The steepest descent (or ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool neither taught nor even mentioned K12 education. We study whether it feasible for elementary school students to learn algorithm, while also aligning with standard curriculum. look at can be create enriching act...

The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the...

Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...

Low-rank matrix completion aims to recover an unknown from a subset of observed entries. In this paper, we solve the problem via optimization manifold. Specially, apply QR factorization retraction during optimization. We devise two fast algorithms based on steepest gradient descent and conjugate descent, demonstrate their superiority over promising baseline with ratio at least 24%.