Consider the function f : R → R defined by f(x) = 0.25 cos(2x)^2 − x^2. Implement the methods of computing a root of the equation f(x) = 0 based on the first-order approximation of the function. In ...

For a square matrix ( A ), an eigenvalue ( \lambda ) and a corresponding eigenvector ( v ) are defined by the equation: [ Av = \lambda v ] The eigenvalue ( \lambda ) is a scalar that scales the ...

1 School of Mathematics, KNT University of Technology, Tehran, Iran. 2 Department of Mathematics, College of Basic Sciences, Karaj branch Islamic Azad University, Alborz, Iran. In this paper, we ...

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 ...

The area under a curve refers to the region enclosed between the curve and the horizontal axis of a graph. This area is found by integrating an equation across an interval. Understanding this concept ...

To overcome the problem of calculation errors in the Born approximation when the forward accumulation effect is strong in VTI media, this article combines the De Wolf approximation method with VTI ...

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 ...