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Relevant bibliographies by topics / ESTIMATES OF CONVERGENCE

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Academic literature on the topic 'ESTIMATES OF CONVERGENCE'

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Published: 26 October 2023

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Journal articles on the topic "ESTIMATES OF CONVERGENCE"

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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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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "ESTIMATES OF CONVERGENCE"

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Beckmann, Matthias [Verfasser], and Armin [Akademischer Betreuer] Iske. "Error Estimates and Convergence Rates for Filtered Back Projection Reconstructions / Matthias Beckmann ; Betreuer: Armin Iske." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2018. http://d-nb.info/1161530479/34.

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Beckmann, Matthias Verfasser], and Armin [Akademischer Betreuer] [Iske. "Error Estimates and Convergence Rates for Filtered Back Projection Reconstructions / Matthias Beckmann ; Betreuer: Armin Iske." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2018. http://nbn-resolving.de/urn:nbn:de:gbv:18-91742.

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Verbitsky, Anton [Verfasser], and W. [Akademischer Betreuer] Reichel. "Positive Solutions for the Discrete Nonlinear Schrödinger Equation: A Priori Estimates and Convergence / Anton Verbitsky. Betreuer: W. Reichel." Karlsruhe : KIT-Bibliothek, 2014. http://d-nb.info/1061069214/34.

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Schroeder, Gregory C. "Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality." Master's thesis, University of Cape Town, 1993. http://hdl.handle.net/11427/17404.

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Bibliography: pages 93-101.
The main aim of this thesis is to analyse two types of general finite element approximations to the solution of a time-dependent variational inequality. The two types of approximations considered are the following: 1. Semi-discrete approximations, in which only the spatial domain is discretised by finite elements; 2. fully discrete approximations, in which the spatial domain is again discretised by finite elements and, in addition, the time domain is discretised and the time-derivatives appearing in the variational inequality are approximated by backward differences. Estimates of the error inherent in the above two types of approximations, in suitable Sobolev norms, are obtained; in particular, these estimates express the rate of convergence of successive finite element approximations to the solution of the variational inequality in terms of element size h and, where appropriate, in terms of the time step size k. In addition, the above analysis is preceded by related results concerning the existence and uniqueness of the solution to the variational inequality and is followed by an application in elastoplasticity theory.

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Braun, Alina [Verfasser], Michael [Akademischer Betreuer] Kohler, and Volker [Akademischer Betreuer] Betz. "In Theory and Practice - On the Rate of Convergence of Implementable Neural Network Regression Estimates / Alina Braun ; Michael Kohler, Volker Betz." Darmstadt : Universitäts- und Landesbibliothek, 2021. http://d-nb.info/1238783104/34.

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Miraglio, Pietro. "Estimates and rigidity for stable solutions to some nonlinear elliptic problems." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/668832.

