. Vasudevan,et al.  A Homotopy Approach for Solving Constrained Optimization Problems , 1989, 1989 American Control Conference.

[19]  E. Miersemann,et al.  Continuation for parametrized nonlinear variational inequalities , 1989 .

[20]  Tien-Yien Li,et al.  Homotopy algorithm for symmetric eigenvalue problems , 1989 .

[21]  W. Zulehner.  On the solutions to polynomial systems obtained by homotopy methods , 1989 .

[22]  L. T. Watson,et al.  Globally convergent homotopy methods: a tutorial , 1989, Conference on Numerical Ordinary Differential Equations.

[23]  S. Mizuno,et al.  PRACTICAL POLYNOMIAL TIME ALGORITHMS FOR LINEAR COMPLEMENTARITY PROBLEMS , 1989 .

[24]  Shinji Mizuno,et al.  A new continuation method for complementarity problems with uniformP-functions , 1989, Math. Program..

[25]  E. Miersemann,et al.  On the continuation for variational inequalities depending on an eigenvalue parameter , 1989 .

[26]  A. Morgan,et al.  Coefficient-parameter polynomial continuation , 1989 .

[27]  M. Kojima,et al.  A primal-dual interior point algorithm for linear programming , 1988 .

[28]  M. Kuno,et al.  Computing all real solutions to systems of nonlinear equations with a global fixed-point homotopy , 1988 .

[29]  Kiyotaka Yamamura,et al.  Solving nonlinear resistive networks by a homotopy method using a rectangular subdivision , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[30]  K. Schilling,et al.  Constructive proofs of fixed point theorems for set valued operators by simplicial algorithms , 1988 .

[31]  James B. Orlin,et al.  Parametric linear programming and anti-cycling pivoting rules , 1988, Math. Program..

[32]  Layne T. Watson,et al.  Tracing structural optima as a function of available resources by a homotopy method , 1988 .

[33]  James A. Yorke,et al.  Numerically determining solutions of systems of polynomial equations , 1988 .

[34]  A. B. Poore,et al.  The expanded Lagrangian system for constrained optimization problems , 1988 .

[35]  Yoshitsugu Yamamoto.  ORIENTABILITY OF PSEUDOMANIFOLD AND GENERALIZATIONS OF SPERNER'S LEMMA , 1988 .

[36]  R. Seydel.  From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .

[37]  James Renegar.  Rudiments of an average case complexity theory for piecewise-linear path following algorithms , 1988, Math. Program..

[38]  James Renegar,et al.  A polynomial-time algorithm, based on Newton's method, for linear programming , 1988, Math. Program..

[39]  H. Walker.  Implementation of the GMRES method using householder transformations , 1988 .

[40]  W. Rheinboldt.  On the computation of multi-dimensional solution manifolds of parametrized equations , 1988 .

[41]  W. Zulehner.  A simple homotopy method for determining all isolated solutions to polynomial systems , 1988 .

[42]  L. Watson,et al.  Solving spline-collocation approximations to nonlinear two-point boundary-value problems by a homoto , 1987 .

[43]  H. Mittelmann.  On continuation for variational inequalities , 1987 .

[44]  H. Schwetlick,et al.  Higher order predictors and adaptive steplength control in path following algorithms , 1987 .

[45]  A. Morgan,et al.  Errata: Computing all solutions to polynomial systems using homotopy continuation , 1987 .

[46]  A. Morgan,et al.  A homotopy for solving general polynomial systems that respects m-homogeneous structures , 1987 .

[47]  C. A. Tiahrt,et al.  Bifurcation problems in nonlinear parametric programming , 1987, Math. Program..

[48]  James A. Yorke,et al.  The random product homotopy and deficient polynomial systems , 1987 .

[49]  Tien-Yien Li.  Solving polynomial systems , 1987 .

[50]  Layne T. Watson,et al.  Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms , 1987, TOMS.

[51]  A. Talman,et al.  Simplicial variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using a general labelling , 1987 .

