Статті в журналах: "ESTIMATES OF CONVERGENCE"

1

Heinrichs, Wilhelm. "Strong convergence estimates for pseudospectral methods." Applications of Mathematics 37, no. 6 (1992): 401–17. http://dx.doi.org/10.21136/am.1992.104520.

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2

Shen, Xiaotong, and Wing Hung Wong. "Convergence Rate of Sieve Estimates." Annals of Statistics 22, no. 2 (June 1994): 580–615. http://dx.doi.org/10.1214/aos/1176325486.

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3

Kang, K. S., and D. Y. Kwak. "Convergence estimates for multigrid algorithms." Computers & Mathematics with Applications 34, no. 9 (November 1997): 15–22. http://dx.doi.org/10.1016/s0898-1221(97)00185-5.

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4

Borwein, J. M., and A. S. Lewis. "Convergence of Best Entropy Estimates." SIAM Journal on Optimization 1, no. 2 (May 1991): 191–205. http://dx.doi.org/10.1137/0801014.

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5

Gupta, Vijay. "Convergence Estimates for Gamma Operator." Bulletin of the Malaysian Mathematical Sciences Society 43, no. 3 (June 19, 2019): 2065–75. http://dx.doi.org/10.1007/s40840-019-00791-z.

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6

Falgout, Robert D., Panayot S. Vassilevski, and Ludmil T. Zikatanov. "On two-grid convergence estimates." Numerical Linear Algebra with Applications 12, no. 5-6 (2005): 471–94. http://dx.doi.org/10.1002/nla.437.

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7

SOYBAŞ, DANYAL, and NEHA MALIK. "Convergence Estimates for Gupta-Srivastava Operators." Kragujevac Journal of Mathematics 45, no. 5 (2021): 739–49. http://dx.doi.org/10.46793/kgjmat2105.739s.

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Анотація:

The Grüss-Voronovskaya-type approximation results for the modiﬁed Gupta-Srivastava operators are considered. Moreover, the magnitude of diﬀerences of two linear positive operators deﬁned on an unbounded interval has been estimated. Quantitative type results are established as we initially obtain the moments of generalized discrete operators and then estimate the diﬀerence of these operators with the Gupta-Srivastava operators.

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8

Teboulle, M., and I. Vajda. "Convergence of best phi -entropy estimates." IEEE Transactions on Information Theory 39, no. 1 (1993): 297–301. http://dx.doi.org/10.1109/18.179378.

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9

Bramble, James H., and Joseph E. Pasciak. "New convergence estimates for multigrid algorithms." Mathematics of Computation 49, no. 180 (1987): 311. http://dx.doi.org/10.1090/s0025-5718-1987-0906174-x.

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10

Theiler, James, and Leonard A. Smith. "Anomalous convergence of Lyapunov exponent estimates." Physical Review E 51, no. 4 (April 1, 1995): 3738–41. http://dx.doi.org/10.1103/physreve.51.3738.

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11

Măruşter, Ştefan. "Local Convergence of Exquerro-Hernandez Method." Annals of West University of Timisoara - Mathematics and Computer Science 54, no. 1 (July 1, 2016): 159–66. http://dx.doi.org/10.1515/awutm-2016-0009.

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Abstract Local convergence of Ezquerro-Hernandez iteration is investigated in the setting of finite dimensional spaces. A procedure to estimate the local convergence radius for this iteration is proposed. Numerical experiments show that our procedure gives estimates which are very close to the maximum convergence radii.

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12

Mishra, Nav Shakti, and Naokant Deo. "Convergence estimates of certain gamma type operators." Mathematical Methods in the Applied Sciences 45, no. 7 (December 28, 2021): 3802–16. http://dx.doi.org/10.1002/mma.8017.