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My thesis deals with the study of elliptic PDE. It is divided into two parts, the first one concerning a nonlinear equation involving the p-Laplacian, and the second one focused on a nonlocal problem. In the first part, we study the regularity of stable solutions to a nonlinear equation involving the p-Laplacian in a bounded domain. This is the nonlinear version of the widely studied semilinear equation involving the classical Laplacian. Stable solutions to semilinear equations have been very recently proved to be bounded, and therefore smooth, up to dimension n=9 by Cabré, Figalli, Ros-Oton, and Serra. This result is known to be optimal by counterexamples in higher dimensions. In the case of the p-Laplacian, the boundedness of stable solutions is conjectured to hold up to a critical dimension depending on p. Examples of unbounded stable solutions are known if the dimension exceeds the critical one. Moreover, in the radial case or under strong assumptions on the nonlinearity, stable solutions are proved to be bounded in the optimal dimension range. We prove the boundedness of stable solutions under a new condition on n and p, which is optimal in the radial case, and more restrictive in the general one. It improves the known results in the field, and it is the first example, concerning the p-Laplacian, of a technique providing both a result in the nonradial case and the optimal result in the radial case. In the first part, we also investigate Hardy-Sobolev inequalities on hypersurfaces of Euclidean space, all containing a mean curvature term. Our motivation comes from several applications of these inequalities to the study of a priori estimates for stable solutions. Specifically, we give a simplified proof of the celebrated Michael-Simon and Allard inequality, we obtain two new forms of the Hardy inequality on hypersurfaces, and an improved Hardy inequality in the Poincaré sense. In the second part of this thesis, we deal with a Dirichlet to Neumann problem arising in a model for water waves. The system is described by a diffusion equation in a slab of fixed height, containing a weight that depends on a parameter a belonging to (-1,1). The top of the slab is endowed with a 0-Neumann condition, while on the bottom we have a Dirichlet datum and an equation involving a smooth nonlinearity. The system can also be reformulated as a nonlocal problem on the component endowed with the Dirichlet datum, by defining a suitable Dirichlet to Neumann operator. First, we prove a Liouville theorem that establishes the one dimensional symmetry of stable solutions, provided that a control on the growth of the energy associated with the problem is satisfied. As a consequence, we obtain the 1D symmetry of stable solutions to our problem in dimension 2. For n=3, we establish sharp energy estimates for both the energy minimizers and the monotone solutions, deducing the 1D symmetry of these classes of solutions, by an application of our Liouville theorem. Concerning this problem, we also investigate the nature of the associated Dirichlet to Neumann operator. First, we deduce its expression as a Fourier operator, which was known only in the case a=0. This result highlights the mixed nature of the operator, which is nonlocal, but not purely fractional. To better understand the dual behaviour of the operator, we provide a G-convergence result for an energy functional associated with the operator. Specifically, as a G-limit of our energy functional we find a mere interaction energy when a is greater than 0, and the classical perimeter when a is smaller or equal than 0. We point out that the threshold a=0 that we obtain here, as well as the G-limit behaviour for nonpositive values of a, is common to other nonlocal problems treated in the literature. On the contrary, the limit functional that we obtain in the other case appears to be new and structurally different from other nonlocal energy functionals that have been investigated in the literature.
Mi tesis se encaja en el estudio de las EDPs elípticas. Está dividida en dos partes: la primera trata una ecuación no-lineal con el p-Laplaciano, la segunda de un problema no-local. En la primera parte, estudiamos la regularidad de las soluciones estables de una ecuación no lineal con el p-Laplaciano en un dominio acotado. Esta ecuacion es la versión no-lineal de la ámpliamente estudiada ecuacion semilineal con el Laplaciano. Cabré, Figalli, Ros-Oton, y Serra han demostrado recientemente que las soluciones estables de las ecuaciones semilineales son acotadas, y por tanto regulares, hasta la dimensión 9. Este resultado es optimal. En el caso del p-Laplaciano, la regularidad de las soluciones estables se conjetura de ser cierta hasta una dimension critica y, de hecho, se conocen ejemplos de soluciones no acotadas cuando la dimension llega al valor critico. Además, se ha demostrado que en el caso radial o assumiendo hipótesis fuertes sobre la no-linealidad las soluciones estables son acotadas hasta la dimension critica. En el primer capítulo, demostramos que las soluciones estables son acotadas, bajo una nueva condición en n y p, que es optimal en el caso radial, y más restrictiva en el caso general. Esta investigación mejora conocidos resultados del tema y es el primer ejemplo, para el p-Laplaciano, de un método que produce un resultado para el caso general y un resultado