论文信息 - The numerical inversion of functions from the plane to the plane

The numerical inversion of functions from the plane to the plane

This paper contains a description of a program designed to find all the solutions of systems of two real equations in two real unknowns which uses detailed information about the critical set of the associated function from the plane to the plane. It turns out that the critical set and its image are highly structured, and this is employed in their numerical computation. The conceptual background and details of implementation are presented. The most important features of the program are the ability to provide global information about the function and the robustness derived from such topological information.

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

[2] J. Milnor. Topology from the differentiable viewpoint , 1965 .

[3] Philip E. Gill,et al. Practical optimization , 1981 .

[4] Eugene L. Allgower,et al. Numerical continuation methods - an introduction , 1990, Springer series in computational mathematics.

[5] H. Whitney. On Singularities of Mappings of Euclidean Spaces. I. Mappings of the Plane Into the Plane , 1955 .

[6] Theodor Brocker,et al. Mappings of the plane into the plane , 1975 .

[7] Singularities of vector fields arising from one-dimensional Riemann problems , 1991 .

[8] H. B. Keller. Global Homotopies and Newton Methods , 1978 .

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

[10] J. Quine. A global theorem for singularities of maps between oriented 2-manifolds , 1978 .

[11] R. Fletcher. Practical Methods of Optimization , 1988 .