[52]  Warren D. Seider,et al.  Heterogeneous azeotropic distillation: Experimental and simulation results , 1987 .

[53]  J. D. Seader,et al.  Computing multiple solutions to systems of interlinked separation columns , 1987 .

[54]  Tien-Yien Li,et al.  Homotopy method for generalized eigenvalue problems Ax= ΛBx☆ , 1987 .

[55]  Aubrey B. Poore,et al.  Continuous Homotopies for the Linear Complementarity Problem , 1987 .

[56]  M. J. D. Powell.  On error growth in the Bartels-Golub and Fletcher-Matthews algorithms for updating matrix factorizations , 1987 .

[57]  A. Morgan.  Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems , 1987 .

[58]  J. Yorke,et al.  Numerical solution of a class of deficient polynomial systems , 1987 .

[59]  Computation of an industrial equilibrium , 1987 .

[60]  Computing economic equilibria by variable dimension algorithms: State of the art , 1987 .

[61]  A. Talman,et al.  A convergent price adjustment process , 1987 .

[62]  Continuation Methods for Parameter-Dependent Boundary Value Problems , 1987 .

[63]  T. L. Wayburn,et al.  Homotopy continuation methods for computer-aided process design☆ , 1987 .

[64]  G. van der Laan,et al.  The computation and modelling of economic equilibria , 1987 .

[65]  W. Rheinboldt.  On a Moving-Frame Algorithm and the Triangulation of Equilibrium Manifolds , 1987 .

[66]  Yoshitsugu Yamamoto,et al.  A PATH FOLLOWING ALGORITHM FOR STATIONARY POINT PROBLEMS , 1987 .

[67]  Layne T. Watson,et al.  Solving Galerkin approximation to nonlinear two-point boundary value problems bya globally convergent homotopy method , 1987 .

[68]  L. Watson.  Numerical linear algebra aspects of globally convergent homotopy methods , 1986 .

[69]  Hans D Mittlemann.  A pseudo-arclength continuation method for nonlinear eigenvalue problems , 1986 .

[70]  W. Rheinboldt,et al.  Folds on the solution manifold of a parametrized equation , 1986 .

[71]  H. D. Mittelmann.  Multilevel continuation techniques for nonlinear boundary value problems with parameter dependence , 1986 .

[72]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[73]  Michael J. Todd,et al.  Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems , 1986, Math. Program..

[74]  D. J. Vickery,et al.  Path-following approaches to the solution of multicomponent, multistage separation process problems , 1986 .

[75]  H. B. Keller,et al.  A Direct Method for Computing Higher Order Folds , 1986 .

[76]  R. Mejia.  CONKUB: A conversational path-follower for systems of nonlinear equations , 1986 .

[77]  Mamoru Kaneko,et al.  The existence and computation of competitive equilibria in markets with an indivisible commodity , 1986 .

[78]  Stephen Smale,et al.  Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: II , 1986, SIAM J. Comput..

[79]  W. Rheinboldt.  Numerical analysis of parametrized nonlinear equations , 1986 .

[80]  Hans D. Mittelmann.  Multi-Grid Continuation and Spurious Solutions for Nonlinear Boundary Value Problems. , 1986 .

[81]  Tien Yien Li,et al.  Regularity results for solving systems of polynomials by homotopy method , 1986 .

[82]  Alexander P. Morgan.  A homotopy for solving polynomial systems , 1986 .

[83]  K. Schilling.  Simpliziale Algorithmen zur Berechnung von Fixpunkten mengenwertiger Operatoren , 1986 .

[84]  G. van der Laan,et al.  An algorithm for the linear complementarity problem with upper and lower bounds , 1989 .

[85]  Alfonso Reinoza.  Solving generalized equations via homotopies , 1985, Math. Program..

[86]  S. Smale.  On the efficiency of algorithms of analysis , 1985 .

[87]  H. Schwetlick,et al.  Parametrization via secant length and application to path following , 1985 .