optimal en el caso radial. En la primera parte, nos ocupamos también de las desigualdades funcionales del tipo Hardy y Sobolev sobre hipersuperfícies del espacio Euclideo, todas conteniendo un término de curvatura media. Nuestra motivación proviene de varias apliaciones que tienen estas desigualdades en el estudio de estimaciones para las soluciones estables. En detalle, damos una demostración simple de la conocida desigualdad de Michael-Simon y Allard, obtenemos dos formas nuevas de la desigualdad de Hardy sobre hipersuperfícies, y otra desigualdad de Hardy-Poincaré. En la segunda parte, nos ocupamos de un problema de Dirichlet-Neumann que emerge de un modelo para las ondas en el agua. El sistema se describe con una ecuación de difusión en una tira de altura fija, que contiene un parámetro a en (-1,1). La parte superior de la tira es dotada de una condicion 0 de Neumann, mientras en la parte inferior tenemos un dato de Dirichlet y una ecuación con una nonlinearidad regular. Este problema puede ser reformulado como una ecuación no-local sobre la componente dotada del dato de Dirichlet, definiendo un operador de Dirichlet-Neumann apropiado. Primero, demostramos un teorema del tipo Liouville, que garantiza la simetría unidimensional de las soluciones monótonas, asumiendo un control sobre el crecimiento de la energía asociada. Como consecuencia, obtenemos la simetría 1D de las soluciones estables en dimension 2. Para n=3, obtenemos estimaciónes optimales de la energía para las soluciones que minimizan la energía y para las soluciones monótonas. Estas estimaciones nos conducen a la simetría 1D de estas clases de soluciones, aplicando nuestro teorema del tipo Liouville. Relativo a este problema, estudiamos también la naturaleza del operador de Dirichlet-Neumann. Primero, deducimos su expresión como operador de Fourier, que anteriormente solo se conocía para a=0. Este resultado evidencia la naturaleza del operador, que es no-local pero no puramente fraccionaria. Estudiamos en profundidad este comportamiento mixto del operador a través del estudio de la G-convergencia de un funcional energía asociado al operador. Demostramos la G-convergencia de nuestro funcional a un límite que corresponde a una energía de interacción pura cuando a en (0,1) y al perímetro clásico cuando a en (-1,0]. El límite a=0, así como el G-límite para el régimen a en (-1,0], es común a otros problemas no-locales tratados en la literatura. Al contrario, el funcional límite en el régimen puramente no-local es nuevo y diferente a otros funciona
Questa tesi si occupa di equazioni differenziali alle derivate parziali di tipo ellittico. È divisa in due parti: la prima riguarda un’equazione nonlineare per il p-Laplaciano, mentre la seconda è incentrata su un problema nonlocale, che può essere formulato per mezzo di un operatore di Dirichlet-Neumann collegato con il Laplaciano frazionario. Nella prima parte, studiamo la regolarità delle soluzioni stabili dell’equazione nonlineare per il p-Laplaciano dove W è un dominio limitato, p 2 (1,+¥) e f è una nonlinearità C1. Questa equazione è la versione nonlineare dell’equazione semilineare 􀀀��Du = f (u) in un dominio limitato W Rn, che è stata ampiamente studiata in letteratura. Molto recentemente, Cabré, Figalli, Ros-Oton, e Serra [38] hanno dimostrato che le soluzioni stabili delle equazioni semilineari sono limitate, e quindi regolari, in dimensione n 9. Questo risultato è ottimale, dato che esempi di soluzioni illimitate e stabili sono noti in dimensione n 10. Inoltre, i risultati in [38] forniscono una risposta completa ad un annoso problema aperto, proposto da Brezis e Vázquez [25], sulla regolarità delle soluzioni estremali dell’equazione 􀀀��Du = l f (u). Queste ultime sono infatti esempi non banali di soluzioni stabili di equazioni semilineari, che possono essere limitate o illimitate in dipendenza della dimensione n, del dominio W, e della nonlinearità f . In questa tesi studiamo la limitatezza delle soluzioni stabili di (0.4), che si congettura essere vera fino alla dimensione n < p + 4p/(p 􀀀�� 1). Sono infatti noti esempi di soluzioni stabili e illimitate quando n p + 4p/(p 􀀀�� 1), anche quando il dominio è la palla unitaria. Inoltre, nel caso radiale o assumendo ipotesi forti sulla nonlinearità, è stato dimostrato che le soluzioni stabili di (0.4) sono limitate quando n < p + 4p/(p 􀀀�� 1). Nel Capitolo 1 della tesi dimostriamo una nuova stima L¥ a priori per le soluzioni stabili di (0.4), assumendo una nuova condizione su n e p, che è ottimale nel caso radiale e più restrittiva nel caso generale. Il nostro risultato migliora ciò che è noto in letteratura e ed è il primo esempio di tecnica che produce sia un risultato nel caso non radiale sia il risultato ottimale nel caso radiale. Per ottenere questo risultato estendiamo al caso del p-Laplaciano una tecnica sviluppata da Cabré [30] per il caso classico del problema, con p = 2. La strategia si basa su una disuguaglianza di Hardy sugli insiemi di livello della soluzione, combinata con una disuguaglianza di tipo geometrico per le soluzioni stabili di (0.4). Nella prima parte della tesi ci occupiamo anche di disuguaglianze funzionali di tipo Hardy e Sobolev, su ipersuperfici dello spazio euclideo. Nel fare ciò siamo motivati dalle varie applicazioni di questo tipo di risultati allo studio di stime a priori per le soluzioni stabili, sia nel caso semilineare che nel caso nonlineare ...

