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Journal articles on the topic 'Successive approximation'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 June 2025

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1

Kovacevic, J., R. J. Safranek, and E. M. Yeh. "Deinterlacing by successive approximation." IEEE Transactions on Image Processing 6, no. 2 (1997): 339–44. http://dx.doi.org/10.1109/83.551707.

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2

Xin Li. "Demosaicing by successive approximation." IEEE Transactions on Image Processing 14, no. 3 (2005): 370–79. http://dx.doi.org/10.1109/tip.2004.840683.

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3

Yamada, Yoshio, and Saburo Tazaki. "Successive approximation vector quantization." Electronics and Communications in Japan (Part I: Communications) 69, no. 9 (1986): 11–19. http://dx.doi.org/10.1002/ecja.4410690902.

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4

Schoenberg, Michael A., and Maarten V. de Hoop. "Approximate dispersion relations for qP-qSV-waves in transversely isotropic media." GEOPHYSICS 65, no. 3 (2000): 919–33. http://dx.doi.org/10.1190/1.1444788.

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To decouple qP and qSV sheets of the slowness surface of a transversely isotropic (TI) medium, a sequence of rational approximations to the solution of the dispersion relation of a TI medium is introduced. Originally conceived to allow isotropic P-wave processing schemes to be generalized to encompass the case of qP-waves in transverse isotropy, the sequence of approximations was found to be applicable to qSV-wave processing as well, although a higher order of approximation is necessary for qSV-waves than for qP-waves to yield the same accuracy. The zeroth‐order approximation, about which all other approximations are taken, is that of elliptical TI, which contains the correct values of slowness and its derivative along and perpendicular to the medium’s axis of symmetry. Successive orders of approximation yield the correct values of successive orders of derivatives in these directions, thereby forcing the approximation into increasingly better fit at the intervening oblique angles. Practically, the first‐order approximation for qP-wave propagation and the second‐order approximation for qSV-wave propagation yield sufficiently accurate results for the typical transverse isotropy found in geological settings. After only slight modification to existing programs, the rational approximation allows for ray tracing, (f-k) domain migration, and split‐step Fourier migration in TI media—with little more difficulty than that encountered presently with such algorithms in isotropic media.
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5

Chowdary, I. Hitha, and G. Anitha Chowdary. "Power Efficient Successive Approximation Registers." IOSR journal of VLSI and Signal Processing 4, no. 3 (2014): 10–16. http://dx.doi.org/10.9790/4200-04331016.

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6

Alur, R., A. Itai, R. P. Kurshan, and M. Yannakakis. "Timing Verification by Successive Approximation." Information and Computation 118, no. 1 (1995): 142–57. http://dx.doi.org/10.1006/inco.1995.1059.

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7

Noeiaghdam, S., D. N. Sidorov, and A. I. Dreglea. "Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical Solution." Bulletin of Irkutsk State University. Series Mathematics 50 (2024): 36–50. https://doi.org/10.26516/1997-7670.2024.50.36.

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This research focuses on addressing both linear and nonlinear fuzzy Volterra integral equations that feature piecewise continuous kernels. The problem is tackled using the method of successive approximations. The study discusses the existence and uniqueness of solutions for these fuzzy Volterra integral equations with piecewise kernels. Numerical results are obtained by applying the successive approximations method to examples for both linear and nonlinear scenarios. Error analysis graphs are plotted to illustrate the accuracy of the method. Furthermore, a comparative analysis is presented through graphs of approximate solutions for different fuzzy parameter values. To highlight the effectiveness and significance of the successive approximations method, a comparison is made with the traditional homotopy analysis technique. The results indicate that the successive approximation method outperforms the homotopy analysis method in terms of accuracy and effectiveness.
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8

Fehér, Áron, Lorinc Márton, and Mihály Pituk. "Approximation of a Linear Autonomous Differential Equation with Small Delay." Symmetry 11, no. 10 (2019): 1299. http://dx.doi.org/10.3390/sym11101299.