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13

Heidelberger, Philip, Xi-Ren Cao, Michael A. Zazanis, and Rajan Suri. "Convergence Properties of Infinitesimal Perturbation Analysis Estimates." Management Science 34, no. 11 (November 1988): 1281–302. http://dx.doi.org/10.1287/mnsc.34.11.1281.

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14

Anichkin, S. A. "Rate of convergence estimates in Blackwell's theorem." Journal of Soviet Mathematics 40, no. 4 (February 1988): 449–53. http://dx.doi.org/10.1007/bf01083636.

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15

Kalashnikov, V. V. "Estimates of convergence rate in Renyi's theorem." Journal of Soviet Mathematics 32, no. 6 (March 1986): 609–19. http://dx.doi.org/10.1007/bf01085157.

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16

Brown, Gavin, and Kunyang Wang. "Jacobi polynomial estimates and fourier-laplace convergence." Journal of Fourier Analysis and Applications 3, no. 6 (November 1997): 705–14. http://dx.doi.org/10.1007/bf02648263.

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17

Gomes, Sônia M., and Elsa Cortina. "Convergence Estimates for the Wavelet Galerkin Method." SIAM Journal on Numerical Analysis 33, no. 1 (February 1996): 149–61. http://dx.doi.org/10.1137/0733009.

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18

Shu, Lian-Ta, Guorong Zhou, and Qing-Bo Cai. "On the Convergence of a Family of Chlodowsky Type Bernstein-Stancu-Schurer Operators." Journal of Function Spaces 2018 (July 18, 2018): 1–15. http://dx.doi.org/10.1155/2018/6385451.

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Анотація:

We construct a new family of univariate Chlodowsky type Bernstein-Stancu-Schurer operators and bivariate tensor product form. We obtain the estimates of moments and central moments of these operators, obtain weighted approximation theorem, establish local approximation theorems by the usual and the second order modulus of continuity, estimate the rate of convergence, give a convergence theorem for the Lipschitz continuous functions, and also obtain a Voronovskaja-type asymptotic formula. For the bivariate case, we give the rate of convergence by using the weighted modulus of continuity. We also give some graphs and numerical examples to illustrate the convergent properties of these operators to certain functions and show that the new ones have a better approximation to functions f for one dimension.

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19

Scully, Kevin. "Mesh-based interpolation on2-manifolds." International Journal of Mathematics and Mathematical Sciences 2005, no. 7 (2005): 1067–83. http://dx.doi.org/10.1155/ijmms.2005.1067.

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This paper presents a globalL1-estimate for the convergence of mesh-based interpolants on 2-manifolds defined over multiple coordinate systems and analyzes the convergence of an integral on a triangulated approximate manifold to the desired integral on the manifold being approximated. To place this estimate in context, previous convergence estimates for interpolation techniques on manifolds are presented. Finally, numerical results demonstrating the value of theL1-estimate are presented.

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20

Dixon, Peter B., and Maureen T. Rimmer. "Analysing Convergence with a Multi-Country Computable General Equilibrium Model: PPP versus Mer." Energy & Environment 16, no. 6 (November 2005): 901–21. http://dx.doi.org/10.1260/095830505775221524.

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In studies of the greenhouse gas implications of convergence by developing countries to the per-capita GNPs of developed countries, considerable discussion has centred on whether purchasing power parity (PPP) or market exchange rates (MER) should be used in measuring per-capita GNPs. We suggest that technology gaps between developing and developed countries should be the starting point for convergence analysis rather than per-capita GNP gaps. We estimate two sets of initial technology gaps, using PPP and MER price assumptions combined with input-output data. In simulating the effects of closing technology gaps (convergence) using a dynamic, multi-country CGE model, we find: the MER/PPP distinction matters. MER-based estimates of initial technology gaps lead to higher estimates of convergence-induced growth in greenhouse-gas-emitting industries in developing countries than do PPP-based estimates. the industry detail in CGE models is valuable. Our simulations show a wide range of convergence-induced changes in output across industries.

