An existence and nonexistence theorem for solutions of nonlinear systems and its application to algebraic equations

Tetsuro Yamamoto; Xiaojun Chen

doi:10.1016/0377-0427(90)90008-N

An existence and nonexistence theorem for solutions of nonlinear systems and its application to algebraic equations

Tetsuro Yamamoto, Xiaojun Chen

Research output: Journal article publication › Journal article › Academic research › peer-review

12 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	87-97
Number of pages	11
Journal	Journal of Computational and Applied Mathematics
Volume	30
Issue number	1
DOIs	https://doi.org/10.1016/0377-0427(90)90008-N
Publication status	Published - 10 Apr 1990
Externally published	Yes

Keywords

a posteriori componentwise error estimates
algebraic equations
Existence and nonexistence theorem
nonlinear equations

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

More information

10.1016/0377-0427(90)90008-N

Cite this

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AU - Chen, Xiaojun

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N2 - 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.

AB - 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.

KW - a posteriori componentwise error estimates

KW - algebraic equations

KW - Existence and nonexistence theorem

KW - nonlinear equations

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U2 - 10.1016/0377-0427(90)90008-N

DO - 10.1016/0377-0427(90)90008-N

M3 - Journal article

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EP - 97

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

An existence and nonexistence theorem for solutions of nonlinear systems and its application to algebraic equations

Abstract

Keywords

ASJC Scopus subject areas

More information

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