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MIRAGLIO, PIETRO. "ESTIMATES AND RIGIDITY FOR STABLE SOLUTIONS TO SOME NONLINEAR ELLIPTIC PROBLEMS." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/704717.

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Questa tesi è incentrata sullo studio di equazioni differenziali alle derivate parziali di tipo ellittico. La prima parte della tesi riguarda la regolarità delle soluzioni stabili per un'equazione nonlineare con il p-Laplaciano, in un dominio limitato dello spazio Euclideo. La tecnica è basata sull'uso di disuguaglianze di tipo Hardy-Sobolev su ipersuperfici, del quale viene approfondito lo studio. Nella seconda parte viene preso in esame un problema nonlocale di tipo Dirichlet-Neumann. Studiamo la simmetria unidimensionale di alcune sottoclassi di soluzioni stabili, ottenendo risultati in dimensione n=2, 3. Inoltre, studiamo il comportamento asintotico dell'operatore associato a questo problema nonlocale, usando tecniche di Γ-convergenza.
This thesis deals with the study of elliptic PDEs. The first part of the thesis is focused on the regularity of stable solutions to a nonlinear equation involving the p-Laplacian, in a bounded domain of the Euclidean space. The technique is based on Hardy-Sobolev inequalities in hypersurfaces involving the mean curvature, which are also investigated in the thesis. The second part concerns, instead, a nonlocal problem of Dirichlet-to-Neumann type. We study the one-dimensional symmetry of some subclasses of stable solutions, obtaining new results in dimensions n=2, 3. In addition, we carry out the study of the asymptotic behaviour of the operator associated with this nonlocal problem, using Γ-convergence techniques.

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Courtès, Clémentine. "Analyse numérique de systèmes hyperboliques-dispersifs." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS467/document.

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Le but de cette thèse est d’étudier certaines équations aux dérivées partielles hyperboliques-dispersives. Une part importante est consacrée à l’analyse numérique et plus particulièrement à la convergence de schémas aux différences finies pour l’équation de Korteweg-de Vries et les systèmes abcd de Boussinesq. L’étude numérique suit les étapes classiques de consistance et de stabilité. Nous transposons au niveau discret la propriété de stabilité fort-faible des lois de conservations hyperboliques. Nous déterminons l’ordre de convergence des schémas et le quantifions en fonction de la régularité de Sobolev de la donnée initiale. Si nécessaire, nous régularisons la donnée initiale afin de toujours assurer les estimations de consistance. Une étape d’optimisation est alors nécessaire entre cette régularisation et l’ordre de convergence du schéma. Une seconde partie est consacrée à l’existence d’ondes progressives pour l’équation de Korteweg de Vries-Kuramoto-Sivashinsky. Par des méthodes classiques de systèmes dynamiques : système augmenté, fonction de Lyapunov, intégrale de Melnikov, par exemple, nous démontrons l’existence d’ondes oscillantes de petite amplitude
The aim of this thesis is to study some hyperbolic-dispersive partial differential equations. A significant part is devoted to the numerical analysis and more precisely to the convergence of some finite difference schemes for the Korteweg-de Vries equation and abcd systems of Boussinesq. The numerical study follows the classical steps of consistency and stability. The main idea is to transpose at the discrete level the weak-strong stability property for hyperbolic conservation laws. We determine the convergence rate and we quantify it according to the Sobolev regularity of the initial datum. If necessary, we regularize the initial datum for the consistency estimates to be always valid. An optimization step is thus necessary between this regularization and the convergence rate of the scheme. A second part is devoted to the existence of traveling waves for the Korteweg-de Vries-Kuramoto-Sivashinsky equation. By classical methods of dynamical systems : extended systems, Lyapunov function, Melnikov integral, for instance, we prove the existence of oscillating small amplitude traveling waves

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Bazan, Rodolfo S. Cermeno. "Evaluating convergence with median-unbiased estimators in panel data." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1277906836.

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Pieczynski, Wojciech. "Sur diverses applications de la décantation des lois de probabilité dans la théorie générale de l'estimation statistique." Paris 6, 1986. http://www.theses.fr/1986PA066064.

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On cherche à construire des estimateurs convergents dans le cas des V. A. Non nécessairement indépendantes et équidistribuées. La méthode de la décantation est particulièrement adaptée car elle permet la construction explicite de tels estimateurs et donne des renseignements sur leur vitesse de convergence.

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Books on the topic "ESTIMATES OF CONVERGENCE"

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Gupta, Vijay, and Ravi P. Agarwal. Convergence Estimates in Approximation Theory. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02765-4.

