Results 1 to 10 of about 11,431,838 (210)

Corrigendum to "Robotic-Assisted Arthroscopy Promises Enhanced Procedural Efficiency, Visualization, and Control but Must Overcome Barriers to Adoption". [PDF]

HSS J
europepmc   +1 more source

Transformers Learn to Achieve Second-Order Convergence Rates for In-Context Linear Regression

Neural Information Processing Systems, 2023
Transformers excel at in-context learning (ICL) -- learning from demonstrations without parameter updates -- but how they do so remains a mystery. Recent work suggests that Transformers may internally run Gradient Descent (GD), a first-order optimization
Deqing Fu, Tian Chen, Robin Jia, V. Sharan   +3 more
semanticscholar   +1 more source

CMMSE: A novel scheme having seventh-order convergence for nonlinear systems

Journal of Computational and Applied Mathematics, 2020
In this paper, we present a new three-point iterative scheme for obtaining the solution of nonlinear system having seventh-order convergence. The beauty of our scheme is that we obtained the seventh-order convergence with minimal computational cost as ...
R. Behl, H. Arora
semanticscholar   +1 more source

Predefined-time convergence in fractional-order systems

, 2021
The contribution of this paper is the design of a novel controller that enforces predefined-time convergence in fractional-order systems, which are defined by means of the Caputo derivative, whose order lays between zero and one.
A. Muñoz‐Vázquez, J. Sánchez‐Torres, M. Defoort, Salah Boulaaras   +3 more
semanticscholar   +1 more source

A high order numerical method and its convergence for time-fractional fourth order partial differential equations

Applied Mathematics and Computation, 2020
This paper is concerned with design and analysis of a high order numerical approach based on a uniform mesh to approximate the solution of time-fractional fourth order partial differential equations.
P. Roul, V. Prasad Goura
semanticscholar   +1 more source

A sixth order numerical method and its convergence for generalized Black-Scholes PDE

Journal of Computational and Applied Mathematics, 2020
The main aim of this paper is to construct a new computational approach for the numerical solution of generalized Black–Scholes equation. In this approach, the temporal variable is discretized using Crank–Nicolson scheme and spatial variable is ...
P. Roul, V. Prasad Goura
semanticscholar   +1 more source

Some loose ends on unbounded order convergence

, 2016
The notion of almost everywhere convergence has been generalized to vector lattices as unbounded order convergence, which proves to be a very useful tool in the theory of vector and Banach lattices.
Hui Li, Zi-li Chen
semanticscholar   +1 more source

Higher Order Convergence Rates in Theory of Homogenization: Equations of Non-divergence Form

, 2014
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form.
Sunghan Kim, Ki-Ahm Lee
semanticscholar   +1 more source

A fractional Newton method with 2αth-order of convergence and its stability

Applied Mathematics Letters, 2019
The use of fractional calculus in many branches of Science and Engineering is wide in the last years. There are different kinds of derivatives that can be useful in different problems.
Ali Akgül, A. Cordero, J. Torregrosa
semanticscholar   +1 more source