Ludyk, G. Einschließungsverfahren und ihre Anwendung in der Regelungstheorie. (Embedding methods and their application in control theory). (German) Zbl 0698.93021 Automatisierungstechnik 37, No. 11, 415-423 (1989). Summary: Embedding methods for the solution of linear and nonlinear systems of equations are described. These methods give highly accurate solutions in the form of intervals using the methods of interval mathematics with the optimal scalar product implemented in PASCAL-SC and FORTRAN-SC, where it is guaranteed that the solutions lie within the calculated very narrow intervals. It is described, how the problem of control theory must be formulated in order to be solvable using the new method. Besides the pole placement problem treated in great details the eigenvalue problem, the singular value decomposition and the simulation of nonlinear discrete- time systems are discussed. Cited in 1 Review MSC: 93B40 Computational methods in systems theory (MSC2010) 65F05 Direct numerical methods for linear systems and matrix inversion 65H10 Numerical computation of solutions to systems of equations 65G30 Interval and finite arithmetic Keywords:interval mathematics; pole placement problem; eigenvalue problem; singular value decomposition; nonlinear discrete-time systems PDFBibTeX XMLCite \textit{G. Ludyk}, Automatisierungstechnik 37, No. 11, 415--423 (1989; Zbl 0698.93021) Full Text: DOI