[88]  James Renegar.  On the complexity of a piecewise linear algorithm for approximating roots of complex polynomials , 1985, Math. Program..

[89]  James Renegar,et al.  On the cost of approximating all roots of a complex polynomial , 1985, Math. Program..

[90]  Michael J. Todd.  ‘Fat’ triangulations, or solving certain nonconvex matrix optimization problems , 1985, Math. Program..

[91]  Rita Meyer-Spasche,et al.  Some Bifurcation Diagrams for Taylor Vortex Flows , 1985 .

[92]  Gerard van der Laan,et al.  The Computation of General Equilibrium in Economies with a Block Diagonal Pattern , 1985 .

[93]  H. Weber.  Multigrid Bifurcation Iteration , 1985 .

[94]  Regularity results for real analytic homotopies , 1985 .

[95]  Hans D. Mittelmann,et al.  Multi-Grid Solution of Bifurcation Problems , 1985 .

[96]  A. Wright.  Finding all solutions to a system of polynomial equations , 1985 .

[97]  M. Todd.  Complementarity in Oriented Matroids , 1984 .

[98]  Yoshitsugu Yamamoto.  A variable dimension fixed point algorithm and the orientation of simplices , 1984, Math. Program..

[99]  Michael J. Todd,et al.  J': A new Triangulation of R^n , 1984 .

[100]  A. Spence,et al.  THE COMPUTATION OF SYMMETRY-BREAKING BIFURCATION POINTS* , 1984 .

[101]  M. Fukushima,et al.  A continuation method for solving separable nonlinear least squares problems , 1984 .

[102]  Ze-ke Wang,et al.  On the cost of computing roots of polynomials , 1984, Math. Program..

[103]  Romesh Saigal.  Computational complexity of a piecewise linear homotopy algorithm , 1984, Math. Program..

[104]  Yoshitsugu Yamamoto,et al.  A unifying model based on retraction for fixed point algorithms , 1984, Math. Program..

[105]  W. Rheinboldt.  Differential-algebraic systems as differential equations on manifolds , 1984 .

[106]  H. Mittelmann,et al.  Numerical Methods for Bifurcation Problems , 1984 .

[107]  Hans D. Mittelmann.  Continuation Near Symmetry-Breaking Bifurcation Points , 1984 .

[108]  G. van der Laan,et al.  Shortest paths for simplicial algorithms , 1984 .

[109]  On the Choice of Steplength in Path Following Methods , 1984 .

[110]  M. Kojima,et al.  Continuous deformation of nonlinear programs , 1984 .

[111]  W. Rheinboldt.  On Some Methods for the Computational Analysis of Manifolds , 1984 .

[112]  R. Seydel,et al.  A Continuation Algorithm with Step Control , 1984 .

[113]  A. Spence,et al.  The Numerical Calculation of Cusps, Bifurcation Points and Isola Formation Points in Two Parameter Problems , 1984 .

[114]  L. Chua,et al.  Tracing solution curves of nonlinear equa-tions with sharp turning points , 1984 .

[115]  Hans D. Mittelmann,et al.  Numerical methods for bifurcation problems : proceedings of the conference at the University of Dortmund, August 22-26, 1983 , 1984 .

[116]  Gerard van der Laan,et al.  On the existence and approximation of zeroes , 1984, Math. Program..

[117]  R. Saigal,et al.  A Homotopy for Solving Large, Sparse and Structured Fixed Point Problems , 1983, Math. Oper. Res..

[118]  Milan Kubíček,et al.  Book-Review - Computational Methods in Bifurcation Theory and Dissipative Structures , 1983 .

[119]  Gerard van der Laan,et al.  Note on the path following approach of equilibrium programming , 1983, Math. Program..

[120]  D. Saupe.  Global bifurcation of periodic solutions to some autonomous differential delay equations , 1983 .

[121]  Shinji Mizuno,et al.  Computation of all solutions to a system of polynomial equations , 1983, Math. Program..

