scholarly journals General Robust Bayes Pseudo-Posteriors: Exponential Convergence Results with Applications

2022 ◽  
Author(s):  
Abhik Ghosh ◽  
Tuhin Majumder ◽  
Ayanendranath Basu
Keyword(s):  
Exponential Convergence ◽  
Convergence Results

scholarly journals Basic principles of hp virtual elements on quasiuniform meshes

2016 ◽  
Vol 26 (08) ◽  
pp. 1567-1598 ◽  
Author(s):  
L. Beir ao da Veiga ◽  
A. Chernov ◽  
L. Mascotto ◽  
A. Russo
Keyword(s):  
Numerical Experiments ◽  
Exponential Convergence ◽  
Mesh Size ◽  
Initial Study ◽  
Analytic Solutions ◽  
Basis Functions ◽  
Basic Principles ◽  
Polynomial Degree ◽  
Convergence Results ◽  
Convergence Estimates

In the present paper we initiate the study of [Formula: see text] Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size [Formula: see text] and in the polynomial degree [Formula: see text] in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included.

Stability of Implicit Difference Equations Generated by Parabolic Functional Differential Problems

2007 ◽  
Vol 7 (1) ◽  
pp. 68-82
Author(s):  
K. Kropielnicka
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Numerical Examples ◽  
Convergence Results ◽  
Nonlinear Parabolic ◽  
Implicit Difference Methods ◽  
Neumann Type ◽  
Difference Methods ◽  
Functional Differential

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.

A cell-based smoothed point interpolation method (CS-PIM) for 2D thermoelastic problems

2017 ◽  
Vol 27 (6) ◽  
pp. 1249-1265 ◽  
Author(s):  
Yijun Liu ◽  
Guiyong Zhang ◽  
Huan Lu ◽  
Zhi Zong
Keyword(s):  
Thermal Stresses ◽  
Interpolation Method ◽  
Content Type ◽  
Novel Approach ◽  
Convergence Results ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Thermoelastic Problems ◽  
Gradient Smoothing ◽  
Practical Implications

Purpose Due to the strong reliance on element quality, there exist some inherent shortcomings of the traditional finite element method (FEM). The model of FEM behaves overly stiff, and the solutions of automated generated linear elements are generally of poor accuracy about especially gradient results. The proposed cell-based smoothed point interpolation method (CS-PIM) aims to improve the results accuracy of the thermoelastic problems via properly softening the overly-stiff stiffness. Design/methodology/approach This novel approach is based on the newly developed G space and weakened weak (w2) formulation, and of which shape functions are created using the point interpolation method and the cell-based gradient smoothing operation is conducted based on the linear triangular background cells. Findings Owing to the property of softened stiffness, the present method can generally achieve better accuracy and higher convergence results (especially for the temperature gradient and thermal stress solutions) than the FEM does by using the simplest linear triangular background cells, which has been examined by extensive numerical studies. Practical implications The CS-PIM is capable of producing more accurate results of temperature gradients as well as thermal stresses with the automated generated and unstructured background cells, which make it a better candidate for solving practical thermoelastic problems. Originality/value It is the first time that the novel CS-PIM was further developed for solving thermoelastic problems, which shows its tremendous potential for practical implications.

scholarly journals Nonparametric inference for interventional effects with multiple mediators

2021 ◽  
Vol 9 (1) ◽  
pp. 172-189
Author(s):  
David Benkeser ◽  
Jialu Ran
Keyword(s):  
Interval Estimation ◽  
Small Sample ◽  
Parametric Models ◽  
Nonparametric Bootstrap ◽  
Mediation Effects ◽  
Specific Effects ◽  
Convergence Results ◽  
Large Sample Theory ◽  
Scientific Goal ◽  
Statistical Learning Techniques

Abstract Understanding the pathways whereby an intervention has an effect on an outcome is a common scientific goal. A rich body of literature provides various decompositions of the total intervention effect into pathway-specific effects. Interventional direct and indirect effects provide one such decomposition. Existing estimators of these effects are based on parametric models with confidence interval estimation facilitated via the nonparametric bootstrap. We provide theory that allows for more flexible, possibly machine learning-based, estimation techniques to be considered. In particular, we establish weak convergence results that facilitate the construction of closed-form confidence intervals and hypothesis tests and prove multiple robustness properties of the proposed estimators. Simulations show that inference based on large-sample theory has adequate small-sample performance. Our work thus provides a means of leveraging modern statistical learning techniques in estimation of interventional mediation effects.

scholarly journals A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

2021 ◽  
Vol 47 (3) ◽  
Author(s):  
Timon S. Gutleb
Keyword(s):  
Open Source ◽  
Spectral Method ◽  
Jacobi Polynomial ◽  
Numerical Experiments ◽  
Exponential Convergence ◽  
Analytic Solutions ◽  
Convolution Type ◽  
Volterra Equations ◽  
Polynomial Bases ◽  
Sparsity Structure

AbstractWe present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments based on an open-source implementation for problems with and without known analytic solutions and comparisons with other methods.

scholarly journals A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games

2021 ◽  
Author(s):  
Stefano Almi ◽  
Marco Morandotti ◽  
Francesco Solombrino
Keyword(s):  
Mean Field ◽  
Evolutionary Games ◽  
Type Systems ◽  
Convergence Result ◽  
Performance Criterion ◽  
Mean Field Limit ◽  
Spatially Inhomogeneous ◽  
Convergence Results ◽  
Special Cases ◽  
Lagrangian Scheme

AbstractA multi-step Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as a mean-field limit of spatially inhomogeneous evolutionary games, describing the evolution of a system of spatially distributed agents with strategies, or labels, whose payoff depends also on the current position of the agents. The scheme is Lagrangian, as it traces the evolution of position and labels along characteristics, and is a multi-step scheme, as it develops on the following two stages: First, the distribution of strategies or labels is updated according to a best performance criterion, and then, this is used by the agents to evolve their position. A general convergence result is provided in the space of probability measures. In the special cases of replicator-type systems and reversible Markov chains, variants of the scheme, where the explicit step in the evolution of the labels is replaced by an implicit one, are also considered and convergence results are provided.

scholarly journals The alternate direction iterative methods for generalized saddle point systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shuanghua Luo ◽  
Angang Cui ◽  
Cheng-yi Zhang
Keyword(s):  
Saddle Point ◽  
Iterative Methods ◽  
Iterative Schemes ◽  
Numerical Example ◽  
Convergence Results ◽  
Alternate Direction ◽  
Saddle Point Matrix

Abstract The paper studies two splitting forms of generalized saddle point matrix to derive two alternate direction iterative schemes for generalized saddle point systems. Some convergence results are established for these two alternate direction iterative methods. Meanwhile, a numerical example is given to show that the proposed alternate direction iterative methods are much more effective and efficient than the existing one.

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