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A linear autonomous differential equation with small delay is considered in this paper. It is shown that under a smallness condition the delay differential equation is asymptotically equivalent to a linear ordinary differential equation with constant coefficients. The coefficient matrix of the ordinary differential equation is a solution of an associated matrix equation and it can be written as a limit of a sequence of matrices obtained by successive approximations. The eigenvalues of the approximating matrices converge exponentially to the dominant characteristic roots of the delay differential equation and an explicit estimate for the approximation error is given.
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9

Petrus, Setyo Prabowo, and Mungkasi Sudi. "A multistage successive approximation method for Riccati differential equations." Bulletin of Electrical Engineering and Informatics 10, no. 3 (2021): pp. 1589~1597. https://doi.org/10.11591/eei.v10i3.3043.

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Riccati differential equations have played important roles in the theory and practice of control systems engineering. Our goal in this paper is to propose a new multistage successive approximation method for solving Riccati differential equations. The multistage successive approximation method is derived from an existing piecewise variational iteration method for solving Riccati differential equations. The multistage successive approximation method is simpler in terms of computing implementation in comparison with the existing piecewise variational iteration method. Computational tests show that the order of accuracy of the multistage successive approximation method can be made higher by simply taking more number of successive iterations in the multistage evolution. Furthermore, taking small size of each subinterval and taking large number of iterations in the multistage evolution lead that our proposed method produces small error and becomes high order accurate.
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10

C. Mayer, Daniel. "Successive Approximation of p-Class Towers." Advances in Pure Mathematics 07, no. 12 (2017): 660–85. http://dx.doi.org/10.4236/apm.2017.712041.

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11

da Silva, E. A. B., D. A. Fonini, and M. Craizer. "Successive approximation quantization for image compression." IEEE Circuits and Systems Magazine 2, no. 3 (2002): 20–45. http://dx.doi.org/10.1109/mcas.2002.1167626.

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12

Yang, Yang, and Marius Pesavento. "A Unified Successive Pseudoconvex Approximation Framework." IEEE Transactions on Signal Processing 65, no. 13 (2017): 3313–28. http://dx.doi.org/10.1109/tsp.2017.2684748.

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13

Craizer, M., E. A. B. da Silva, and E. G. Ramos. "Results on successive approximation vector quantisation." Electronics Letters 34, no. 1 (1998): 59. http://dx.doi.org/10.1049/el:19980052.

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14

Preston, Kenzie L., Annie Umbricht, Conrad J. Wong, and David H. Epstein. "Shaping cocaine abstinence by successive approximation." Journal of Consulting and Clinical Psychology 69, no. 4 (2001): 643–54. http://dx.doi.org/10.1037/0022-006x.69.4.643.

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15

Fussell, Donald, and Ramakrishna Thurimella. "Successive approximation in parallel graph algorithms." Theoretical Computer Science 74, no. 1 (1990): 19–35. http://dx.doi.org/10.1016/0304-3975(90)90004-2.

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16

Tesima, Kiusau. "The Angular Ordering in Soft-Gluon Emission." International Journal of Modern Physics A 02, no. 04 (1987): 1425–33. http://dx.doi.org/10.1142/s0217751x87000788.

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The way to evaluate multi-parton cross-sections systematically is discussed. In the leading-double-log approximation in QCD, the successive emission of soft gluons is at successively smaller angles. The angular ordering, however, is violated in the next-to-leading order.
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17

Dr. Sharad Pawar. "Application of some fixed-point theorems in approximation theory." International Journal of Science and Research Archive 7, no. 2 (2022): 607–13. http://dx.doi.org/10.30574/ijsra.2022.7.2.0367.

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In this paper, we study some fixed point theorems in approximation theory. Fixed point theory initially emerged in the article demonstrating existence of solutions of differential equations .which appeared in the second quarter of the 18th century. Lateral on this technique was improved as a method of successive approximations which was extracted and abstracted as a fixed point theorem in the framework of complete normed space. It is stated that fixed point theory is initiated by Stefan Banach. Fixed point theorem have been used in many instances in approximation theory. Brosowski gave some application of fixed point theory for approximation.
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18

Cengizci, Süleyman, and Aytekin Eryılmaz. "Successive Complementary Expansion Method for Solving Troesch’s Problem as a Singular Perturbation Problem." International Journal of Engineering Mathematics 2015 (October 27, 2015): 1–6. http://dx.doi.org/10.1155/2015/949463.

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A simple and efficient method that is called Successive Complementary Expansion Method (SCEM) is applied for approximation to an unstable two-point boundary value problem which is known as Troesch’s problem. In this approach, Troesch’s problem is considered as a singular perturbation problem. We convert the hyperbolic-type nonlinearity into a polynomial-type nonlinearity using an appropriate transformation, and then we use a basic zoom transformation for the boundary layer and finally obtain a nonlinear ordinary differential equation that contains SCEM complementary approximation. We see that SCEM gives highly accurate approximations to the solution of Troesch’s problem for various parameter values. Moreover, the results are compared with Adomian Decomposition Method (ADM) and Homotopy Perturbation Method (HPM) by using tables.
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19

Bedi, Amrit Singh, Ketan Rajawat, Vaneet Aggarwal, and Alec Koppel. "Escaping Saddle Points for Successive Convex Approximation." IEEE Transactions on Signal Processing 70 (2022): 307–21. http://dx.doi.org/10.1109/tsp.2021.3138242.

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20

Lan, J., M. J. Simoneau, R. K. Jeffers, and S. G. Boucher. "A universal shading method—successive approximation method." Journal of the Acoustical Society of America 93, no. 4 (1993): 2325. http://dx.doi.org/10.1121/1.406336.

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21

BUCKLEY, R. C. "Short note Successive approximation in pattern analysis." Australian Journal of Ecology 8, no. 3 (2006): 333–37. http://dx.doi.org/10.1111/j.1442-9993.1983.tb01330.x.

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22

Azal, Mera, Stepanenko Vitaly A., and Tarkhanov Nikolai. "Successive Approximation for the Inhomogeneous Burgers Equation." Journal of Siberian Federal University. Mathematics & Physics 11, no. 4 (2018): 519–31. http://dx.doi.org/10.17516/1997-1397-2018-11-4-519-531.

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23

TANG, XIAN, and KONG PANG PUN. "A NOVEL SWITCHED-CURRENT SUCCESSIVE APPROXIMATION ADC." Journal of Circuits, Systems and Computers 20, no. 01 (2011): 15–27. http://dx.doi.org/10.1142/s0218126611007049.

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A novel switched-current successive approximation ADC is presented in this paper with high speed and low power consumption. The proposed ADC contains a new high-accuracy and power-efficient switched-current S/H circuit and a speed-improved current comparator. Designed and simulated in a 0.18-μm CMOS process, this 8-bit ADC achieves 46.23 dB SNDR at 1.23 MS/s consuming 73.19 μW under 1.2 V voltage supply, resulting in an ENOB of 7.38-bit and an FOM of 0.357 pJ/Conv.-step.
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24

Malek-Mohammadi, Mohammadreza, Ali Koochakzadeh, Massoud Babaie-Zadeh, Magnus Jansson, and Cristian R. Rojas. "Successive Concave Sparsity Approximation for Compressed Sensing." IEEE Transactions on Signal Processing 64, no. 21 (2016): 5657–71. http://dx.doi.org/10.1109/tsp.2016.2585096.

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25

Beard, Randal W., Timothy W. McLain, and John T. Wen. "Successive galerkin approximation of the isaacs equation." IFAC Proceedings Volumes 32, no. 2 (1999): 2071–76. http://dx.doi.org/10.1016/s1474-6670(17)56351-x.

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26

Bűrmen, Árpád, and Tadej Tuma. "Unconstrained derivative-free optimization by successive approximation." Journal of Computational and Applied Mathematics 223, no. 1 (2009): 62–74. http://dx.doi.org/10.1016/j.cam.2007.12.017.

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27

Goldberg, Andrew V., and Robert E. Tarjan. "Finding Minimum-Cost Circulations by Successive Approximation." Mathematics of Operations Research 15, no. 3 (1990): 430–66. http://dx.doi.org/10.1287/moor.15.3.430.

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28

Wright, J. A. "HVAC simulation studies: Solution by successive approximation." Building Services Engineering Research and Technology 14, no. 4 (1993): 179–82. http://dx.doi.org/10.1177/014362449301400409.

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29

Han, Deren, and Liqun Qi. "A successive approximation method for quantum separability." Frontiers of Mathematics in China 8, no. 6 (2013): 1275–93. http://dx.doi.org/10.1007/s11464-013-0274-1.

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30

Cochran, James A. "A successive substitution procedure for eigenvalue approximation." Journal of Mathematical Analysis and Applications 127, no. 2 (1987): 388–402. http://dx.doi.org/10.1016/0022-247x(87)90117-x.