[122]  Raymond A. DeCarlo,et al.  Continuation methods: Theory and applications , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[123]  M. Todd.  Piecewise-Linear Homotopy Algorithms for Sparse Systems of Nonlinear Equations , 1983 .

[124]  Alexander P. Morgan,et al.  A Method for Computing All Solutions to Systems of Polynomials Equations , 1983, TOMS.

[125]  G. McCormick.  Nonlinear Programming: Theory, Algorithms and Applications , 1983 .

[126]  Rüdiger Seydel,et al.  Branch switching in bifurcation problems for ordinary differential equations , 1983 .

[127]  L. Watson,et al.  Tracking nonlinear equilibrium paths by a homotopy method , 1983 .

[128]  Global topological perturbations of nonlinear elliptic eigenvalue problems , 1983 .

[129]  Alfonso Reinoza,et al.  Piecewise nonlinear homotopies , 1983 .

[130]  Dietmar Saupe,et al.  On accelerating PL continuation algorithms by predictor—corrector methods , 1982, Math. Program..

[131]  Masakazu Kojima,et al.  Variable dimension algorithms: Basic theory, interpretations and extensions of some existing methods , 1982, Math. Program..

[132]  Michael J. Todd,et al.  An implementation of the simplex method for linear programming problems with variable upper bounds , 1982, Math. Program..

[133]  Michael J. Todd.  On the computational complexity of piecewise-linear homotopy algorithms , 1982, Math. Program..

[134]  R. Decarlo,et al.  A homotopy-method for eigenvalue assignment using decentralized state feedback , 1984, 1982 21st IEEE Conference on Decision and Control.

[135]  T. Ojika,et al.  Sequential Substitution Method for the Resultant of a System of Nonlinear Algebraic Equations , 1982 .

[136]  H. Siegberg,et al.  Fixed point index and chain approximations , 1982 .

[137]  L. Reinhart,et al.  On the numerical analysis of the Von Karman equations: Mixed finite element approximation and continuation techniques , 1982 .

[138]  H. Schwetlick,et al.  Ein lokal überlinear konvergentes Verfahren zur Bestimmung von Rückkehrpunkten implizit definierter Raumkurven , 1982 .

[139]  T. Ypma.  Following paths through turning points , 1982 .

[140]  K. Murota.  Global Convergence of a Modified Newton Iteration for Algebraic Equations , 1982 .

[141]  W. Rheinboldt.  Computation of Critical Boundaries on Equilibrium Manifolds , 1982 .

[142]  H. Weber.  Numerical solution of a class of nonlinear boundary value problems for analytic functions , 1982 .

[143]  H. Weber.  Zur Verzweigung bei einfachen Eigenwerten , 1982 .

[144]  Gerard van der Laan,et al.  On the Computation of Fixed Points in the Product Space of Unit Simplices and an Application to Noncooperative N Person Games , 1982, Math. Oper. Res..

[145]  M. Todd.  An introduction to piecewise-linear homotopy algorithms for solving systems of equations , 1982 .

[146]  A fast solver for nonlinear eigenvalue problems , 1982 .

[147]  Joseph Padovan,et al.  Self-adaptive predictor-corrector algorithms for static nonlinear structural analysis , 1982 .

[148]  R. E. Müller.  Numerical Solution of Multiparameter Eigenvalue Problems , 1982 .

[149]  Josef Stoer,et al.  Solution of Large Linear Systems of Equations by Conjugate Gradient Type Methods , 1982, ISMP.

[150]  R. Seydel.  Numerical computation of periodic orbits that bifurcate from stationary solutions of ordinary differential equations , 1981 .

[151]  N. D. Villiers,et al.  A Continuation Method for Nonlinear Regression , 1981 .

[152]  Gerard van der Laan,et al.  A class of simplicial restart fixed point algorithms without an extra dimension , 1981, Math. Program..

[153]  Daniel Solow,et al.  Homeomorphisms of triangulations with applications to computing fixed points , 1981, Math. Program..

