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, ...

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 ...

The circumference of a sphere is measured to be 24 cm, with a possible error of 0.25 cm. Use the differential \(dV\) to estimate the maximum error in the calculated ...

This is a preview. Log in through your library . Abstract We analyze the convergence of an extended Krylov subspace method for the approximation of operator functions that appear in exponential ...

This article describes three approximation methods I used to solve the growth model (Model 1) studied by the National Bureau of Economic Research's nonlinear rational-expectations-modeling group ...

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 ...

Researchers have developed new mathematical techniques to advance the study of molecules at the quantum level. Mathematical and algorithmic developments along these lines are necessary for enabling ...

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 ...