The numerical inversion of functions from the plane to the plane

Malta, Iaci; Saldanha, Nicolau; Tomei, Carlos

doi:10.1090/S0025-5718-96-00770-3

The numerical inversion of functions from the plane to the plane
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by Iaci Malta, Nicolau C. Saldanha and Carlos Tomei PDF

Math. Comp. 65 (1996), 1531-1552 Request permission

Abstract:

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.

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