On certain computable tests and componentwise error bounds
The authors give an overview on some existence and uniqueness tests for zeros of nonlinear functions \(f: \mathbb{R}^ n\to\mathbb{R}^ n\). They recall results of \textit{R. E. Moore} and \textit{J. B. Kioustelidis} [SIAM J. Numer. Anal. 17, 521-529 (1980; Zbl 0457.65031)], \textit{M. C. Pandian} [ibid. 22, 779-791 (1985; Zbl 0586.65041)], \textit{L. Qi} [ibid. 19, 851-857 (1982; Zbl 0506.65020)], the first author and \textit{A. Neumaier} [Computing 40, 85-90 (1988; Zbl 0629.65054)], the authors [Nonlinear Anal., Theory Methods Appl. 15, No. 3, 229-232 (1990; Zbl 0727.65045)]. They generalize some of these results, and they compare them in order to find out their quality. This is partly done theoretically and partly by examples.
scientific article; zbMATH DE number 425530
scientific article