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Full-Text Articles in Computer Engineering
Towards An Efficient Bisection Of Ellipsoids, Paden Portillo, Martine Ceberio, Vladik Kreinovich
Towards An Efficient Bisection Of Ellipsoids, Paden Portillo, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
Constraints are often represented as ellipsoids. One of the main advantages of such constrains is that, in contrast to boxes, over which optimization of even quadratic functions is NP-hard, optimization of a quadratic function over an ellipsoid is feasible. Sometimes, the area described by constrains is too large, so it is reasonable to bisect this area (one or several times) and solve the optimization problem for all the sub-areas. Bisecting a box, we still get a box, but bisecting an ellipsoid, we do not get an ellipsoid. Usually, this problem is solved by enclosing the half-ellipsoid in a larger ellipsoid, …
Estimating Information Amount Under Uncertainty: Algorithmic Solvability And Computational Complexity, Vladik Kreinovich, Gang Xiang
Estimating Information Amount Under Uncertainty: Algorithmic Solvability And Computational Complexity, Vladik Kreinovich, Gang Xiang
Departmental Technical Reports (CS)
Measurement results (and, more generally, estimates) are never absolutely accurate: there is always an uncertainty, the actual value x is, in general, different from the estimate X. Sometimes, we know the probability of different values of the estimation error dx=X-x, sometimes, we only know the interval of possible values of dx, sometimes, we have interval bounds on the cdf of dx. To compare different measuring instruments, it is desirable to know which of them brings more information - i.e., it is desirable to gauge the amount of information. For probabilistic uncertainty, this amount of information is described by Shannon's entropy; …