The Experts below are selected from a list of 252 Experts worldwide ranked by ideXlab platform
Eduardo Fabiano - One of the best experts on this subject based on the ideXlab platform.
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assessment of interaction strength Interpolation Formulas for gold and silver clusters
Journal of Chemical Physics, 2018Co-Authors: Sara Giarrusso, Paola Gorigiorgi, Fabio Della Sala, Eduardo FabianoAbstract:The performance of functionals based on the idea of interpolating between the weak- and the strong-interaction limits the global adiabatic-connection integrand is carefully studied for the challenging case of noble-metal clusters. Different Interpolation Formulas are considered and various features of this approach are analyzed. It is found that these functionals, when used as a correlation correction to Hartree-Fock, are quite robust for the description of atomization energies, while performing less well for ionization potentials. Future directions that can be envisaged from this study and a previous one on main group chemistry are discussed.
A.r. Hayotov - One of the best experts on this subject based on the ideXlab platform.
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optimal Interpolation Formulas in the space w_2 m m 1 w 2 m m 1
Calcolo, 2019Co-Authors: S.s. Babaev, A.r. HayotovAbstract:In the present paper we investigate the problem of construction of the optimal Interpolation Formulas in the space $$W_2^{(m,m-1)}(0,1)$$ . We find the norm of the error functional which gives the upper bound for the error of the Interpolation Formulas in the space $$W_2^{(m,m-1)}(0,1)$$ . Further we get the system of linear equations for coefficients of the optimal Interpolation Formulas. Using the discrete analogue of the differential operator $$\frac{\,\mathrm{d}^{2m}}{\,\mathrm{d}x^{2m}}-\frac{\,\mathrm{d}^{2m-2}}{\,\mathrm{d}x^{2m-2}}$$ and its properties we find explicit Formulas for the coefficients of the optimal Interpolation Formulas. Finally, we give some numerical results which the confirm theoretical results of the paper.
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Optimal Interpolation Formulas in the space $$W_2^{(m,m-1)}$$ W 2 ( m , m - 1 )
Calcolo, 2019Co-Authors: S.s. Babaev, A.r. HayotovAbstract:In the present paper we investigate the problem of construction of the optimal Interpolation Formulas in the space $$W_2^{(m,m-1)}(0,1)$$ . We find the norm of the error functional which gives the upper bound for the error of the Interpolation Formulas in the space $$W_2^{(m,m-1)}(0,1)$$ . Further we get the system of linear equations for coefficients of the optimal Interpolation Formulas. Using the discrete analogue of the differential operator $$\frac{\,\mathrm{d}^{2m}}{\,\mathrm{d}x^{2m}}-\frac{\,\mathrm{d}^{2m-2}}{\,\mathrm{d}x^{2m-2}}$$ and its properties we find explicit Formulas for the coefficients of the optimal Interpolation Formulas. Finally, we give some numerical results which the confirm theoretical results of the paper.
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Optimal Interpolation Formulas in the space $$W_2^{(m,m-1)}$$ W 2
Calcolo, 2019Co-Authors: S.s. Babaev, A.r. HayotovAbstract:In the present paper we investigate the problem of construction of the optimal Interpolation Formulas in the space $$W_2^{(m,m-1)}(0,1)$$ W 2 ( m , m - 1 ) ( 0 , 1 ) . We find the norm of the error functional which gives the upper bound for the error of the Interpolation Formulas in the space $$W_2^{(m,m-1)}(0,1)$$ W 2 ( m , m - 1 ) ( 0 , 1 ) . Further we get the system of linear equations for coefficients of the optimal Interpolation Formulas. Using the discrete analogue of the differential operator $$\frac{\,\mathrm{d}^{2m}}{\,\mathrm{d}x^{2m}}-\frac{\,\mathrm{d}^{2m-2}}{\,\mathrm{d}x^{2m-2}}$$ d 2 m d x 2 m - d 2 m - 2 d x 2 m - 2 and its properties we find explicit Formulas for the coefficients of the optimal Interpolation Formulas. Finally, we give some numerical results which the confirm theoretical results of the paper.
