Dive deep into the Muon Optimizer and learn how it enhances dense linear layers using the Newton-Schulz method combined with ...

Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. We present an efficient two-level strategy to accelerate the solution of the CASSCF ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

Abstract: In this paper, we propose a derivative free algorithm for solving non-linear monotone equations with convex constraints. The proposed algorithm combines the method of spectral gradient and ...

College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China. Nonlinear phenomena exist in many fields of natural science, such as quantum mechanics, condensed matter, ...

In this article, we construct exact traveling wave solutions of the loaded Korteweg-de Vries, the loaded modified Korteweg-de Vries, and the loaded Gardner equation by the functional variable method.

Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...

We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster ...