Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.

Analysis of a data-based TV–holography system used to measure small vibration amplitudes

Abstract: We present a system that measures the full-field amplitude and phase distributions of objects that vibrate with small amplitudes. The system is based on TV–holography combined with sinusoidal phase modulation, discrete vibration-phase shifts, and digital image processing. Different new algorithms, based on a linear approximation of the fringe function, are discussed. Averaging techniques, used to reduce the effects of noise sources and to increase the resolution of the system, are also introduced. For one of the algorithms, tested in combination with the averaging techniques, the amplitude threshold was approximately 1/3000 of the wavelength of the applied laser light. The amplitude resolution was of the same magnitude. The phase accuracy is amplitude dependent and was about 3° for amplitudes greater than 5 nm.

Applied Optimization Methods for Wireless Networks

Abstract: 1. Introduction Part I. Methods for Optimal Solutions: 2. Linear programming and applications 3. Convex programming and applications 4. Design of polynomial-time exact algorithm Part II. Methods for Near-Optimal and Approximation Solutions: 5. Branch-and-bound framework and application 6. Reformulation-linearization technique and applications 7. Linear approximation 8. Approximation algorithm and its applications - part 1 9. Approximation algorithm and its applications - part 2 Part III. Methods for Efficient Heuristic Solutions: 10. An efficient technique for mixed-integer optimization 11. Metaheuristic methods Part IV. Other Topics: 12. Asymptotic capacity analysis.

Exchange and correlation potentials for finite temperature quantum calculations at intermediate degeneracies

Abstract: The exchange and correlation potentials which are needed in the study of electron systems (atoms, plasmas) at finite temperatures and finite degeneracies have been calculated and presented in a parametrised form convenient for use in Thomas-Fermi, Hartree-Fock, density-functional type effective single-particle models. The exchange corrected single-particle energies and chemical potential are calculated self-consistently and in the linear approximation. The natural generalisation of the Debye-Huckel screening length is used to extract a static model valid at intermediate degeneracies. The higher-order corrections (i.e., beyond Hartree-Fock) are evaluated from the ring sum and the second-order screened contributions to the thermodynamic grand potential. The ring sum is calculated via an approximation to the polarisation function which is known to be satisfactory at 0K and exact in the Debye-Huckel limit. The numerical results show that the correlation potential at finite temperatures consists of a static contribution and a dynamic part which goes to zero at high temperatures.

Optimal Reactive Power Dispatch With Accurately Modeled Discrete Control Devices: A Successive Linear Approximation Approach

Abstract: In this paper, a novel solution to the optimal reactive power dispatch (ORPD) problem is proposed. The nonlinearity of the power flow equations is handled by a new successive linear approximation approach. For the voltage magnitude terms, a mathematical transformation that improves the accuracy and facilitates the linear modeling of shunt capacitors is used. Without loss of accuracy, the load tap changers and shunt capacitors are both modeled by linear constraints using discrete variables, which facilitates the linearly constrained mixed-integer formulation of the proposed ORPD model. An efficient iterative solving algorithm is introduced. The obtained solution strictly satisfies the power flow equations. Case studies on several IEEE benchmark systems show that the proposed algorithm can efficiently provide near-optimal solutions with the error of the objective functions of less than 0.1%. Compared with several commercial solvers, the proposed method shows distinct advantages in terms of both robustness and efficiency. Moreover, based on the round-off results, a heuristic method that reduces the optimization ranges of the discrete control variables is proposed. This method can further improve the computational efficiency with small losses in accuracy.