Understanding the behavior of norms on Schur multiplier operators is of significant interest in functional analysis and applications in physics, particularly in quantummechanics. In this study, we focus on the Schur multiplier induced by the divided difference matrix of the absolute value function f (x) = |x|, all set in the finite space Mn(C). The primary objective is to approximate the operator norm ∥TBf ∥ and to analyze its behavior as a function of the Schatten normparameter p and the matrix size n. To achieve this, various numerical methods, including brute-force sampling and gradient ascent algorithms, are explored. Among these, the Adam optimization algorithm, combining momentum and RMSProp techniques, is found to be effective in achieving accurate approximations. The results are analyzed within a theoretical framework, revealing insights into the growth of the norm as well as the effectiveness of the chosen optimization method. Future research directions are suggested, particularly in the study of multilinear Schur multipliers, which present an intriguing challenge yet to be tackled.