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21

Bulinski, Alexander, and Nikolay Slepov. "Sharp Estimates for Proximity of Geometric and Related Sums Distributions to Limit Laws." Mathematics 10, no. 24 (December 14, 2022): 4747. http://dx.doi.org/10.3390/math10244747.

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The convergence rate in the famous Rényi theorem is studied by means of the Stein method refinement. Namely, it is demonstrated that the new estimate of the convergence rate of the normalized geometric sums to exponential law involving the ideal probability metric of the second order is sharp. Some recent results concerning the convergence rates in Kolmogorov and Kantorovich metrics are extended as well. In contrast to many previous works, there are no assumptions that the summands of geometric sums are positive and have the same distribution. For the first time, an analogue of the Rényi theorem is established for the model of exchangeable random variables. Also within this model, a sharp estimate of convergence rate to a specified mixture of distributions is provided. The convergence rate of the appropriately normalized random sums of random summands to the generalized gamma distribution is estimated. Here, the number of summands follows the generalized negative binomial law. The sharp estimates of the proximity of random sums of random summands distributions to the limit law are established for independent summands and for the model of exchangeable ones. The inverse to the equilibrium transformation of the probability measures is introduced, and in this way a new approximation of the Pareto distributions by exponential laws is proposed. The integral probability metrics and the techniques of integration with respect to sign measures are essentially employed.

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22

DelVecchio, Micah. "International Income Convergence to a Common Trend and Long Run Growth Estimation Using Economic Institutions of OECD Economies." Journal of International Business and Economy 20, no. 1 (July 1, 2019): 1–31. http://dx.doi.org/10.51240/jibe.2019.1.1.

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In traditional studies of regional income convergence, the economies are assumed to follow a common long-run trend determined by common technology. For the group of OECD economies, this is a defensible assumption. In this paper, we estimate this long run component by recovering estimates of steady-state levels of output from the standard convergence estimates in a panel data set. We use institutional indicators to help estimate production technology. Results indicate that many OECD economies were above their steady states last decade, explaining the subsequent slower pace of long-run growth.

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23

Bunyaratavej, Kraiwinee, and Eugene D. Hahn. "An Integrative Approach to Measuring Economic Convergence: The Case of the European Union." Global Economy Journal 5, no. 2 (June 6, 2005): 1850039. http://dx.doi.org/10.2202/1524-5861.1065.

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Empirical convergence analyses have helped provide insight as to whether economies are converging. Previous works on convergence have tended to focus on a particular economic indicator exclusively, even though the convergence process has multiple components. Improved estimates of convergence are likely to result from an integrated approach wherein several indicators are considered simultaneously. The proposed model integrates convergence analyses for three convergence variables to estimate the overall rate of economic convergence in the EU during 1960 to 1990. The research indicates that convergence is occurring overall, but that employment convergence is happening at a considerably slower pace than are the other types of convergence.

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24

Hahn, Jinyong, and Zhipeng Liao. "Bootstrap Standard Error Estimates and Inference." Econometrica 89, no. 4 (2021): 1963–77. http://dx.doi.org/10.3982/ecta17912.

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Asymptotic justification of the bootstrap often takes the form of weak convergence of the bootstrap distribution to some limit distribution. Theoretical literature recognized that the weak convergence does not imply consistency of the bootstrap second moment or the bootstrap variance as an estimator of the asymptotic variance, but such concern is not always reflected in the applied practice. We bridge the gap between the theory and practice by showing that such common bootstrap based standard error in fact leads to a potentially conservative inference.

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25

Shubat, O. M. "Statistical Estimates of the Decline of the Russian Fertility: Regional Specifcs." Voprosy statistiki 28, no. 5 (October 27, 2021): 39–48. http://dx.doi.org/10.34023/2313-6383-2021-28-5-39-48.