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31

Lee, Ching-pei, and Stephen J. Wright. "Inexact Successive quadratic approximation for regularized optimization." Computational Optimization and Applications 72, no. 3 (2019): 641–74. http://dx.doi.org/10.1007/s10589-019-00059-z.

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32

Matsuura, Tatsuji. "Recent progress on CMOS successive approximation ADCs." IEEJ Transactions on Electrical and Electronic Engineering 11, no. 5 (2016): 535–48. http://dx.doi.org/10.1002/tee.22290.

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33

Matalytski, Mikhail. "FINDING NON-STATIONARY STATE PROBABILITIES OF G-NETWORK WITH SIGNALS AND CUSTOMERS BATCH REMOVAL." Probability in the Engineering and Informational Sciences 31, no. 4 (2017): 396–412. http://dx.doi.org/10.1017/s0269964817000109.

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This paper is devoted to the research of an open Markov queueing network with positive customers and signals, and positive customers batch removal. A way of finding in a non-stationary regime time-dependent state probabilities has been proposed. The Kolmogorov system of difference-differential equations for state probabilities of such network was derived. The technique of its building, based on the use of the modified method of successive approximations combined with a series method, has been proposed. It is proved that the successive approximations converge over time to the stationary state probabilities, and the sequence of approximations converges to the unique solution of the Kolmogorov equations. Any successive approximation can be represented as a convergent power series with infinite radius of convergence, the coefficients of which satisfy the recurrence relations; that is useful for estimations. Model example illustrating the finding of time-dependent state probabilities of the network has been provided.
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34

Lin, Ching-Lung, Liren Lin, and Gen Nakamura. "Born approximation and sequence for hyperbolic equations." Asymptotic Analysis 121, no. 2 (2021): 101–23. http://dx.doi.org/10.3233/asy-201596.

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The Born approximation and the Born sequence are considered for hyperbolic equations when we perturb their leading parts. The Born approximation is a finite successive approximation such as the finite terms Neumann series for the solution of a hyperbolic equation in terms of the smallness of the perturbation and if the successive approximation is infinitely many times, then we have the Born series. Due to the so called regularity loss for solutions of hyperbolic equations, we need to assume that data such as the inhomogeneous term of the equation, Cauchy datum and boundary datum are C ∞ , and also they satisfy the compatibility condition of any order in order to define the Born series. Otherwise we need to smooth each term of the Born series. The convergence of the Born series and the Born series with smoothing are very natural questions to be asked. Also giving an estimate of approximating the solution for finite terms Born series is also an important question in practice. The aims of this paper are to discuss about these questions. We would like to emphasize that we found a small improvement in the usual energy estimate for solutions of an initial value problem for a hyperbolic equation, which is very useful for our aims. Since the estimate of approximation is only giving the worst estimate for the approximation, we also provide some numerical studies on these questions which are very suggestive for further theoretical studies on the Born approximation for hyperbolic equations.
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35

Menelaou, Charalambos, Stelios Timotheou, Panayiotis Kolios, and Christos Panayiotou. "Convexification approaches for regional route guidance and demand management with generalized MFDs." Transportation Research Part C: Emerging Technologies 154, Emerging Technologies (2023): 104245. https://doi.org/10.1016/j.trc.2023.104245.

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Traffic congestion is one of the main concerns in big cities with many adverse socioeconomic effects. A promising solution is to simultaneously regulate the admission of vehicles (i.e., demand management) and redistribute traffic flows within the network (i.e., route guidance). In this work, we integrate demand management with route guidance within a Model Predictive Control framework using regional traffic dynamics with generalized Macroscopic Fundamental Diagram (MFD) shapes. Dealing with generalized MFD shapes is challenging due to the resulting nonlinear and non-convex optimization formulation. To tackle this challenge, we develop two real-time solution approaches: (i) a successive convexification approach that constructs convex bounding sets for all nonlinear terms, and (ii) a linear approximation approach that solves the problem using triangular macroscopic fundamental diagram approximations. The proposed approaches offer a trade-off between execution speed and solution quality, as the linear approximation approach runs faster while the successive convexification approach yields better quality and accuracy solutions. Macroscopic simulation results illustrate the efficiency of the successive convexification and linear approximation approaches yielding an optimality gap of less than 3.5% and 10% in all considered cases, respectively. Furthermore, both approaches outperform a state-of-practice nonlinear solver in terms of solution quality and execution time. Finally, substantial gains are also obtained regarding travel time and traffic flow efficiency in a realistic microsimulation environment.
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36

Hristova, S., A. Golev, and K. Stefanova. "Quasilinearization of the Initial Value Problem for Difference Equations with “Maxima”." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/159031.