[154]  Alden H. Wright,et al.  The octahedral algorithm, a new simplicial fixed point algorithm , 1981, Math. Program..

[155]  C. B. García,et al.  Equilibrium programming:The path following approach and dynamics , 1981, Math. Program..

[156]  M. Prüfer,et al.  Complementary pivoting and the Hopf Degree Theorem , 1981 .

[157]  Michael J. Todd.  Approximate Labelling for Simplicial Algorithms and Two Classes of Special Subsets of the Sphere , 1981, Math. Oper. Res..

[158]  L. Watson.  Engineering applications of the Chow-Yorke algorithm , 1981 .

[159]  A. Talman,et al.  Algorithms for the linear complementarity problem which allow an arbitrary starting point , 1981 .

[160]  W. Rheinboldt.  Numerical analysis of continuation methods for nonlinear structural problems , 1981 .

[161]  Wei H. Yang,et al.  METHODS FOR OPTIMAL ENGINEERING DESIGN PROBLEMS BASED ON GLOBALLY CONVERGENT METHODS , 1981 .

[162]  H. Siegberg.  Some Historical Remarks Concerning Degree Theory , 1981 .

[163]  L. Mansfield.  Finite element methods for nonlinear shell analysis , 1981 .

[164]  J. Ilavský,et al.  Global simulation of countercurrent separation processes via one-parameter imbedding techniques , 1981 .

[165]  Chang Y. Wang,et al.  A homotopy method applied to elastica problems , 1981 .

[166]  M. Kubicek,et al.  Numerical solution of nonlinear equations by one-parameter imbedding methods , 1981 .

[167]  A. Talman,et al.  Labelling rules and orientation: On Sperner's lemma and brouwer degree , 1981 .

[168]  M. Kojima.  An introduction to variable dimension algorithms for solving systems of equations , 1981 .

[169]  M. Powell.  AN UPPER TRIANGULAR MATRIX METHOD FOR QUADRATIC PROGRAMMING , 1981 .

[170]  H. Peitgen,et al.  Positive and spurious solutions of nonlinear eigenvalue problems , 1981 .

[171]  S. Smale.  The fundamental theorem of algebra and complexity theory , 1981 .

[172]  L. Watson.  Solving Finite Difference Approximations to Nonlinear Two-Point Boundary Value Problems by a Homotopy Method , 1980 .

[173]  Layne T. Watson,et al.  Computational experience with the Chow—Yorke algorithm , 1980, Math. Program..

[174]  Michael J. Todd,et al.  Exploiting structure in piecewise-linear homotopy algorithms for solving equations , 1980, Math. Program..

[175]  Gerard van der Laan,et al.  A new subdivision for computing fixed points with a homotopy algorithm , 1980, Math. Program..

[176]  Michael J. Todd,et al.  A quadratically-convergent fixed-point algorithm for economic equilibria and linearly constrained optimization , 1980, Math. Program..

[177]  C. Pan,et al.  Multiple solutions of nonlinear equations: Roots of polynomials , 1980 .

[178]  G. Moore,et al.  The Calculation of Turning Points of Nonlinear Equations , 1980 .

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

[180]  Michael J. Todd.  Traversing Large Pieces of Linearity in Algorithms that Solve Equations by Following Piecewise-Linear Paths , 1980, Math. Oper. Res..

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

[182]  Rita Meyer-Spasche,et al.  Computations of the axisymmetric flow between rotating cylinders , 1980 .

[183]  Michael J. Todd,et al.  A Note on Optimally Dissecting Simplices , 1980, Math. Oper. Res..

[184]  Об определении начальных значений решений нелинейных краевых задач методом продолжения решения по параметру, Determination of the initial values of the solutions of nonlinear boundary value problems by the method of continuation of the solution with respect to the para , 1980 .

[185]  J. Whalley,et al.  General Equilibrium Analysis of Taxation Policy , 1980 .

[186]  M. Todd,et al.  A variable-dimension simplicial algorithm for antipodal fixed-point theorems , 1980 .

