The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Josip Pecaric - One of the best experts on this subject based on the ideXlab platform.
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generalizations of hardy type inequalities by abel gontscharoff s Interpolating Polynomial
Mathematics, 2021Co-Authors: Kristina Krulic Himmelreich, Josip Pecaric, Dora Pokaz, Marjan PraljakAbstract:In this paper, we extend Hardy’s type inequalities to convex functions of higher order. Upper bounds for the generalized Hardy’s inequality are given with some applications.
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estimation of f divergence and shannon entropy by using levinson type inequalities for higher order convex functions via hermite Interpolating Polynomial
Journal of Inequalities and Applications, 2020Co-Authors: Muhammad Adeel, Khuram Ali Khan, ðilda Pecaric, Josip PecaricAbstract:Levinson type inequalities are generalized by using Hermite Interpolating Polynomial for the class of $\mathfrak{n}$-convex functions. In seek of application to information theory, some estimates for new functional are obtained based on f divergence. Inequalities involving Shannon entropies are also discussed.
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estimation of different entropies via hermite Interpolating Polynomial using jensen type functionals
The Journal of Analysis, 2020Co-Authors: Khuram Ali Khan, Tasadduq Niaz, đilda Pecaric, Josip PecaricAbstract:We estimated the different entropies like Shannon entropy, Renyi divergences, Csiszar divergence by using the Jensen’s type functionals. The Zipf’s mandelbrot law and hybrid Zipf’s mandelbrot law are used to estimate the Shannon entropy. Further the Hermite Interpolating Polynomial is used to generalize the new inequalities for m-convex function.
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generalization of popoviciu type inequalities via green function and abel gontscharoff Interpolating Polynomial
Journal of Mathematical and Computational Science, 2017Co-Authors: Saad Ihsan Butt, Khuram Ali Khan, Josip PecaricAbstract:The inequality of Popoviciu for convex functions is generalized via Abel-Gontscharoff Interpolating Polynomial for higher order convex functions. Bounds are found for new identities, exponential convexity and Cauchy means are presented for linear functionals coming from the general inequality.
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integral error representation of hermite Interpolating Polynomial and related inequalities for quadrature formulae
Mathematical Modelling and Analysis, 2016Co-Authors: Gorana Arasgazic, Josip Pecaric, Ana VukelicAbstract:AbstractWe consider integral error representation related to the Hermite inter-polating Polynomial and derive some new estimations of the remainder in quadrature formulae of Hermite type, using Holder’s inequality and some inequalities for the Cebysev functional. As a special case, generalizations for the zeros of orthogonal Polynomials are considered.
Faheem Khan - One of the best experts on this subject based on the ideXlab platform.
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generalized subdivision surface scheme based on 2d lagrange Interpolating Polynomial and its error estimation
Communications in Mathematics and Applications, 2018Co-Authors: Muhammad Omar, Faheem KhanAbstract:This work gives the idea for constructing subdivision rules for surface based on 2D Lagrange Interpolating Polynomial [13]. In this method, subdivision rules for quad mesh has been obtained directly from the Lagrange Interpolating Polynomial. We also see that the simple interpolatory subdivision scheme for quadrilateral nets with arbitrary topology is presented by L. Kobbelt [5], can be directly calculated from the proposed generalized formula for subdivision surface refinement rules. Furthermore, some characteristics, applications and error bounds of the proposed work are also discussed.
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a new approach to approximating subdivision surface scheme using lagrange Interpolating Polynomial
2014Co-Authors: Faheem Khan, N Batool, M S HashmiAbstract:This paper presents the general formula for surface subdivision scheme to subdivide quad meshes by using Lagrange Interpolating Polynomial. We can see that the result obtained is equivalent to the tensor product of (2N + 4)-point n-ary approximating curve scheme for
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a unified Interpolating subdivision scheme for curves surfaces by using newton Interpolating Polynomial
Open Journal of Applied Sciences, 2013Co-Authors: Faheem Khan, Irem Mukhtar, N BatoolAbstract:This paper presents a general formula for (2m + 2)-point n-ary Interpolating subdivision scheme for curves for any integer m ≥ 0 and n ≥ 2 by using Newton Interpolating Polynomial. As a consequence, the proposed work is extended for surface case, which is equivalent to the tensor product of above proposed curve case. These formulas merge several notorious curve/surface schemes. Furthermore, visual performance of the subdivision schemes is also presented.
Ana Vukelic - One of the best experts on this subject based on the ideXlab platform.
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integral error representation of hermite Interpolating Polynomial and related inequalities for quadrature formulae
Mathematical Modelling and Analysis, 2016Co-Authors: Gorana Arasgazic, Josip Pecaric, Ana VukelicAbstract:AbstractWe consider integral error representation related to the Hermite inter-polating Polynomial and derive some new estimations of the remainder in quadrature formulae of Hermite type, using Holder’s inequality and some inequalities for the Cebysev functional. As a special case, generalizations for the zeros of orthogonal Polynomials are considered.
