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Related papers: Novel Extrapolation for Strong Coupling Expansions

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We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…

We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation…

Machine Learning · Statistics 2016-05-04 Will Wei Sun , Junwei Lu , Han Liu , Guang Cheng

Using elementary methods, we define and derive a particular weighted average of the trapezoidal and composite trapezoidal rules and show that this approximation, as well as its composite, is straightforward in computation. This…

Numerical Analysis · Mathematics 2012-08-06 Michael Brandon Youngberg

We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which…

Numerical Analysis · Mathematics 2022-05-11 Yulong Pan , Per-Olof Persson

We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant electric field…

Mathematical Physics · Physics 2024-10-29 Christian D. Tica , Eric A. Galapon

We present a general-purpose algorithm to extrapolate a low rank function of two variables from a small domain to a larger one. It is based on the cross-interpolation formula. We apply it to reconstruct physical quantities in some quantum…

Strongly Correlated Electrons · Physics 2024-07-25 Matthieu Jeannin , Yuriel Núñez-Fernández , Thomas Kloss , Olivier Parcollet , Xavier Waintal

Almost every numerical task can be cast as extrapolation with respect to the fidelity or tolerance parameters of a consistent numerical method. This perspective enables probabilistic uncertainty quantification and optimal experimental…

Methodology · Statistics 2026-04-03 Chris. J. Oates , Richard Howey , Toni Karvonen

In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…

Numerical Analysis · Mathematics 2025-05-06 Xiaorong Zou

This paper constructs adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space. The sparse grid method is a popular technique for high dimensional problems, and the associated collocation method has been well…

Numerical Analysis · Mathematics 2019-12-10 Zhanjing Tao , Yan Jiang , Yingda Cheng

We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with…

Optimization and Control · Mathematics 2020-07-14 Ahmet Alacaoglu , Olivier Fercoq , Volkan Cevher

In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…

Numerical Analysis · Mathematics 2012-05-09 S. M. Abrarov , B. M. Quine

We present a general procedure for incorporating higher-order information into the scale-setting prescription of Brodsky, Lepage and Mackenzie. In particular, we show how to apply this prescription when the leading coefficient or…

High Energy Physics - Phenomenology · Physics 2009-11-07 K. Hornbostel , G. P. Lepage , C. Morningstar

Richardson extrapolation is applied to a simple first-order upwind difference scheme for the approximation of solutions of singularly perturbed convection-diffusion problems in one dimension. Robust a posteriori error bounds are derived for…

Numerical Analysis · Mathematics 2023-08-07 Torsten Linß , Goran Radojev

We propose an extrapolation method utilizing energy variance in the Monte Carlo shell model in order to estimate the energy eigenvalue and observables accurately. We derive a formula for the energy variance with deformed Slater…

Large language models (LLMs), although having revolutionized many fields, still suffer from the challenging extrapolation problem, where the inference ability of LLMs sharply declines beyond their max training lengths. In this work, we…

Machine Learning · Computer Science 2024-10-25 Xin Ma , Yang Liu , Jingjing Liu , Xiaoxu Ma

We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behaviour of a coupled cluster wavefunction representation…

Chemical Physics · Physics 2018-08-14 Charles J. C. Scott , Alex J. W. Thom

Recognition of objects with subtle differences has been used in many practical applications, such as car model recognition and maritime vessel identification. For discrimination of the objects in fine-grained detail, we focus on deep…

Computer Vision and Pattern Recognition · Computer Science 2019-07-23 Kaan Karaman , Erhan Gundogdu , Aykut Koc , A. Aydin Alatan

High-temperature series are computed for a generalized $3d$ Ising model with arbitrary potential. Two specific ``improved'' potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are…

Statistical Mechanics · Physics 2009-10-31 Massimo Campostrini , Andrea Pelissetto , Paolo Rossi , Ettore Vicari

Complex Networks are a good approach to find internal relationships and represent the structure of classes in a dataset then they are used for High Level Classification. Previous works use K-Nearest Neighbors to build each Complex Network…

Machine Learning · Computer Science 2021-10-26 Josimar Chire

A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…

Statistical Mechanics · Physics 2009-11-10 V. I. Yukalov , S. Gluzman , D. Sornette