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 ...

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 ...