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ON THE ORDER OF APPROXIMATION BY FEJÉR SUMS
Mathematics of the USSR-Izvestiya, 1969In this paper we study the degree of approximation almost everywhere by Fejer sums of orthogonal series , where the coefficients satisfy special conditions.
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An Approximate Distribution for the Maximum Order Complexity
Designs, Codes and Cryptography, 1997This paper deals with the maximum order complexity of a finite binary sequence meant as the shortest feedback shift-register that can generate this sequence. In order to utilize this notion for cryptographic purposes, it is necessary to know about the distribution of the maximum order complexity for random sequences.
Diane Erdmann, Sean Murphy
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An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications, 1996An approximative minimum degree ordering algorithm (AMD) based on the symmetric analogue of the degree bounds in the unsymmetric-pattern multifrontal method is described. The analysis of the performance and accuracy on a set of test matrices show that AMD is typically much faster compared with other established codes that compute minimum degree ...
Davis, Timothy A. +2 more
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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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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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