Nature

Function Approximation and Sobolev Spaces

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, ...
Nature

Matrix Functions and Their Approximations

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 ...
Risk

A new improvement scheme for approximation methods of probability density functions

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 ...
Harvard Business School

Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations

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 ...
Risk

Value function approximation or stopping time approximation: a comparison of two recent numerical methods for American option pricing using simulation and regression

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 ...