A Study on the Fast Fourier Transform Applications

Abstract

A fundamental issue in many branches of mathematics, science, and engineering is polynomial evaluation. Numerous applications, such as cryptography, banking, and the fields of economic analysis, numerical analysis, and sign processing, can advantage considerably from the use of environment friendly polynomial contrast algorithms. We seemed at some of the most famous polynomial comparison methods in this topic, which includes Horner's approach, Newton-Raphson method, and Lagrange interpolation method. We additionally reviewed extra state-of-the-art strategies that can consider polynomials extra correctly in some situations, such as the Fast Fourier Transform (FFT) and Fast Multipoint Evaluation (FME). The preference of algorithm will matter on the specific hassle and software at hand as every algorithm has benefits and cons of its own. It is indispensable to take computational complexity into account.