1

ALEXANDER, J. C. The topological theory of an embedding method. In Continuation Methods, H. G. Wacker (Ed.), Academic Press, New York, 1978, pp. 87-88.

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ALEXANDER, J. C., AND YORKE, J. A. The homotopy communication method: Numerically implementable topological procedures Trans. Am. Math. Soc. 242 (Aug. 1978), 271-284.

3

ALLGOWER, E., AND GEORG, K. Simplicial and continuation methods for approximating fixed points and solutions to systems of equations. SIAM Rev. 22 (Jan. 1980), 28-85.

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BRANIN, F.H., JR. Widely convergent methods for finding multiple solutions of simultaneous non-linear equations. IBM J. Res. Dev. 16 (Sept. 1972), 506-522.

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BRENT, R.P. On the Davidenko-Branin method for finding multiple solutions of simultaneous nonlinear equations. IBM J. Res. Dev. 16 (July 1972), 434-436.

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BROWN, K.M.,ANDGEARHART, W.B. Deflation techniques for the calculation offurther solutions of a nonlinear system. Nurner. Math. 16 (1971), 334-342.

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CHAO, K.S., LIU, D.K., AND PAN, C.T. A systematic search method for obtaining multiple solutions of simultaneous nonlinear equations. IEEE Trans. Circuits Syst. CAS-22 (Sept. 1975), 748-753.

8

CHIEN, M.J. Searching for multiple solutions of nonlinear systems. IEEE Trans., Circuits Syst. CAS-26 (Oct. 1979), 817-827.

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CHOW, S.N., MALLET-PARET, J., AND YORKE, J.A. Finding zeros of maps: Homotopy methods that are constructive with probability one. Math. Comput. 32 (July 1978), 887-899.

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CHOW, S.N., MALLET-PARET, J., AND YORKE, J.A. A homotopy method for locating all zeros of a system of polynomials. In Functional Differential Equations and Approximation of F~xed Points, H.O. Peitgen and H.O. Walther (Eds.), Springer-Verl~g Lecture Notes in Mathematics ~~730. Springer-Verlag, New York, 1979, pp. 228-237.

11

CROWDER, H., DEMBO, R., AND MULVEY, J. Reporting computational experiments m mathematical programming. Math. Program. 15 (1978), 316-329.

12

DONGARRA, J J., MOLER, C.B., BUNCH, J.R., AND STEWART, G.W. LINPACK User's Guide. Society for Industrial and Applied Mathematics, Philadelphia, 1979.

13

DREXLER, F.J. Eine Methode zur Berechung samtlicher Losunger yon Polynomgleichungessystemen. Numer. Math. 29 (1977), 45-58.

14

DREXLER, F.J. A homotopy method for the calculation of zeros of zero-dimensional polynomial ideals. In Continuation Methods, H.G. Wacker (Ed.), Academic Press, New York, 1978, pp. 69-93.

15

GARCIA C.B., AND LI, T.Y. On the number of solutions to polynomial systems of equations. SIAM J. Numer. Anal. 17 (Aug. 1980), 540-546.

16

GARCIA C.B., AND LI, T.Y On a path following method for systems of equations. Bull. Inst. Math Academw Sinwa (Ta~pei) 9 (1981), 249-259.

17

GARCIA C.B., AND ZANGWILL, W.I. Finding all solutions to polynomial systems and other systems of equations. Math. Program. 16 (1979), 159-176.

18

GARCIA C.B., AND ZANGWILL, W.I. An approach to homotopy and degree theory. Math. Oper. Res. 4 (Nov. 1979), 390-405.

19

GARCIA C.B., AND ZANGWILL, W.I. Determming all solutions to certain systems of nonlinear equations. Math. Oper. Res. 4 (Feb 1979), 1-14.

20

GARCIA C.B., AND ZANGWILL, W.I. Pathways to Solutions, Fixed Points, and Equilibria. Prentice-Hall, Englewood Cliffs, N.J., 1981.

21

GUILLEMIN, V., AND POLLACK, A. Differential Topology. Prentice-Hall, Englewood Cliffs, N.J., 1974.

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HINDMARSH, A.C. "GEAR" ordinary differential equation system solver. Rep. UCID-30001, ReD. 3, Lawrence Livermore Lab., Livermore, Calif., Dec. 1974.