[187]  L. Watson,et al.  Optimal design by a homotopy method , 1980 .

[188]  H. Weber,et al.  Numerical solution of Hopf bifurcation problems , 1980 .

[189]  P. Percell.  Note on a global homotopy , 1980 .

[190]  W. Rheinboldt.  Schwetlick H., Numerische Lösung nichtlinearer Gleichungen. Berlin VEB Deutscher Verlag der Wissenschaften 1979. 346 S., 21 Abb., M 68,— , 1980 .

[191]  Hans D. Mittelmann,et al.  Bifurcation Problems and their Numerical Solution , 1980 .

[192]  Chang Y. Wang,et al.  ON THE LARGE DEFORMATIONS OF C-SHAPED SPRINGS , 1980 .

[193]  M. Kojima.  Strongly Stable Stationary Solutions in Nonlinear Programs. , 1980 .

[194]  M. Todd.  Numerical Stability and Sparsity in Piecewise-Linear Algorithms , 1980 .

[195]  L. Watson,et al.  Deceleration of a rotating disk in a viscous fluid , 1979 .

[196]  P. Toint.  On the Superlinear Convergence of an Algorithm for Solving a Sparse Minimization Problem , 1979 .

[197]  Gerard van der Laan,et al.  A restart algorithm for computing fixed points without an extra dimension , 1979, Math. Program..

[198]  Hoang Tuy.  Pivotal methods for computing equilibrium points: Unified approach and new restart algorithm , 1979, Math. Program..

[199]  Michael J. Todd.  Piecewise linear paths to minimize convex functions may not be monotonic , 1979, Math. Program..

[200]  Masakazu Kojima,et al.  A Complementary Pivoting Approach to Parametric Nonlinear Programming , 1979, Math. Oper. Res..

[201]  Roger D. Nussbaum,et al.  Uniqueness and nonuniqueness for periodic solutions of x′(t) = −g(x(t − 1)) , 1979 .

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

[203]  R. Seydel.  Numerical computation of branch points in nonlinear equations , 1979 .

[204]  Chang Y. Wang,et al.  Viscous flow between rotating discs with injection on the porous disc , 1979 .

[205]  J. H. Wilkinson,et al.  Inverse Iteration, Ill-Conditioned Equations and Newton’s Method , 1979 .

[206]  J. Yorke,et al.  A Simple Reliable Numerical Algorithm for Following Homotopy Paths , 1979 .

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

[208]  R. Saigal.  On Piecewise Linear Approximations to Smooth Mappings , 1979, Math. Oper. Res..

[209]  R. Seydel.  Numerical computation of branch points in ordinary differential equations , 1979 .

[210]  M. Prüfer,et al.  On computational aspects of topological degree in ℝn , 1979 .

[211]  Mark D. Meyerson,et al.  A new and constructive proof of the Borsuk-Ulam theorem , 1979 .

[212]  L. Watson.  Solving the Nonlinear Complementarity Problem by a Homotopy Method , 1979 .

[213]  K. Tanabe.  Continuous Newton-Raphson method for solving and underdetermined system of nonlinear equations☆ , 1979 .

[214]  E. Riks.  An incremental approach to the solution of snapping and buckling problems , 1979 .

[215]  M. Kubicek,et al.  Solution of nonlinear boundary value problems—XI , 1979 .

[216]  M. Todd.  Hamiltonian triangulations of Rn , 1979 .

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

[218]  Michael J. Todd,et al.  Bimatrix games—an addendum , 1978, Math. Program..

[219]  M. Kubíek,et al.  One-parameter imbedding techniques for the solution of nonlinear boundary-value problems , 1978 .

[220]  C. Pan,et al.  A computer-aided root-locus method , 1978 .

[221]  T. Y. Li,et al.  Fluid Dynamics of the Elliptic Porous Slider , 1978 .

[222]  Michael J. Todd.  Optimal Dissection of Simplices , 1978 .

