Example ill-conditioned nonlinear system of equations

Question

I need ill-conditioned multivariate nonlinear systems of equations for testing purposes of a computer program. Do u know any specific problems from science? I read about chebyschev polynoms, but they are only one-dimensional.

Thank you

Greetings, Howard

Answer 1

Try this one:

$$x^2 − 2x + 3y = − 1 \\ 2x^2 - 3.9999x + 6.0001y = - 1.9999$$