Computing singular solutions to polynomial systems

[1]  L. B. Rall.  Convergence of the newton process to multiple solutions , 1966 .

[2]  Gerd Fischer,et al.  Complex Analytic Geometry , 1976 .

[3]  Michael A. Malcolm,et al.  Computer methods for mathematical computations , 1977 .

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

[5]  G. Reddien.  On Newton’s Method for Singular Problems , 1978 .

[6]  C. B. García,et al.  An Approach to Homotopy and Degree Theory , 1979, Math. Oper. Res..

[7]  C. B. García,et al.  Finding all solutions to polynomial systems and other systems of equations , 1979, Math. Program..

[8]  J. Yorke,et al.  A homotopy method for locating all zeros of a system of polynomials , 1979 .

[9]  C. B. García,et al.  Determining All Solutions to Certain Systems of Nonlinear Equations , 1979, Math. Oper. Res..

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

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

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

[13]  C. Kelley,et al.  Newton’s Method at Singular Points. I , 1980 .

[14]  H. Keller,et al.  Geometrically Isolated Nonisolated Solutions and Their Approximation , 1981 .

[15]  Eugene L. Allgower,et al.  A survey of homotopy methods for smooth mappings , 1981 .

[16]  H. Keller,et al.  CONVERGENCE RATES FOR NEWTON'S METHOD AT SINGULAR POINTS* , 1983 .

[17]  R. Kellogg,et al.  Pathways to solutions, fixed points, and equilibria , 1983 .

[18]  Werner C. Rheinboldt,et al.  Algorithm 596: a program for a locally parameterized , 1983, TOMS.

[19]  M. R. Osborne,et al.  Analysis of Newton’s Method at Irregular Singularities , 1983 .

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

[21]  P. Brunovský,et al.  Solving systems of polynomial equations by bounded and real homotopy , 1984 .

[22]  A. Griewank.  On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions , 1985 .

[23]  D. Trigiante,et al.  A globally convergent method for simultaneously finding polynomial roots , 1985 .

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

[25]  L. Watson,et al.  HOMPACK: a suite of codes for globally convergent homotopy algorithms. Technical report No. 85-34 , 1985 .

[26]  Carl Tim Kelley,et al.  Broyden’s Method for a Class of Problems Having Singular Jacobian at the Root , 1985 .

[27]  A. Morgan.  A transformation to avoid solutions at infinity for polynomial systems , 1986 .

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

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

[30]  A. Morgan,et al.  A methodology for solving chemical equilibrium systems , 1987 .

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

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

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

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

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

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

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

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

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

[40]  Layne T. Watson,et al.  Finding all isolated solutions to polynomial systems using HOMPACK , 1989, TOMS.

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

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