[223]  Michael J. Todd.  On the Jacobian of a Function at a Zero Computed by a Fixed Point Algorithm , 1978, Math. Oper. Res..

[224]  An analog of the method of continuation of solution with respect to the parameter for nonlinear operator equations , 1978 .

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

[226]  Masakazu Kojima,et al.  Studies on Piecewise-Linear Approximations of Piecewise-C1 Mappings in Fixed Points and Complementarity Theory , 1978, Math. Oper. Res..

[227]  M. Kojima.  On the homotopic approach to systems of equations with separable mappings , 1978 .

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

[229]  W. Rheinboldt.  An adaptive continuation process for solving systems of nonlinear equations , 1978 .

[230]  K. G. Murty.  Computational complexity of complementary pivot methods , 1978 .

[231]  N. Megiddo.  On the parametric nonlinear complementarity problem , 1978 .

[232]  M. J. D. Powell,et al.  Restart procedures for the conjugate gradient method , 1977, Math. Program..

[233]  Nimrod Megiddo,et al.  On the existence and uniqueness of solutions in nonlinear complementarity theory , 1977, Math. Program..

[234]  Willard I. Zangwill,et al.  An Eccentric Barycentric fixed Point Algorithm , 1977, Math. Oper. Res..

[235]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[236]  R. Saigal,et al.  On the Convergence Rate of Algorithms for Solving Equations that are Based on Methods of Complementary Pivoting , 1977, Math. Oper. Res..

[237]  H. Wacker,et al.  Bemerkungen zur Aufwandsminimierung bei Stetigkeitsmethoden sowie Alternativen bei der Behandlung der Singulären Situation , 1977 .

[238]  James MacKinnon.  Solving Economic General Equilibrium Models by the Sandwich Method , 1977 .

[239]  M. Todd.  Union Jack Triangulations , 1977 .

[240]  H. Kuhn.  Finding Roots of Polynomials By Pivoting , 1977 .

[241]  M. Kojima,et al.  An Extension of Lemke’s Method to the Piecewise Linear Complementarity Problem , 1976 .

[242]  M. Todd.  Extensions of Lemke's algorithm for the linear complementarity problem , 1976 .

[243]  M. J. D. Powell,et al.  Some convergence properties of the conjugate gradient method , 1976, Math. Program..

[244]  Stephen J. Grotzinger,et al.  On generalizing shapley's index theory to labelled pseudomanifolds , 1976, Math. Program..

[245]  Michael J. Todd,et al.  On triangulations for computing fixed points , 1976, Math. Program..

[246]  R. Saigal.  Fixed Point Computing Methods , 1976 .

[247]  Romesh Saigal,et al.  On Paths Generated by Fixed Point Algorithms , 1976, Math. Oper. Res..

[248]  A. N. Netravali,et al.  Optimum quantizer design using a fixed-point algorithm , 1976, The Bell System Technical Journal.

[249]  Romesh Saigal,et al.  Extension of the Generalized Complementarity Problem , 1976, Math. Oper. Res..

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

[251]  Milan Kubicek,et al.  Algorithm 502: Dependence of Solution of Nonlinear Systems on a Parameter [C5] , 1976, TOMS.

[252]  Michael J. Todd.  Orientation in Complementary Pivot Algorithms , 1976, Math. Oper. Res..

[253]  H. Lüthi.  Komplementaritäts- und Fixpunktalgorithmen in der mathematischen Programmierung, Spieltheorie und Ökonomie , 1976 .

[254]  L. Santaló.  Integral geometry and geometric probability , 1976 .

[255]  Hans-Jakob Lüthi.  A simplicial approximation of a solution for the nonlinear complementarity problem , 1975, Math. Program..

[256]  A computing method for bifurcation boughs of nonlinear eigenvalue problems , 1975 .

[257]  H. Troger.  Ein Beitrag zum Durchschlagen einfacher Strukturen , 1975 .

[258]  Roger D. Nussbaum,et al.  A global bifurcation theorem with applications to functional differential equations , 1975 .