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Senatov, V. V. Qualitative effects in the estimates of the convergence rate in the central limit theorem in multidimensional spaces. Moscow: Maik Nauka/Interperiodica Publishing, 1996.

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M, Křížek, Neittaanmäki P, and Stenberg R. 1953-, eds. Finite element methods: Superconvergence, post-processing, and a posteriori estimates. New York: M. Dekker, 1998.

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Newey, Whitney K. Convergence rates for series estimators. Cambridge, Mass: Dept. of Economics, Massachusetts Institute of Technology, 1993.

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Newey, Whitney K. Convergence rates & asymptotic normality for series estimators. Cambridge, Mass: Dept. of Economics, Massachusetts Institute of Technology, 1995.

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Ferger, D. On the almost sure convergence of maximum likelihood-type estimators for a change point. Dresden: Technische Universität Dresden, Institut für Mathematische Stochastik, 2004.

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J, Kavanagh Michael, Armstrong Laboratory (U.S.), and State University of New York at Albany., eds. Transferability of skills: Convergent, postdictive, criterion-related, and construct validation of cross-job retraining time estimates. Brooks AFB, TX: U.S. Air Force, Armstrong Laboratory, 1997.

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Agarwal, Ravi P., and Vijay Gupta. Convergence Estimates in Approximation Theory. Springer London, Limited, 2014.

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Agarwal, Ravi P., and Vijay Gupta. Convergence Estimates in Approximation Theory. Springer, 2016.

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Convergence Estimates In Approximation Theory. Springer International Publishing AG, 2014.

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Book chapters on the topic "ESTIMATES OF CONVERGENCE"

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Heinrich, Bernd. "Error Estimates and Convergence." In Finite Difference Methods on Irregular Networks, 96–149. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-7196-9_5.

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Gupta, Vijay, and Ravi P. Agarwal. "Preliminaries." In Convergence Estimates in Approximation Theory, 1–16. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02765-4_1.

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Gupta, Vijay, and Ravi P. Agarwal. "Rate of Convergence in Simultaneous Approximation." In Convergence Estimates in Approximation Theory, 313–43. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02765-4_10.

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Gupta, Vijay, and Ravi P. Agarwal. "Future Scope and Open Problems." In Convergence Estimates in Approximation Theory, 345–47. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02765-4_11.

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Gupta, Vijay, and Ravi P. Agarwal. "Approximation by Certain Operators." In Convergence Estimates in Approximation Theory, 17–92. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02765-4_2.

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Gupta, Vijay, and Ravi P. Agarwal. "Complete Asymptotic Expansion." In Convergence Estimates in Approximation Theory, 93–107. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02765-4_3.

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Gupta, Vijay, and Ravi P. Agarwal. "Linear and Iterative Combinations." In Convergence Estimates in Approximation Theory, 109–39. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02765-4_4.

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Gupta, Vijay, and Ravi P. Agarwal. "Better Approximation." In Convergence Estimates in Approximation Theory, 141–53. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02765-4_5.

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Gupta, Vijay, and Ravi P. Agarwal. "Complex Operators in Compact Disks." In Convergence Estimates in Approximation Theory, 155–212. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02765-4_6.

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Gupta, Vijay, and Ravi P. Agarwal. "Rate of Convergence for Functions of Bounded Variation." In Convergence Estimates in Approximation Theory, 213–47. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02765-4_7.

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Conference papers on the topic "ESTIMATES OF CONVERGENCE"

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Paxman, Richard G., and John H. Seldin. "Operational convergence of estimates in phase diversity." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.thtt3.

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A phased-array telescope will suffer from phase errors unless the subtelescopes are mutually aligned to within a small fraction of a wavelength. In this presentation we describe the use of Gonsalves' phase-diversity method to sense misalignments in a phased-array telescope. The technique requires the simultaneous collection of two images. The first is the conventional focal-plane image that has been degraded by the unknown misalignments. The second image is collected in an out-of-focus plane so that there is an additional (known) degradation due to defocus. Conventional nonlinear optimization methods are employed to estimate misalignment parameters that are consistent with both degraded images. One of the dangers of nonlinear optimization is the possibility of entrapment by local minima, which are known to exist in the phase-diversity objective function. An extensive Monte Carlo simulation was performed to quantify the probability of undesirable entrapment for a particular phased-array telescope. The results suggest that the probability of convergence to within a prescribed tolerance is large.