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The study focuses on analyzing regional features of the decline in the birth rate in Russia in 2016–2019. Taking into account regional specifcs is crucial when perfecting the implemented measures for improving the general demographic situation in the Russian Federation.The information base of the study contained time series of the total fertility rate in selected Russian regions. The author used methods of descriptive statistics and assessed convergent trends based on the sigma-, beta- and gamma-convergence methods. Spatial eﬀects in regional diﬀerentiation of fertility were assessed based on Moran's I.As a result of the analysis, the following features were established. Firstly, in recent years in Russia, there has been a high degree of diﬀerentiation in the recorded declining birth rates. Secondly, the processes of falling fertility in the regions have specifc characteristics, the absence of typical trajectories in those subjects where it fell most or least of all. Thirdly, in Russia, there are no pronounced territo rial localizations of the processes of fertility decline. And fourthly, based on a comparison of the birth rate dynamics in Russian regions, no convergent trends have been identifed, i. e., there is no convergence of territorial entities in terms of the birth rate.According to the author, the demographic policy of recent years has not yet responded positively either in terms of birth rate growth or leveling of regional diﬀerences. The results obtained indicate that unifed approaches are unsuited to solving the demographic problems of Russian territories, and there is a need for demographic policy measures that take into account regional variability and are aimed at smoothing regional disproportions. Consequently, it is necessary to conduct regular statistical and demographic studies of the specificity of regional situations using methods of convergence and spatial autocorrelation analysis, rarely used in demography

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26

Glasserman, Paul, Jian-Qiang Hu, and Stephen G. Strickland. "Strongly Consistent Steady-State Derivative Estimates." Probability in the Engineering and Informational Sciences 5, no. 4 (October 1991): 391–413. http://dx.doi.org/10.1017/s0269964800002199.

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We establish strong consistency (i.e., almost sure convergence) of infinitesimal perturbation analysis (IPA) estimators of derivatives of steady-state means for a broad class of systems. Our results substantially extend previously available results on steady-state derivative estimation via IPA.Our basic assumption is that the process under study is regenerative, but our analysis uses regenerative structure in an indirect way: IPA estimators are typically biased over regenerative cycles, so straightforward differentiation of the regenerative ratio formula does not necessarily yield a valid estimator of the derivative of a steady-state mean. Instead, we use regeneration to pass from unbiasedness over fixed, finite time horizons to convergence as the time horizon grows. This provides a systematic way of extending results on unbiasedness to strong consistency.Given that the underlying process regenerates, we provide conditions under which a certain augmented process is also regenerative. The augmented process includes additional information needed to evaluate derivatives; derivatives of time averages of the original process are time averages of the augmented process. Thus, through this augmentation we are able to apply standard renewal theory results to the convergence of derivatives.

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27

Mazza, Davide, Florian Mueller, Timothy J. Stasevich, and James G. McNally. "Convergence of chromatin binding estimates in live cells." Nature Methods 10, no. 8 (July 30, 2013): 691–92. http://dx.doi.org/10.1038/nmeth.2573.

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28

Pavlov, A., N. van de Wouw, and H. Nijmeijer. "The Local Output Regulation Problem: Convergence Region Estimates." IEEE Transactions on Automatic Control 49, no. 5 (May 2004): 814–19. http://dx.doi.org/10.1109/tac.2004.828322.

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29

Bramble, James H., Joseph E. Pasciak, Jun Ping Wang, and Jinchao Xu. "Convergence estimates for multigrid algorithms without regularity assumptions." Mathematics of Computation 57, no. 195 (September 1, 1991): 23. http://dx.doi.org/10.1090/s0025-5718-1991-1079008-4.

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30

ALBANESE, CLAUDIO. "KERNEL CONVERGENCE ESTIMATES FOR DIFFUSIONS WITH CONTINUOUS COEFFICIENTS." International Journal of Theoretical and Applied Finance 14, no. 07 (November 2011): 979–1004. http://dx.doi.org/10.1142/s0219024911006619.

