Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods, and ...

SIAM Journal on Applied Mathematics, Vol. 50, No. 6 (Dec., 1990), pp. 1517-1532 (16 pages) An approximation method of Moore for Kelvin-Helmotz instability is formulated as a general method for ...

Dynamical low-rank approximation (DLRA) methods have emerged as a powerful numerical framework for addressing the challenges posed by high-dimensional problems. By restricting the evolution of a ...

This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in the Hilbert space projection theorem. Moreover, we apply ...

In this topic we will advance the fundamental mathematical understanding of artificial neural networks, e.g., through the design and rigorous analysis of stochastic gradient descent methods for their ...