Πλοήγηση ανά Συγγραφέα "Karampetakis, Nicholas"
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Τεκμήριο An Optimal Bivariate Polynomial Interpolation Basis for the Application of the Evaluation-Interpolation Technique(2014-01-01) Varsamis, Dimitris; Karampetakis, Nicholas; Mastorocostas, ParisA new basis of interpolation points for the special case of the Newton two variable polynomial interpolation problem is proposed. This basis is implemented when the upper bound of the total degree and the degree in each variable is known. It is shown that this new basis under certain conditions (that depends on the degrees of the interpolation polynomial), coincides either with the known triangular/rectangular basis or it is a polygonal basis. In all cases it uses the least interpolation points with further consequences to the complexity of the algorithms that we use.Τεκμήριο Optimal Degree Estimation of the Determinant of a Polynomial Matrix(2014-03-01) Varsamis, Dimitris; Karampetakis, NicholasIn this paper we present a recursive formula to find the degree of the determinant of a bivariate polynomial matrix. The proposed algorithm returns the optimal estimation of the degree but has a very large computational cost. The recursive formula can be represented as an assignment problem which is solved with the Hungarian method that has a very small computational cost. The contribution of the proposed formula is to reduce the required interpolation points for the evaluation–interpolation technique. That is, we reduce the evaluations which are computations of determinants or inverse matrices.