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Bidirectional valuation models are based on numerical methods to obtain kernels of parabolic equations. Here we address the problem of robustness of kernel calculations vis a vis floating point errors from a theoretical standpoint. We are interested in kernels of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step h > 0 in the limit as h → 0. We consider both semidiscrete triangulations with continuous time and explicit Euler schemes with time step so small that the Courant condition is satisfied. We find uniform bounds for the convergence rate as a function of the degree of smoothness. We conjecture these bounds are indeed sharp. The bounds also apply to the time derivatives of the kernel and its first two space derivatives. The proof is constructive and is based on a new technique of path conditioning for Markov chains and a renormalization group argument. We make the simplifying assumption of time-independence and use longitudinal Fourier transforms in the time direction. Convergence rates depend on the degree of smoothness and Hölder differentiability of the coefficients. We find that the fastest convergence rate is of order O(h2) and is achieved if the coefficients have a bounded second derivative. Otherwise, explicit schemes still converge for any degree of Hölder differentiability except that the convergence rate is slower. Hölder continuity itself is not strictly necessary and can be relaxed by an hypothesis of uniform continuity.

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31

Neymeyr, Klaus. "A geometric theory forpreconditioned inverse iterationII: Convergence estimates." Linear Algebra and its Applications 322, no. 1-3 (January 2001): 87–104. http://dx.doi.org/10.1016/s0024-3795(00)00236-6.

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32

Ata, Mustafa Y. "A convergence criterion for the Monte Carlo estimates." Simulation Modelling Practice and Theory 15, no. 3 (March 2007): 237–46. http://dx.doi.org/10.1016/j.simpat.2006.12.002.

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33

Cai, Zhijie. "Convergence and error estimates for meshless Galerkin methods." Applied Mathematics and Computation 184, no. 2 (January 2007): 908–16. http://dx.doi.org/10.1016/j.amc.2006.05.194.

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34

Güler, Osman. "Convergence rate estimates for the gradient differential inclusion." Optimization Methods and Software 20, no. 6 (December 2005): 729–35. http://dx.doi.org/10.1080/10556780500094770.

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35

Kasitskaya, E. I., and P. S. Knopov. "Convergence of empirical estimates in stochastic optimization problems." Cybernetics 27, no. 2 (1991): 297–303. http://dx.doi.org/10.1007/bf01068383.

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36

Giorgilli, Antonio, Ugo Locatelli, and Marco Sansottera. "Improved convergence estimates for the Schröder–Siegel problem." Annali di Matematica Pura ed Applicata (1923 -) 194, no. 4 (February 15, 2014): 995–1013. http://dx.doi.org/10.1007/s10231-014-0408-4.

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37

Antos, Andr�s, and Ioannis Kontoyiannis. "Convergence properties of functional estimates for discrete distributions." Random Structures and Algorithms 19, no. 3-4 (2001): 163–93. http://dx.doi.org/10.1002/rsa.10019.

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38

Babakus, Emin, Carl E. Ferguson, and Karl G. Jöreskog. "The Sensitivity of Confirmatory Maximum Likelihood Factor Analysis to Violations of Measurement Scale and Distributional Assumptions." Journal of Marketing Research 24, no. 2 (May 1987): 222–28. http://dx.doi.org/10.1177/002224378702400209.

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Анотація:

A large-scale simulation design was used to study the sensitivity of maximum likelihood (ML) factor analysis to violations of measurement scale and distributional assumptions in the input data. Product-moment, polychoric. Spearman's rho, and Kendall's tau- b correlations computed from ordinal data were used to estimate a single-factor model. The resulting ML estimates were compared on the bases of convergence rates and improper solutions, accuracy of the loading estimates, fit statistics, and estimated standard errors. The LISREL maximum likelihood solution algorithm was used to estimate model parameters. The polychoric correlation procedure was found to provide the most accurate estimates of pairwise correlations and factor loadings but performed worst on all goodness-of-fit criteria. LISREL overestimated all standard errors, thus not reflecting the effects of standardization as previously assumed. When the data were categorized, the polychoric correlations led to the best estimates of the standard errors.