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

[260]  D. Leder.  Automatische Schrittweitensteuerung bei global konvergenten Einbettungsmethoden , 1974 .

[261]  C. van de PANNE.  A complementary variant of Lemke's method for the linear complementary problem , 1974, Math. Program..

[262]  Jorge J. Moré,et al.  Classes of functions and feasibility conditions in nonlinear complementarity problems , 1974, Math. Program..

[263]  Michael J. Todd,et al.  A generalized complementary pivoting algorithm , 1974, Math. Program..

[264]  H. Scarf,et al.  The Computation of Economic Equilibria , 1974 .

[265]  H. Kuhn.  A new proof of the fundamental theorem of algebra , 1974 .

[266]  J. J. Moré.  Coercivity Conditions in Nonlinear Complementarity Problems , 1974 .

[267]  The extended continuation method and invariant imbedding , 1974 .

[268]  小島 政和.  Computational methods for solving the nonlinear complementarity problem , 1974 .

[269]  L. Nirenberg,et al.  Topics in nonlinear functional analysis, 1973-1974 , 1974 .

[270]  L. Shapley.  A note on the Lemke-Howson algorithm , 1974 .

[271]  Romesh Saigal,et al.  Generic properties of the complementarity problem , 1973, Math. Program..

[272]  Axel Ruhe.  ALGORITHMS FOR THE NONLINEAR EIGENVALUE PROBLEM , 1973 .

[273]  K. S. Banerjee,et al.  Generalized Inverse of Matrices and Its Applications , 1973 .

[274]  H. Scarf.  The computation of equilibrium prices , 1973 .

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

[276]  L. Shapley.  On Balanced Games Without Side Payments , 1973 .

[277]  R. Saigal.  On the Alass of Complementary Cones and Lemke’s Algorithm , 1972 .

[278]  C. Rourke,et al.  Introduction to Piecewise-Linear Topology , 1972 .

[279]  E. Wasserstrom,et al.  Solving Boundary-Value Problems by Imbedding , 1971, JACM.

[280]  J. Rosenmüller.  On a Generalization of the Lemke–Howson Algorithm to Noncooperative N-Person Games , 1971 .

[281]  I. Stakgold,et al.  Branching of Solutions of Nonlinear Equations , 1971 .

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

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

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

[285]  J. Schwartz.  Nonlinear Functional Analysis , 1969 .

[286]  Olvi L. Mangasarian,et al.  Nonlinear Programming , 1969 .

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

[288]  S. M. Roberts,et al.  Continuation in quasilinearization , 1968 .

[289]  M. A. Krasnoselʹskii.  Topological methods in the theory of nonlinear integral equations , 1968 .

[290]  S.M Roberts,et al.  Justification for the continuation method in two-point boundary value problems , 1968 .

[291]  J. Milnor.  Singular points of complex hypersurfaces , 1968 .

[292]  Herbert E. Scarf,et al.  The Approximation of Fixed Points of a Continuous Mapping , 1967 .

[293]  S. M. Roberts,et al.  Continuation in shooting methods for two-point boundary value problems , 1967 .

[294]  H. Scarf.  The Core of an N Person Game , 1967 .

[295]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[296]  C. E. Lemke,et al.  Equilibrium Points of Bimatrix Games , 1964 .

[297]  Harold W. Kuhn,et al.  Some Combinatorial Lemmas in Topology , 1960, IBM J. Res. Dev..

[298]  W. Rogosinski,et al.  The Geometry of the Zeros of a Polynomial in a Complex Variable , 1950, The Mathematical Gazette.

[299]  A. Sard,et al.  The measure of the critical values of differentiable maps , 1942 .

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

[301]  J. Leray,et al.  Topologie et équations fonctionnelles , 1934 .

[302]  E. Sperner.  Neuer beweis für die invarianz der dimensionszahl und des gebietes , 1928 .

[303]  R. Ho.  Algebraic Topology , 2022 .