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cauchy s error representation of lidstone Interpolating Polynomial and related results
Journal of Mathematical Inequalities, 2015Co-Authors: Gorana Arasgazic, Josip Pecaric, Vera Culjak, Ana VukelicAbstract:In this paper we consider the Cauchy’s error representation of Lidstone Interpolating Polynomial and as a consequence the results concerning to the Hermite-Hadamard inequalities. Using these inequalities, we produce new exponentially convex functions. Also, we give several examples of the families of functions for which the obtained results can be applied.
Jim Q Smith - One of the best experts on this subject based on the ideXlab platform.
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discovery of statistical equivalence classes using computer algebra
International Journal of Approximate Reasoning, 2018Co-Authors: Christiane Gorgen, Anna Maria Bigatti, Eva Riccomagno, Jim Q SmithAbstract:Discrete statistical models supported on labeled event trees can be specified using so-called Interpolating Polynomials which are generalizations of generating functions. These admit a nested representation which is a notion formalized in this paper. A new algorithm exploits the primary decomposition of monomial ideals associated with an Interpolating Polynomial to quickly compute all nested representations of that Polynomial. It hereby determines an important subclass of all trees representing the same statistical model. To illustrate this method we analyze the full Polynomial equivalence class of a staged tree representing the best fitting model inferred from a real-world dataset.
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discovery of statistical equivalence classes using computer algebra
arXiv: Statistics Theory, 2017Co-Authors: Christiane Gorgen, Anna Maria Bigatti, Eva Riccomagno, Jim Q SmithAbstract:Discrete statistical models supported on labelled event trees can be specified using so-called Interpolating Polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the primary decomposition of monomial ideals associated with an Interpolating Polynomial to quickly compute all nested representations of that Polynomial. It hereby determines an important subclass of all trees representing the same statistical model. To illustrate this method we analyze the full Polynomial equivalence class of a staged tree representing the best fitting model inferred from a real-world dataset.
Konstantinos K Delibasis - One of the best experts on this subject based on the ideXlab platform.
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New Closed Formula for the Univariate Hermite Interpolating Polynomial of Total Degree and its Application in Medical Image Slice Interpolation
IEEE Transactions on Signal Processing, 2012Co-Authors: Konstantinos K Delibasis, Aristides I Kechriniotis, Nicholas D. AssimakisAbstract:This work investigates the usefulness of univariate Hermite interpolation of the total degree (HTD) for a biomedical signal processing task: slice interpolation in a variety of medical imaging modalities. The HTD is an algebraically demanding interpolation method that utilizes information of the values of the signal to be interpolated at distinct support positions, as well as the values of its derivatives up to a maximum available order. First a novel closed form solution for the univariate Hermite Interpolating Polynomial is presented for the general case of arbitrarily spaced support points and its computational and algebraic complexity is compared to that of the classical expression of the Hermite Interpolating Polynomial. Then, an implementation is proposed for the case of equidistant support positions with computational complexity comparable to any convolution-based interpolation method. We assess the proposed implementation of HTD interpolation with equidistant support points in the task of slice interpolation, which is usually treated as a one-dimensional problem. We performed a large number of interpolation experiments for 220 Magnetic Resonance Imaging (MRI) datasets and 50 Computer Tomography (CT) datasets and compared the proposed HTD implementation to several other well established interpolation techniques. In our experiments, we approximated the signal derivatives using finite differences, however the proposed HTD can accommodate any type of derivative calculation. Results show that the HTD interpolation outperforms the other interpolation methods under comparison, in terms of root mean square error (RMSE), in every one of the interpolation experiments, resulting in higher accuracy interpolated images. Finally, the behavior of the HTD with respect to its controlling parameters is explored and its computational complexity is determined.
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a new closed formula for the hermite Interpolating Polynomial with applications on the spectral decomposition of a matrix
arXiv: Rings and Algebras, 2011Co-Authors: Aristides I Kechriniotis, Konstantinos K Delibasis, C Tsonos, Nicholas PetropoulosAbstract:We present a new closed form for the Interpolating Polynomial of the general univariate Hermite interpolation that requires only calculation of Polynomial derivatives, instead of derivatives of rational functions. This result is used to obtain a new simultaneous Polynomial division by a common divisor over a perfect field. The above findings are utilized to obtain a closed formula for the semi–simple part of the Jordan decomposition of a matrix. Finally, a number of new identities involving Polynomial derivatives are obtained, based on the proposed simultaneous Polynomial division. The proposed explicit formula for the semi–simple part has been implemented using the Matlab programming environment.