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39

GAL, SORIN G., and CONSTANTIN P. NICULESCU. "Approximation of random functions by stochastic Bernstein polynomials in capacity spaces." Carpathian Journal of Mathematics 37, no. 2 (June 9, 2021): 185–94. http://dx.doi.org/10.37193/cjm.2021.02.04.

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Анотація:

Given a submodular capacity space, we firstly obtain a quantitative estimate for the uniform convergence in the Choquet p-mean, 1\le p<\infty, of the multivariate stochastic Bernstein polynomials associated to a random function. Also, quantitative estimates concerning the uniform convergence in capacity in the univariate case are given.

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40

Wallace, Tim, and Ali Sekmen. "Kaczmarz Iterative Projection and Nonuniform Sampling with Complexity Estimates." Journal of Medical Engineering 2014 (December 15, 2014): 1–15. http://dx.doi.org/10.1155/2014/908984.

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Анотація:

Kaczmarz’s alternating projection method has been widely used for solving mostly over-determined linear system of equations Ax=b in various fields of engineering, medical imaging, and computational science. Because of its simple iterative nature with light computation, this method was successfully applied in computerized tomography. Since tomography generates a matrix A with highly coherent rows, randomized Kaczmarz algorithm is expected to provide faster convergence as it picks a row for each iteration at random, based on a certain probability distribution. Since Kaczmarz’s method is a subspace projection method, the convergence rate for simple Kaczmarz algorithm was developed in terms of subspace angles. This paper provides analyses of simple and randomized Kaczmarz algorithms and explains the link between them. New versions of randomization are proposed that may speed up convergence in the presence of nonuniform sampling, which is common in tomography applications. It is anticipated that proper understanding of sampling and coherence with respect to convergence and noise can improve future systems to reduce the cumulative radiation exposures to the patient. Quantitative simulations of convergence rates and relative algorithm benchmarks have been produced to illustrate the effects of measurement coherency and algorithm performance, respectively, under various conditions in a real-time kernel.

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41

Willis, Brian H., Mohammed Baragilly, and Dyuti Coomar. "Maximum likelihood estimation based on Newton–Raphson iteration for the bivariate random effects model in test accuracy meta-analysis." Statistical Methods in Medical Research 29, no. 4 (June 11, 2019): 1197–211. http://dx.doi.org/10.1177/0962280219853602.

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A bivariate generalised linear mixed model is often used for meta-analysis of test accuracy studies. The model is complex and requires five parameters to be estimated. As there is no closed form for the likelihood function for the model, maximum likelihood estimates for the parameters have to be obtained numerically. Although generic functions have emerged which may estimate the parameters in these models, they remain opaque to many. From first principles we demonstrate how the maximum likelihood estimates for the parameters may be obtained using two methods based on Newton–Raphson iteration. The first uses the profile likelihood and the second uses the Observed Fisher Information. As convergence may depend on the proximity of the initial estimates to the global maximum, each algorithm includes a method for obtaining robust initial estimates. A simulation study was used to evaluate the algorithms and compare their performance with the generic generalised linear mixed model function glmer from the lme4 package in R before applying them to two meta-analyses from the literature. In general, the two algorithms had higher convergence rates and coverage probabilities than glmer. Based on its performance characteristics the method of profiling is recommended for fitting the bivariate generalised linear mixed model for meta-analysis.

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42

Bojović, Dejan, and Boško Jovanović. "Fractional Order Convergence Rate Estimates Of Finite Difference Method On Nonuniform Meshes." Computational Methods in Applied Mathematics 1, no. 3 (2001): 213–21. http://dx.doi.org/10.2478/cmam-2001-0015.