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Fang Cai, Jie Xiao, and Zhao-Hong Xiang. "Estimates for convergence rate of nested iterative methods." In 2011 IEEE International Conference on Computer Science and Automation Engineering (CSAE). IEEE, 2011. http://dx.doi.org/10.1109/csae.2011.5953268.

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Hale, Matthew T., and Magnus Egerstedt. "Convergence rate estimates for consensus over random graphs." In 2017 American Control Conference (ACC). IEEE, 2017. http://dx.doi.org/10.23919/acc.2017.7963087.

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4

Pavlov, A., N. van de Wouw, and H. Nijmeijer. "The local output regulation problem: Convergence region estimates." In 2003 European Control Conference (ECC). IEEE, 2003. http://dx.doi.org/10.23919/ecc.2003.7085042.

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Zhang, Fu, Ehsan Keikha, Behrooz Shahsavari, and Roberto Horowitz. "Adaptive Mismatch Compensation for Rate Integrating Vibratory Gyroscopes With Improved Convergence Rate." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-6053.

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This paper presents an online adaptive algorithm to compensate damping and stiffness frequency mismatches in rate integrating Coriolis Vibratory Gyroscopes (CVGs). The proposed adaptive compensator consists of a least square estimator that estimates the damping and frequency mismatches, and an online compensator that corrects the mismatches. In order to improve the adaptive compensator’s convergence rate, we introduce a calibration phase where we identify relations between the unknown parameters (i.e. mismatches, rotation rate and rotation angle). Calibration results show that the unknown parameters lie on a hyperplane. When the gyro is in operation, we project parameters estimated from the least square estimator onto the hyperplane. The projection will reduce the degrees of freedom in parameter estimates, thus guaranteeing persistence of excitation and improving convergence rate. Simulation results show that utilization of the projection method will drastically improve convergence rate of the least square estimator and improve gyro performance.

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Marfurt, Kurt J., and Jamie Rich. "Beyond curvature — volumetric estimates of reflector rotation and convergence." In SEG Technical Program Expanded Abstracts 2010. Society of Exploration Geophysicists, 2010. http://dx.doi.org/10.1190/1.3513118.

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Chong, Edwin K. P., and Peter J. Ramadge. "Convergence of Recursive Optimization Algorithms using IPA Derivative Estimates." In 1990 American Control Conference. IEEE, 1990. http://dx.doi.org/10.23919/acc.1990.4790894.

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Seldin, John H., and Richard G. Paxman. "Operational convergence of estimates from noisy phase-diversity measurements." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1993. http://dx.doi.org/10.1364/oam.1993.mbbb.6.

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Bianchi, P., G. Fort, W. Hachem, and J. Jakubowicz. "Convergence of a distributed parameter estimator for sensor networks with local averaging of the estimates." In ICASSP 2011 - 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2011. http://dx.doi.org/10.1109/icassp.2011.5947170.

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Brock, Jerry. "Bounded Numerical Error Estimates for Oscillatory Convergence of Simulation Data." In 18th AIAA Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-4091.

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Reports on the topic "ESTIMATES OF CONVERGENCE"

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Zhao, L. C., P. R. Krishnaiah, and X. R. Chen. Almost Sure L(Gamma)-Norm Convergence for Data-Based Histogram Density Estimates. Fort Belvoir, VA: Defense Technical Information Center, August 1987. http://dx.doi.org/10.21236/ada189944.

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Chen, X. R., and L. C. Zhao. Almost Sure L(1)-Norm Convergence for Data-Based Histogram Density Estimates. Fort Belvoir, VA: Defense Technical Information Center, March 1986. http://dx.doi.org/10.21236/ada170059.

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Bai, Z. D., P. R. Krishnaiah, and L. C. Zhao. On Rate of Convergence of Equivariation Linear Prediction Estimates of the Number of Signals and Frequencies of Multiple Sinusoids. Fort Belvoir, VA: Defense Technical Information Center, December 1986. http://dx.doi.org/10.21236/ada186034.

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Chen, X. R., and L. C. Zhoa. Necessary and Sufficient Conditions for the Convergence of Integrated and Mean-Integrated r-th Order Error of Histogram Density Estimates. Fort Belvoir, VA: Defense Technical Information Center, April 1987. http://dx.doi.org/10.21236/ada186037.

