The numerical inversion of functions from the plane to the plane

Authors:
Iaci Malta, Nicolau C. Saldanha and Carlos Tomei

Journal:
Math. Comp. **65** (1996), 1531-1552

MSC (1991):
Primary 57R45, 65H10; Secondary 57R42, 65H20

MathSciNet review:
1361809

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Iaci Malta**

Affiliation:
Departamento de Matemática, PUC-Rio, Rua Marquês de São Vicente 225, Rio de Janeiro 22453-900, Brasil

Email:
malta@mat.puc-rio.br

**Nicolau C. Saldanha**

Affiliation:
IMPA, Estr. Dona Castorina 110, Rio de Janeiro 22460-320, Brasil

Email:
nicolau@impa.br

**Carlos Tomei**

Affiliation:
Departamento de Matemática, PUC-Rio, Rua Marquês de São Vicente 225, Rio de Janeiro 22453-900, Brasil

Email:
tomei@mat.puc-rio.br

DOI:
http://dx.doi.org/10.1090/S0025-5718-96-00770-3

Received by editor(s):
May 31, 1994

Received by editor(s) in revised form:
July 10, 1995

Additional Notes:
The authors received support from MCT and CNPq, Brazil.

Article copyright:
© Copyright 1996
American Mathematical Society