Function approximation, a central theme in numerical analysis and applied mathematics, seeks to represent complex functions through simpler or more computationally tractable forms. In this context, ...

Matrix functions, such as the exponential, square root and cosine, play an indispensable role in various fields including quantum mechanics, control theory and numerical solution of differential ...

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 ...

Han, Tessa, Suraj Srinivas, and Himabindu Lakkaraju. "Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations." Advances in Neural Information ...

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 ...

In their 2001 paper, Longstaff and Schwartz suggested a method for American option pricing using simulation and regression, and since then this method has rapidly gained importance. However, the idea ...

The area \(A\) of a square of side length \(s\) is \(A=s^2\text{.}\) Suppose \(s\) increases by an amount \(\Delta s=ds\text{.}\) Draw a square and then illustrate ...