In this paper, we first present a componentwise existence and nonexistence theorem for solutions of nonlinear equations in Rn or Cn, which improves those of Alefeld (1986) and Yamamoto (1978,1979,1980,1984). Next, the theorem is applied to algebraic equations. Finally, the results are illustrated with examples.
- a posteriori componentwise error estimates
- algebraic equations
- Existence and nonexistence theorem
- nonlinear equations
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics