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Morgan, Alexander P.

A transformation to avoid solutions at infinity for polynomial systems. (English) Zbl 0597.65045

Appl. Math. Comput. 18, 77-86 (1986).
This paper is reviewed together with the following one.

Cited in 19 Documents

MSC:

65H10 Numerical computation of solutions to systems of equations

Keywords:

polynomial systems; continuation method; solutions; at infinity; geometric modeling

Citations:

Zbl 0597.65046
Cite Review PDF
Full Text: DOI

References:

[1] Allgower, E. L., A survey of homotopy methods for smooth mappings, (Allgower, E. L.; Glashoff, K.; Peitgen, H.-O., Numerical Solution of Nonlinear Equations, No. 878 (1981), Springer), 1-29, Lecture Notes in Mathematics · Zbl 0461.65037
[2] Allgower, E. L.; Georg, K., Simplicial and continuation methods for approximating fixed points and solutions to systems of equations, SIAM Rev., 22, 28-85 (1980) · Zbl 0432.65027
[3] Chow, S.; Mallet-Paret, J.; York, J., A homotopy method for locating all zeros of a system of polynomials, (Peitgen, H. O.; Walther, H. O., Functional Differential Equations and Approximation of Fixed Points, No. 730 (1979), Springer), 228-237, Lecture Notes in Mathematics · Zbl 0427.65034
[4] Drexler, F. J., Eine Methode zur Berechnung samtlicher Lösungen von Polynomgleichungssystemen, Numer. Math., 29, 45-58 (1977) · Zbl 0352.65023
[5] Drexler, F. J., A homotopy method for the calculation of zeros of zero-dimensional polynomial ideals, (Wacker, H. G., Continuation Methods (1978), Academic), 69-93 · Zbl 0465.55003
[6] Garcia, C. B.; Li, T. Y., On the number of solutions to polynomial systems of equations, SIAM J. Numer. Anal., 17, 540-546 (1980) · Zbl 0445.65037
[7] Garcia, C. B.; Zangwill, W. I., Finding all solutions to polynomial systems and other systems of equations, Math. Programming, 16, 159-176 (1979) · Zbl 0409.65026
[8] Garcia, C. B.; Zangwill, W. I., An approach to homotopy and degree theory, Math. Oper. Res., 4, 390-405 (1979) · Zbl 0422.55001
[9] Garcia, C. B.; Zangwill, W. I., Determining all solutions to certain systems of nonlinear equations, Math. Oper. Res., 4, 1-14 (1979) · Zbl 0408.90086
[10] Garcia, C. B.; Zangwill, W. I., Pathways to Solutions, Fixed Points, and Equilibria (1981), Prentice-Hall · Zbl 0512.90070
[11] Guillemin, V.; Pollack, A., Differential Topology (1974), Prentice-Hall · Zbl 0361.57001
[12] Kendig, K., Elementary Algebraic Geometry (1977), Springer · Zbl 0364.14001
[13] Morgan, A. P., A method for computing all solutions to systems of polynomial equations, ACM Trans. Math. Software, 9, 1-17 (1983) · Zbl 0516.65026
[14] Saigal, R., On computing all real roots of a polynomial with real coefficients, Technical Report (Jan. 1982), Northwestern Univ
[15] Waerden, B. L.van der, Modern Algebra, 2 vols. (1953), Ungar: Ungar New York
[16] A.H. Wright, Finding all solutions to a system of polynomial equations, Math. Comp., to appear.; A.H. Wright, Finding all solutions to a system of polynomial equations, Math. Comp., to appear. · Zbl 0567.55002
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