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On Polyhedral Approximations of the Second-Order Cone
Mathematics of Operations Research, 2001We demonstrate that a conic quadratic problem, [Formula: see text] is “polynomially reducible” to Linear Programming. We demonstrate this by constructing, for every ϵ ∈ (0, ½], an LP program (explicitly given in terms of ϵ and the data of (CQP)) [Formula: see text] with the following properties: the number dim x + dim u of variables and the number dim
Aharon Ben-Tal, Arkadi Nemirovski
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An Approximate Theory of Order in Alloys
Physical Review, 1950Short-range order parameters ${\ensuremath{\alpha}}_{i}$ are defined to express the interaction of a given atom in an alloy with the atoms of the ith shell of atoms surrounding it. From simple thermodynamic reasoning, involving a certain degree of approximation, equations relating the ${\ensuremath{\alpha}}_{i}$ with energy terms and the temperature ...
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On the Approximation Order of Splines on Spherical Triangulations
Advances in Computational Mathematics, 2004The standard splines on Euclidean spaces are piecewise algebraic polynomials on triangulations (in two dimensions) or on other partitions in higher dimensions. Polynomials on spheres which are suitable to approximation functions defined there are usually homogeneous polynomials, restricted to spheres.
Marian Neamtu, Larry L. Schumaker
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2021
This chapter focuses on the approximation of nonlinear hyperbolic systems using finite elements. We describe a somewhat loose adaptation to finite elements of a scheme introduced by Lax. The method, introduced by Guermond, Nazarov, and Popov, can be informally shown to be first-order accurate in time and space and to preserve every invariant set of the
Alexandre Ern, Jean-Luc Guermond
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This chapter focuses on the approximation of nonlinear hyperbolic systems using finite elements. We describe a somewhat loose adaptation to finite elements of a scheme introduced by Lax. The method, introduced by Guermond, Nazarov, and Popov, can be informally shown to be first-order accurate in time and space and to preserve every invariant set of the
Alexandre Ern, Jean-Luc Guermond
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2021
The objective of this chapter is to describe techniques that preserve the invariant domain property of the algorithm introduced in the previous chapter and increase its accuracy in time and space. The argumentation for the time approximation is done for general hyperbolic systems, but the argumentation for the space approximation is done for scalar ...
Alexandre Ern, Jean-Luc Guermond
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The objective of this chapter is to describe techniques that preserve the invariant domain property of the algorithm introduced in the previous chapter and increase its accuracy in time and space. The argumentation for the time approximation is done for general hyperbolic systems, but the argumentation for the space approximation is done for scalar ...
Alexandre Ern, Jean-Luc Guermond
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Spectral Approximation of Third-Order Problems
Journal of Scientific Computing, 1999The author introduces a Chebyshev collocation method for the partial differential equation \(u_t = u_{xxx}\) on the set \((x, t) \in (-1, 1) \times (0, T]\). The boundary conditions are of a Dirichlet sort which ensure stability. A computational investigation suggests that collocation at the Gauss-Lobatto points produces a stable numerical method.
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1995
Abstract We have shown that the central limit theorem can be used to calculate useful approximations to both univariate and multivariate pdfs that are generally easy to evaluate numerically. However, there are circumstances in which Gaussian approximations may be qualitatively inaccurate.
Uri Shmueli, George H Weiss
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Abstract We have shown that the central limit theorem can be used to calculate useful approximations to both univariate and multivariate pdfs that are generally easy to evaluate numerically. However, there are circumstances in which Gaussian approximations may be qualitatively inaccurate.
Uri Shmueli, George H Weiss
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Journal of Circuits, Systems and Computers, 2023
The use of fractional-order (FO) calculus for the solution of different problems in many fields has increased recently. However, the usage of FO system models in practice brings some difficulties. The FO operator, fractance device, is usually realized via several integer-order approximation methods, which have pros and cons in the aspect of operation ...
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The use of fractional-order (FO) calculus for the solution of different problems in many fields has increased recently. However, the usage of FO system models in practice brings some difficulties. The FO operator, fractance device, is usually realized via several integer-order approximation methods, which have pros and cons in the aspect of operation ...
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2016
Two-level factorial or fractional factorial experimental designs are used for obtaining a first-order approximation to the response function. They are particularly useful for selecting a smaller subset of potential input factors with which to formulate a better approximation equation.
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Two-level factorial or fractional factorial experimental designs are used for obtaining a first-order approximation to the response function. They are particularly useful for selecting a smaller subset of potential input factors with which to formulate a better approximation equation.
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2011
Because optimal policies require the solution of an m – 1 dimensional dynamic program, finding optimal policies is feasible only for moderately small values of m. For that reason, approximate policies are of particular interest. The first issue to be addressed when trying to find approximations is the form of the approximate policy.
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Because optimal policies require the solution of an m – 1 dimensional dynamic program, finding optimal policies is feasible only for moderately small values of m. For that reason, approximate policies are of particular interest. The first issue to be addressed when trying to find approximations is the form of the approximate policy.
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