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AbstractIn this paper we show how the theory of interpolation of function spaces can be used to establish convergence rate estimates for finite difference schemes on nonuniform meshes. As a model problem we consider the first boundary value problem for the Poisson equation. Using the interpolation theory we construct a fractional-order convergence rate estimate which is consistent with the smoothness of data.

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43

Özger, Faruk. "Weighted statistical approximation properties of univariate and bivariate λ-Kantorovich operators". Filomat 33, № 11 (2019): 3473–86. http://dx.doi.org/10.2298/fil1911473o.

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In this study, we consider statistical approximation properties of univariate and bivariate ?-Kantorovich operators. We estimate rate of weighted A-statistical convergence and prove a Voronovskajatype approximation theorem by a family of linear operators using the notion of weighted A-statistical convergence. We give some estimates for differences of ?-Bernstein and ?-Durrmeyer, and ?-Bernstein and ?-Kantorovich operators. We establish a Voronovskaja-type approximation theorem by weighted A-statistical convergence for the bivariate case.

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44

Shige, Shoichi, Satoshi Kida, Hiroki Ashiwake, Takuji Kubota, and Kazumasa Aonashi. "Improvement of TMI Rain Retrievals in Mountainous Areas." Journal of Applied Meteorology and Climatology 52, no. 1 (January 2013): 242–54. http://dx.doi.org/10.1175/jamc-d-12-074.1.

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AbstractHeavy rainfall associated with shallow orographic rainfall systems has been underestimated by passive microwave radiometer algorithms owing to weak ice scattering signatures. The authors improve the performance of estimates made using a passive microwave radiometer algorithm, the Global Satellite Mapping of Precipitation (GSMaP) algorithm, from data obtained by the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) for orographic heavy rainfall. An orographic/nonorographic rainfall classification scheme is developed on the basis of orographically forced upward vertical motion and the convergence of surface moisture flux estimated from ancillary data. Lookup tables derived from orographic precipitation profiles are used to estimate rainfall for an orographic rainfall pixel, whereas those derived from original precipitation profiles are used to estimate rainfall for a nonorographic rainfall pixel. Rainfall estimates made using the revised GSMaP algorithm are in better agreement with estimates from data obtained by the radar on the TRMM satellite and by gauge-calibrated ground radars than are estimates made using the original GSMaP algorithm.

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45

Smith, Rebecca A., and Christian D. Kummerow. "A Comparison of in Situ, Reanalysis, and Satellite Water Budgets over the Upper Colorado River Basin." Journal of Hydrometeorology 14, no. 3 (June 1, 2013): 888–905. http://dx.doi.org/10.1175/jhm-d-12-0119.1.

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Abstract Using in situ, reanalysis, and satellite-derived datasets, surface and atmospheric water budgets of the Upper Colorado River basin are analyzed. All datasets capture the seasonal cycle for each water budget component. For precipitation, all products capture the interannual variability, though reanalyses tend to overestimate in situ while satellite-derived precipitation underestimates. Most products capture the interannual variability of evapotranspiration (ET), though magnitudes differ among the products. Variability and magnitude among storage volume change products widely vary. With regards to the surface water budget, the strongest connections exist among precipitation, ET, and soil moisture, while snow water equivalent (SWE) is best correlated with runoff. Using in situ precipitation estimates, the Max Planck Institute (MPI) ET estimates, and accumulated runoff, changes in storage are calculated and compare well with estimated changes in storage calculated using SWE, reservoir, and the Climate Prediction Center’s soil moisture. Using in situ precipitation estimates, MPI ET estimates, and atmospheric divergence estimates from the European Centre for Medium-Range Weather Forecasts Interim Re-Analysis (ERA-Interim) results in a long-term atmospheric storage change estimate of −73 mm. Long-term surface storage estimates combined with long-term runoff come close to balancing with long-term atmospheric convergence from ERA-Interim. Increasing the MPI ET by 5% leads to a better balance between surface storage changes, runoff, and atmospheric convergence. It also brings long-term atmospheric storage changes to a better balance at +13 mm.

