![]() Strong solvability of interval systems of equations and inequalities: characterization and complexity.Įigenvalues of symmetric interval matrices: complexity, Herz formula, enclosures. Interval systems of linear inequalities: Gerlach theorem, NP-hardness. Special case of tolerable solutions and their application. AE solution set: characterization, special cases briefly. Interval parametric linear systems: necessary condition, residual form, preconditioning, symmetic case. Regularity of an interval matrix: characterization, Beeck's sufficient condition (with the case when it is a complete characterization), necessary condition. Inverse nonnegative matrices and Kuttler's theorem. ![]() Topology of the solution set and Jansson's algorithm. Method of Hansen-Bliek-Rohn and a comparison of methods. Iterative methods: initial enclosure, Jacobi, Gauss-Seidel and Krawczyk methods (+bounds for overestimation), epsilon-inflation method.Īn application of the epsilon-inflation method: verification in linear equations solving. Interval Gaussian elimination for M-matrices. Methods for the square case: preconditioning, residual form, Interval Gaussian elimination. Interval systems of linear equations: The solution set and characterization of Oettli-Prager, orthant decomposition, NP-hardness of testing solvability. Interval functions: inclusion isotonicity, interval extension, natural interval extension, Fundamental theorem of interval analysis. ![]() Motivation for interval computation (numerical issues, computer assisted proofs, representation of uncertainty.). Just write me an e-mail and we will agree on a date. The exam terms are negotiated individually. Tutorials are conducted by Elif Garajová. Interval methods (NOPT051), winter semester 2021/2022 ![]()
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