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The object of investigation of the paper is a special type of difference equations containing the maximum value of the unknown function over a past time interval. These equations are adequate models of real processes which present state depends significantly on their maximal value over a past time interval. An algorithm based on the quasilinearization method is suggested to solve approximately the initial value problem for the given difference equation. Every successive approximation of the unknown solution is the unique solution of an appropriately constructed initial value problem for a linear difference equation with “maxima,” and a formula for its explicit form is given. Also, each approximation is a lower/upper solution of the given mixed problem. It is proved the quadratic convergence of the successive approximations. The suggested algorithm is realized as a computer program, and it is applied to an example, illustrating the advantages of the suggested scheme.
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37

Bounaya, Mohammed Charif, Samir Lemita, Sami Touati, and Mohamed Zine Aissaoui. "Analytical and numerical approach for a nonlinear Volterra-Fredholm integro-differential equation." Boletim da Sociedade Paranaense de Matemática 41 (December 21, 2022): 1–14. http://dx.doi.org/10.5269/bspm.52191.

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An approach for Volterra- Fredholm integro-differential equations using appropriate fixed point theorems of existence, uniqueness is presented. The approximation of the solution is performed using Nystrom method in conjunction with successive approximations algorithm. Finally, we give a numerical example, in order to verify the effectiveness of the proposed method with respect to the analytical study.
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38

Seke, J., A. V. Soldatov, and N. N. Bogolubov. "Novel Technique for Quantum-Mechanical Eigenstate and Eigenvalue Calculations based on Seke's Self-Consistent Projection-Operator Method." Modern Physics Letters B 11, no. 06 (1997): 245–58. http://dx.doi.org/10.1142/s0217984997000311.

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Seke's self-consistent projection-operator method has been developed for deriving non-Markovian equations of motion for probability amplitudes of a relevant set of state vectors. This method, in a Born-like approximation, leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamiltonians. In the present paper, in order to explain the efficiency of Seke's method in particular applications, its algebraic operator structure is analyzed and a new successive approximation technique for the calculation of eigenstates and eigenvalues of an arbitrary quantum-mechanical system is developed. Unlike most perturbative techniques, in the present case each order of the approximation determines its own effective (approximating) Hamiltonian ensuring self-consistency and formal exactness of all results in the corresponding approximation order.
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39

Lakshmi Bhavani, G., Patan Muzafar, T. Usha Rani та ін. "A 1.2v ΔΣ ADC Modulator Using 4-bit SAR Quantizer for Biomedical Applications by using 65nm CMOS Technology". MATEC Web of Conferences 392 (2024): 01060. http://dx.doi.org/10.1051/matecconf/202439201060.

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This research focuses on enhancing Sigma-Delta ADC modulators for biomedical applications by leveraging the working principle of Successive Approximation ADC circuits. The proposed modulator includes a comparator, DAC, successive approximation register, and control circuit. The operational process begins with the sample and holds circuit-initiating conversions by sampling the input signal, and then compared with the DAC output. Using a 4-bit example, the successive approximation register refines the DAC output through iterative bit adjustments until the closest digital code approximation to the input is voltage independent of input voltage, occurring incrementally one bit at a time. The proposed enhancement aims to optimize Sigma-Delta ADC modulator performance for biomedical applications, ensuring high resolution and speed. Typical conversion speeds range from 2 to 5 MSPS, with resolutions varying from 8 to 16 bits, contributing to improved precision and efficiency in capturing and digitizing biomedical signals.
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40

Manaa, Saad A., and Nergiz M. Mosa. "Adomian Decomposition and Successive Approximation Methods for Solving Kaup-Boussinesq System." Science Journal of University of Zakho 7, no. 3 (2019): 101–7. http://dx.doi.org/10.25271/sjuoz.2019.7.3.582.

