Approximation theory and asymptotic methods form a foundational framework that bridges classical ideas with modern numerical analysis, enabling researchers to obtain practical, near‐optimal solutions ...

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 ...

This course teaches commonly used approximation methods in quantum mechanics. They include time-independent perturbation theory, time-dependent perturbation theory, tight binding method, variational ...

We consider the numerical approximation of a semilinear fractional order evolution equation involving a Caputo derivative in time of order α ϵ (0,1). Assuming a Lipschitz continuous nonlinear source ...