On bounding solutions of underdetermined systems (Q5935374)

For a mapping \(f:D\subseteq R^n\to R^m\), \(m\leq n\), where \(D\) is an open convex set, the author constructs a Krawczyk-Moore-type second-derivative operator (generalizing that one given by \textit{L. Qi} [SIAM J. Numer. Anal. 19, 851-857 (1982; Zbl 0506.65020)] for the case \(m=n\)) which can be used for checking existence and uniqueness of a solution to \(Yf(x)=0\), where \(Y\) is the pseudoinverse of \(f'(x)\). In case of \(f'(x)\) having the full rank, an iterative method is provided for bounding a zero of \(f\) in \(D\).