23

INCERTI, S., PARISI, V., AND ZIRILLI, F. A new method for solving nonlinear simultaneous equations. SIAM J. Numer. Anal. 16 (Oct. 1979), 779-789

24

Milan Kubíček, Algorithm 502: Dependence of Solution of Nonlinear Systems on a Parameter [C5], ACM Transactions on Mathematical Software (TOMS), v.2 n.1, p.98-107, March 1976  [doi>10.1145/355666.355675]

25

KUBICEK, M., HOLODNIAK, M., AND MAREK, I. Numerical solution of nonlinear equations by one-parameter imbedding methods. Numer. Func. Anal. Optimtz. 3 (1981), 223-264.

26

LI, T.Y. On locatmg all the zeros of an analytic function within a bounded domain. SIAM J. Numer Anal, to be pubhshed.

27

LI, T.Y., AND YORKE, J A. A simple relmble numerical algorithm for following homotopy paths. In Analys~s and Computation of F~xed Points, S.M. Robinson (Ed.), Academic Press, New York, 1980, pp. 73-91.

28

Jorge J. Moré , Michel Y. Cosnard, Numerical Solution of Nonlinear Equations, ACM Transactions on Mathematical Software (TOMS), v.5 n.1, p.64-85, March 1979  [doi>10.1145/355815.355820]

29

MOROAN, A.P. A method for computing all solutions to systems of polynomial equations. Res. Pub. GMR-3651, Mathematics Dep., G.M. Research Labs, Warren, Mich., July 1981.

30

MORGAN, A.P. An algorithm for solving the line-tube classification problem. Res. Pub. GMR- 3858, Mathematics Dep., G.M. Research Labs., Warren, Mich., Oct 1981

31

MORGAN, A P., AND SARRAGA, R.F. A method for computing three surface intersection points in GMSOLID. Res. Pub. GMR-3964, Mathematics Dep, G.M. Research Labs., Warren, Mich., Feb. 1982

32

SAIGAL, R. On computing all real roots of a polynomial with real coefficients. Jan. 1982, unpubhshed.

33

WATSON, L.T. A globally convergent algorithm for computing fixed points of C2 maps. Appl. Math. Comput. 5 (1979), 297-311.

34

WATSON, L.T. Solving finite difference approximations to nonlinear two-point boundary value problems by a homotopy method. SIAM J. Sct. Stat. Comput I (1980), 467-480.

35

Layne T. Watson , Dan Fenner, Algorithm 555: Chow-Yorke Algorithm for Fixed Points or Zeros of C2 Maps [C5], ACM Transactions on Mathematical Software (TOMS), v.6 n.2, p.252-259, June 1980  [doi>10.1145/355887.355899]

Ren C. Luo , Yawei Ma , David F. McAllister, Tracing tangential surface-surface intersections, Proceedings of the third ACM symposium on Solid modeling and applications, p.255-262, May 17-19, 1995, Salt Lake City, Utah, United States

R. Baker Kearfott, Some tests of generalized bisection, ACM Transactions on Mathematical Software (TOMS), v.13 n.3, p.197-220, Sept. 1987

Alexander P. Morgan , Andrew J. Sommese , Layne T. Watson, Finding all isolated solutions to polynomial systems using HOMPACK, ACM Transactions on Mathematical Software (TOMS), v.15 n.2, p.93-122, June 1989

Steven M. Wise , Andrew J. Sommese , Layne T. Watson, Algorithm 801: POLSYS_PLP: a partitioned linear product homotopy code for solving polynomial systems of equations, ACM Transactions on Mathematical Software (TOMS), v.26 n.1, p.176-200, March 2000

H. C. Chang , N. Prabhu, Canonical coordinates method for equality-constrained nonlinear optimization, Applied Mathematics and Computation, v.140 n.1, p.135-158, 30 July 2003

W. He , N. Prabhu, A globally convergent method for finding zeros of smooth functions, Applied Mathematics and Computation, v.133 n.2-3, p.327-335, 15 December 2002

Hai-Jun Su , J. Michael McCarthy , Masha Sosonkina , Layne T. Watson, Algorithm 857: POLSYS_GLP---a parallel general linear product homotopy code for solving polynomial systems of equations, ACM Transactions on Mathematical Software (TOMS), v.32 n.4, p.561-579, December 2006

Alexander P. Morgan: colleagues