Adaptive Variational-Grid Approximation
نویسندگان
چکیده
We consider approaches to the adaptive choice of an approximation space in variational-grid method for one-dimensional second order boundary value problems, which allows us improve approximations and decrease calculation time numerical solution. The can be applied nondegenerate as well problems with weak or strong degeneration.
منابع مشابه
Grid based variational approximations
Variational methods for approximate Bayesian inference provide fast, flexible, deterministic alternatives to Monte Carlo methods. Unfortunately, unlike Monte Carlo methods, variational approximations cannot, in general, be made to be arbitrarily accurate. This paper develops grid-based variational approximations which endeavor to approximate marginal posterior densities in a spirit similar to t...
متن کاملVariational Bayes Approximation
which is sometimes referred to as the product rule. As we well know, our primary interest lies in the factor pZ|X(z|x). The rest of this lecture is concerned with characterizing this density using the method of variational Bayes (VB) approximation. This is the second example of a deterministic scheme in approximating the conditional density for inferential procedures (the first being Laplace ap...
متن کاملThe Variational Gaussian Approximation Revisited
The variational approximation of posterior distributions by multivariate gaussians has been much less popular in the machine learning community compared to the corresponding approximation by factorizing distributions. This is for a good reason: the gaussian approximation is in general plagued by an Omicron(N)(2) number of variational parameters to be optimized, N being the number of random vari...
متن کاملTutorial on variational approximation methods
Tutorial topics • A bit of history • Examples of variational methods • A brief intro to graphical models • Variational mean field theory – Accuracy of variational mean field – Structured mean field theory • Variational methods in Bayesian estimation • Convex duality and variational factorization methods – Example: variational inference and the QMR-DT Variational methods • Classical setting: " f...
متن کاملAdaptive Variational Integrators
It is now well known that symplectic integrators lose many of their desirable properties when variable step sizes are used. The most common approach to combine adaptive step sizes and symplectic integrators involves the Poincaré transformation of the original Hamiltonian. In this article, we provide a framework for the construction of variational integrators using the Poincaré transformation. S...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-06137-8