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The Kaup-Boussinesq system has been solved numerically by using two methods, Successive approximation method (SAM) and Adomian decomposition method (ADM). Comparison between the two methods has been made and both can solve this kind of problems, also both methods are accurate and has faster convergence. The comparison showed that the Adomian decomposition method much more accurate than Successive approximation method.
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41

Mahmudov, Nazım I., Sedef Emin, and Sameer Bawanah. "On the Parametrization of Caputo-Type Fractional Differential Equations with Two-Point Nonlinear Boundary Conditions." Mathematics 7, no. 8 (2019): 707. http://dx.doi.org/10.3390/math7080707.

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In this paper, we offer a new approach of investigation and approximation of solutions of Caputo-type fractional differential equations under nonlinear boundary conditions. By using an appropriate parametrization technique, the original problem with nonlinear boundary conditions is reduced to the equivalent parametrized boundary-value problem with linear restrictions. To study the transformed problem, we construct a numerical-analytic scheme which is successful in relation to different types of two-point and multipoint linear boundary and nonlinear boundary conditions. Moreover, we give sufficient conditions of the uniform convergence of the successive approximations. Also, it is indicated that these successive approximations uniformly converge to a parametrized limit function and state the relationship of this limit function and exact solution. Finally, an example is presented to illustrate the theory.
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42

Kamanabrou, Sudabeh. "Successful Rules on Successive Fixed-Term Contracts?" International Journal of Comparative Labour Law and Industrial Relations 33, Issue 2 (2017): 221–39. http://dx.doi.org/10.54648/ijcl2017010.

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In 1999 the European social partners negotiated the framework agreement on fixed-term work which was then put into effect by Council Directive 1999/70/EC. It contains, inter alia, measures designed to prevent abuse of successive fixed-term contracts. As the relevant clause of the agreement is rather loosely framed, its effect on legislative approximation in the EU is debatable. However, a study of the law on successive fixed-term employment contracts of fifteen EU Member States showed that legislative approximation in this field of law has largely been achieved.
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43

Micula, Sanda. "Numerical Solution of Two-Dimensional Fredholm–Volterra Integral Equations of the Second Kind." Symmetry 13, no. 8 (2021): 1326. http://dx.doi.org/10.3390/sym13081326.

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The paper presents an iterative numerical method for approximating solutions of two-dimensional Fredholm–Volterra integral equations of the second kind. As these equations arise in many applications, there is a constant need for accurate, but fast and simple to use numerical approximations to their solutions. The method proposed here uses successive approximations of the Mann type and a suitable cubature formula. Mann’s procedure is known to converge faster than the classical Picard iteration given by the contraction principle, thus yielding a better numerical method. The existence and uniqueness of the solution is derived under certain conditions. The convergence of the method is proved, and error estimates for the approximations obtained are given. At the end, several numerical examples are analyzed, showing the applicability of the proposed method and good approximation results. In the last section, concluding remarks and future research ideas are discussed.
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44

Nielsen, Frank. "A Simple Approximation Method for the Fisher–Rao Distance between Multivariate Normal Distributions." Entropy 25, no. 4 (2023): 654. http://dx.doi.org/10.3390/e25040654.

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We present a simple method to approximate the Fisher–Rao distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating the Fisher–Rao distances between successive nearby normal distributions on the curves by the square roots of their Jeffreys divergences. We consider experimentally the linear interpolation curves in the ordinary, natural, and expectation parameterizations of the normal distributions, and compare these curves with a curve derived from the Calvo and Oller’s isometric embedding of the Fisher–Rao d-variate normal manifold into the cone of (d+1)×(d+1) symmetric positive–definite matrices. We report on our experiments and assess the quality of our approximation technique by comparing the numerical approximations with both lower and upper bounds. Finally, we present several information–geometric properties of Calvo and Oller’s isometric embedding.
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45

Dũng, Dinh. "Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 3 (2021): 1163–98. http://dx.doi.org/10.1051/m2an/2021017.