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Optimal Interpolation Formulas with derivative in the space L(m)2(0,1)
Filomat, 2019Co-Authors: M.kh. Shadimetov, A.r. Hayotov, F. A. NuralievAbstract:The paper studies the problem of construction of optimal Interpolation Formulas with derivative in the Sobolev space L(m)2 (0,1). Here the Interpolation formula consists of the linear combination of values of the function at nodes and values of the first derivative of that function at the end points of the interval [0,1]. For any function of the space L(m)2 (0, 1) the error of the Interpolation Formulas is estimated by the norm of the error functional in the conjugate space L(m)* 2 (0,1). For this, the norm of the error functional is calculated. Further, in order to find the minimum of the norm of the error functional, the Lagrange method is applied and the system of linear equations for coefficients of optimal Interpolation Formulas is obtained. It is shown that the order of convergence of the obtained optimal Interpolation Formulas in the space L(m)2 (0,1) is O(hm). In order to solve the obtained system it is suggested to use the Sobolev method which is based on the discrete analog of the differential operator d2m= dx2m. Using this method in the cases m = 2 and m = 3 the optimal Interpolation Formulas are constructed. It is proved that the order of convergence of the optimal Interpolation formula in the case m = 2 for functions of the space C4(0,1) is O(h4) while for functions of the space L(2)2 (0,1) is O(h2). Finally, some numerical results are presented.
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Construction of Optimal Interpolation Formulas in the Sobolev Space
Contemporary Mathematics. Fundamental Directions, 2018Co-Authors: Kh M Shadimetov, A.r. Hayotov, F. A. NuralievAbstract:In the present paper, using the discrete analog of the differential operator d2m/dx2m, optimal Interpolation Formulas are constructed in L2(4)(0, 1) space. The explicit Formulas for coefficients of optimal Interpolation Formulas are obtained.
Sara Giarrusso - One of the best experts on this subject based on the ideXlab platform.
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assessment of interaction strength Interpolation Formulas for gold and silver clusters
Journal of Chemical Physics, 2018Co-Authors: Sara Giarrusso, Paola Gorigiorgi, Fabio Della Sala, Eduardo FabianoAbstract:The performance of functionals based on the idea of interpolating between the weak- and the strong-interaction limits the global adiabatic-connection integrand is carefully studied for the challenging case of noble-metal clusters. Different Interpolation Formulas are considered and various features of this approach are analyzed. It is found that these functionals, when used as a correlation correction to Hartree-Fock, are quite robust for the description of atomization energies, while performing less well for ionization potentials. Future directions that can be envisaged from this study and a previous one on main group chemistry are discussed.
Wolfram Koepf - One of the best experts on this subject based on the ideXlab platform.
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A unified representation for some Interpolation Formulas
Analysis, 2020Co-Authors: Mohammad Masjed-jamei, Zahra Moalemi, Wolfram KoepfAbstract:AbstractAs an extension of Lagrange Interpolation, we introduce a class of Interpolation Formulas and study their existence and uniqueness. In the sequel, we consider some particular cases and construct the corresponding weighted quadrature rules. Numerical examples are finally given and compared.
Fabio Della Sala - One of the best experts on this subject based on the ideXlab platform.
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assessment of interaction strength Interpolation Formulas for gold and silver clusters
Journal of Chemical Physics, 2018Co-Authors: Sara Giarrusso, Paola Gorigiorgi, Fabio Della Sala, Eduardo FabianoAbstract:The performance of functionals based on the idea of interpolating between the weak- and the strong-interaction limits the global adiabatic-connection integrand is carefully studied for the challenging case of noble-metal clusters. Different Interpolation Formulas are considered and various features of this approach are analyzed. It is found that these functionals, when used as a correlation correction to Hartree-Fock, are quite robust for the description of atomization energies, while performing less well for ionization potentials. Future directions that can be envisaged from this study and a previous one on main group chemistry are discussed.