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46

Conte, Gina L., Matthew E. Arnegard, Catherine L. Peichel, and Dolph Schluter. "The probability of genetic parallelism and convergence in natural populations." Proceedings of the Royal Society B: Biological Sciences 279, no. 1749 (October 17, 2012): 5039–47. http://dx.doi.org/10.1098/rspb.2012.2146.

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Genomic and genetic methods allow investigation of how frequently the same genes are used by different populations during adaptive evolution, yielding insights into the predictability of evolution at the genetic level. We estimated the probability of gene reuse in parallel and convergent phenotypic evolution in nature using data from published studies. The estimates are surprisingly high, with mean probabilities of 0.32 for genetic mapping studies and 0.55 for candidate gene studies. The probability declines with increasing age of the common ancestor of compared taxa, from about 0.8 for young nodes to 0.1–0.4 for the oldest nodes in our study. Probability of gene reuse is higher when populations begin from the same ancestor (genetic parallelism) than when they begin from divergent ancestors (genetic convergence). Our estimates are broadly consistent with genomic estimates of gene reuse during repeated adaptation to similar environments, but most genomic studies lack data on phenotypic traits affected. Frequent reuse of the same genes during repeated phenotypic evolution suggests that strong biases and constraints affect adaptive evolution, resulting in changes at a relatively small subset of available genes. Declines in the probability of gene reuse with increasing age suggest that these biases diverge with time.

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47

Jaćimović, Milojica, Izedin Krnić, and Oleg Obradović. "Rate of Convergence of Tikhonov Method of Regularization for Constrained Linear Equations with Operators Having Closed Ranges." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/506368.

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We derive the estimates of the rate of convergence of the Tikhonov method of regularization for a constrained operator linear equation. In case that the range of the corresponding operator is closed, the estimate is of the same order as the estimates for a linear equation without constraints.

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Zhou, Fangqin. "An Analysis on Local Convergence of Inexact Newton-Gauss Method for Solving Singular Systems of Equations." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/752673.

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We study the local convergence properties of inexact Newton-Gauss method for singular systems of equations. Unified estimates of radius of convergence balls for one kind of singular systems of equations with constant rank derivatives are obtained. Application to the Smale point estimate theory is provided and some important known results are extended and/or improved.

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49

Yoldaş, Havva. "On quantitative hypocoercivity estimates based on Harris-type theorems." Journal of Mathematical Physics 64, no. 3 (March 1, 2023): 031101. http://dx.doi.org/10.1063/5.0089698.

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This Review concerns recent results on the quantitative study of convergence toward the stationary state for spatially inhomogeneous kinetic equations. We focus on analytical results obtained by means of certain probabilistic techniques from the ergodic theory of Markov processes. These techniques are sometimes referred to as Harris-type theorems. They provide constructive proofs for convergence results in the L1 (or total variation) setting for a large class of initial data. The convergence rates can be made explicit (for both geometric and sub-geometric rates) by tracking the constants appearing in the hypotheses. Harris-type theorems are particularly well-adapted for equations exhibiting non-explicit and non-equilibrium steady states since they do not require prior information on the existence of stationary states. This allows for significant improvements of some already-existing results by relaxing assumptions and providing explicit convergence rates. We aim to present Harris-type theorems, providing a guideline on how to apply these techniques to kinetic equations at hand. We discuss recent quantitative results obtained for kinetic equations in gas theory and mathematical biology, giving some perspectives on potential extensions to nonlinear equations.

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50

Kamynin, V. L. "Estimates of rate of convergence of solutions of parabolic equations with weakly convergent coefficients." Mathematical Notes of the Academy of Sciences of the USSR 49, no. 2 (February 1991): 158–64. http://dx.doi.org/10.1007/bf01137546.

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