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Marko D. Petkovic

Publications and source records attributed to Marko D. Petkovic.

3 recordsLinked to original sources
arXiv2014

Iterative methods for the inclusion of the inverse matrix

In this paper we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval iterations. The new method is relied on a suitable matrix identity and a modification of a hyper-power method. This method is also feasible in the case of a full-rank $m\times n$ matrix, producing the interval sequence which converges to the Moore-Penrose inverse. It is shown that computational efficiency of the proposed method is equal or higher than the methods of hyper-power's type.

math.NA↗
arXiv2011

Spherical coverage verification

We consider the problem of covering hypersphere by a set of spherical hypercaps. This sort of problem has numerous practical applications such as error correcting codes and reverse k-nearest neighbor problem. Using the reduction of non degenerated concave quadratic programming (QP) problem, we demonstrate that spherical coverage verification is NP hard. We propose a recursive algorithm based on reducing the problem to several lower dimension subproblems. We test the performance of the proposed algorithm on a number of generated constellations. We demonstrate that the proposed algorithm, in spite of its exponential worst-case complexity, is applicable in practice. In contrast, our results indicate that spherical coverage verification using QP solvers that utilize heuristics, due to numerical instability, may produce false positives.

cs.CG↗