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Dorr, Adam, and Tony Seba. Rethinking Energy: The Great Stranding: How Inaccurate Mainstream LCOE Estimates are Creating a Trillion-Dollar Bubble in Conventional Energy Assets. RethinkX, February 2021. http://dx.doi.org/10.61322/uuda4616.

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We are on the cusp of the fastest, deepest, most profound disruption of the energy sector in over a century. Like most disruptions, this one is being driven by the convergence of several key technologies whose costs and capabilities have been improving on consistent and predictable trajectories – namely, solar photovoltaic power, wind power, and lithium-ion battery energy storage. Our analysis shows that 100% clean electricity from the combination of solar, wind, and batteries (SWB) is both physically possible and economically affordable across the entire continental United States as well as the overwhelming majority of other populated regions of the world by 2030. Adoption of SWB is growing exponentially worldwide and disruption is now inevitable because by 2030 they will offer the cheapest electricity option for most regions. Coal, gas, and nuclear power assets will become stranded during the 2020s, and no new investment in these technologies is rational from this point forward.

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McRae, Shaun D. Residential Electricity Consumption and Adaptation to Climate Change by Colombian Households. Inter-American Development Bank, July 2023. http://dx.doi.org/10.18235/0005017.

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This paper provides the first empirical estimates of the relationship between temperatures and household electricity consumption in Colombia, using electricity billing and weather data from 2010 to 2019. I find that higher temperatures (or higher values of the heat index) increase electricity consumption, with the largest effects observed for high-income households in regions with hot climates. However, I show that there has been partial convergence between low- and high-income households, with the effect of temperature on electricity consumption in lower-income neighborhoods more than doubling between 2011 and 2019. These results align with survey evidence of increased air conditioning adoption. Nevertheless, further growth in air conditioning adoption and use is required to alleviate the health effects of more frequent and severe heatwaves due to climate change.

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Tosi, R., R. Codina, J. Principe, R. Rossi, and C. Soriano. D3.3 Report of ensemble based parallelism for turbulent flows and release of solvers. Scipedia, 2022. http://dx.doi.org/10.23967/exaqute.2022.3.06.

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In this work we focus on reducing the wall clock time required to compute statistical estimators of highly chaotic incompressible flows on high performance computing systems. Our approach consists of replacing a single long-term simulation by an ensemble of multiple independent realizations, which are run in parallel with different initial conditions. A failure probability convergence criteria must be satisfied by the statistical estimator of interest to assess convergence. Its error analysis leads to the identification of two error contributions: the initialization bias and the statistical error. We propose an approach to systematically detect the burn-in time in order to minimize the initialization bias, accompanied by strategies to reduce simulation cost. The framework is validated on two very high Reynolds number obstacle problems of wind engineering interest in a high performance computing environment.

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Lio, Y. L., and W. J. Padgett. Some Convergence Results for Kernel-Type Quantile Estimators under Censoring. Fort Belvoir, VA: Defense Technical Information Center, November 1985. http://dx.doi.org/10.21236/ada162837.

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Christensen, Timothy M., and Xiaohong Chen. Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions. IFS, December 2014. http://dx.doi.org/10.1920/wp.cem.2014.4614.

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Cattaneo, Matias D., Richard K. Crump, and Weining Wang. Beta-Sorted Portfolios. Federal Reserve Bank of New York, July 2023. http://dx.doi.org/10.59576/sr.1068.

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Beta-sorted portfolios—portfolios comprised of assets with similar covariation to selected risk factors—are a popular tool in empirical finance to analyze models of (conditional) expected returns. Despite their widespread use, little is known of their statistical properties in contrast to comparable procedures such as two-pass regressions. We formally investigate the properties of beta-sorted portfolio returns by casting the procedure as a two-step nonparametric estimator with a nonparametric first step and a beta-adaptive portfolios construction. Our framework rationalizes the well-known estimation algorithm with precise economic and statistical assumptions on the general data generating process. We provide conditions that ensure consistency and asymptotic normality along with new uniform inference procedures allowing for uncertainty quantification and general hypothesis testing for financial applications. We show that the rate of convergence of the estimator is non-uniform and depends on the beta value of interest. We also show that the widely used Fama-MacBeth variance estimator is asymptotically valid but is conservative in general and can be very conservative in empirically relevant settings. We propose a new variance estimator, which is always consistent and provide an empirical implementation which produces valid inference. In our empirical application we introduce a novel risk factor—a measure of the business credit cycle—and show that it is strongly predictive of both the cross-section and time-series behavior of U.S. stock returns.

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