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By combining a certain approximation property in the spatial domain, and weighted 𝓁2-summability of the Hermite polynomial expansion coefficients in the parametric domain obtained in Bachmayr et al. [ESAIM: M2AN 51 (2017) 341–363] and Bachmayr et al. [SIAM J. Numer. Anal. 55 (2017) 2151–2186], we investigate linear non-adaptive methods of fully discrete polynomial interpolation approximation as well as fully discrete weighted quadrature methods of integration for parametric and stochastic elliptic PDEs with lognormal inputs. We construct such methods and prove convergence rates of the approximations by them. The linear non-adaptive methods of fully discrete polynomial interpolation approximation are sparse-grid collocation methods which are certain sums taken over finite nested Smolyak-type indices sets of mixed tensor products of dyadic scale successive differences of spatial approximations of particular solvers, and of successive differences of their parametric Lagrange interpolating polynomials. The Smolyak-type sparse interpolation grids in the parametric domain are constructed from the roots of Hermite polynomials or their improved modifications. Moreover, they generate in a natural way fully discrete weighted quadrature formulas for integration of the solution to parametric and stochastic elliptic PDEs and its linear functionals, and the error of the corresponding integration can be estimated via the error in the Bochner space L1 (ℝ∞, V, γ) norm of the generating methods where γ is the Gaussian probability measure on ℝ∞ and V is the energy space. We also briefly consider similar problems for parametric and stochastic elliptic PDEs with affine inputs, and problems of non-fully discrete polynomial interpolation approximation and integration. In particular, the convergence rates of non-fully discrete polynomial interpolation approximation and integration obtained in this paper significantly improve the known ones.
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46

Pietruszka, Michał, Łukasz Borchmann, and Filip Graliński. "Successive Halving Top-k Operator." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 18 (2021): 15869–70. http://dx.doi.org/10.1609/aaai.v35i18.17931.

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We propose a differentiable successive halving method of relaxing the top-k operator, rendering gradient-based optimization possible. The need to perform softmax iteratively on the entire vector of scores is avoided using a tournament-style selection. As a result, a much better approximation of top-k and lower computational cost is achieved compared to the previous approach.
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47

Wang, Jia Rong, Xiao Dong Xia, Zong Da Zhang, and Han Yang. "Using Dual-Channel D/A Converters Design Successive Approximation A/D Converter." Applied Mechanics and Materials 719-720 (January 2015): 611–14. http://dx.doi.org/10.4028/www.scientific.net/amm.719-720.611.

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The successive approximation analog-to-digital converter (ADC) has been widely used in electronic devices due to the corresponding characteristics which are low cost, low power consumption, high accuracy and so on. This paper expounds a design of successive approximation A / D converter to show how to use TCL5615 which is a dual-channel serial 10-bit D/A converter (DAC) to make the conversion accuracy to reach 14-bit.
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48

Fan, Hua, Qi Wei, Fei Qiao, and Huazhong Yang. "A novel redundant pipelined successive approximation register ADC." IEICE Electronics Express 10, no. 5 (2013): 20130047. http://dx.doi.org/10.1587/elex.10.20130047.

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49

Miao, Ying, Danyang Shao, and Zhimin Yan. "Privacy-Oriented Successive Approximation Image Position Follower Processing." Complexity 2021 (June 7, 2021): 1–12. http://dx.doi.org/10.1155/2021/6853809.

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In this paper, we analyze the location-following processing of the image by successive approximation with the need for directed privacy. To solve the detection problem of moving the human body in the dynamic background, the motion target detection module integrates the two ideas of feature information detection and human body model segmentation detection and combines the deep learning framework to complete the detection of the human body by detecting the feature points of key parts of the human body. The detection of human key points depends on the human pose estimation algorithm, so the research in this paper is based on the bottom-up model in the multiperson pose estimation method; firstly, all the human key points in the image are detected by feature extraction through the convolutional neural network, and then the accurate labelling of human key points is achieved by using the heat map and offset fusion optimization method in the feature point confidence map prediction, and finally, the human body detection results are obtained. In the study of the correlation algorithm, this paper combines the HOG feature extraction of the KCF algorithm and the scale filter of the DSST algorithm to form a fusion correlation filter based on the principle study of the MOSSE correlation filter. The algorithm solves the problems of lack of scale estimation of KCF algorithm and low real-time rate of DSST algorithm and improves the tracking accuracy while ensuring the real-time performance of the algorithm.
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50

Idrees, Basil M., Javed Akhtar, and Ketan Rajawat. "Practical Precoding via Asynchronous Stochastic Successive Convex Approximation." IEEE Transactions on Signal Processing 69 (2021): 4177–91. http://dx.doi.org/10.1109/tsp.2021.3094971.

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