Defining Data Analysis and Its Purpose Data analysis represents the fundamental procedural core of empirical research, involving the systematic application of numerical, statistical, or charted methodologies to a collected corpus of information. The primary objective of this procedure is to determine underlying patterns, identify standard trends, and effectively summarize the inherent characteristics of the data […]
Differential Relaxation: A Novel Model for Non-linear Optimization Abstract This paper introduces differential relaxation (DR), a novel optimization model for solving non-linear optimization problems. DR is a gradient-based approach that combines the simplicity of gradient descent with the global optimization abilities of traditional methods such as simulated annealing. We explain the fundamentals of DR and […]
Benny: A Novel Fast Algorithm for Solving Systems of Linear Equations Abstract This paper introduces Benny, a new fast algorithm for solving systems of linear equations. Benny is based on the fast Fourier transform technique and has excellent computational complexity. The proposed algorithm is a combination of the FFT-based matrix inversion method and a new […]
Method of Successive Approximations Introduction to the Method of Successive Approximations In the vast fields of engineering, mathematics, and various scientific disciplines, solving certain equations can present significant analytical challenges. Specifically, nonlinear equations, which contain terms where variables are raised to powers other than one or are multiplied together, often defy exact algebraic solutions. These […]