Polynomialbased
Polynomial-based refers to mathematical methods, algorithms, and models that rely on polynomial functions as their foundational component. Polynomials are algebraic expressions consisting of variables and coefficients, structured as sums of terms where each term is a product of a power of the variable and a coefficient, such as *ax^n + bx^(n-1) + ... + k*. These functions are widely used across mathematics, engineering, computer science, and data analysis due to their simplicity and versatility.
In numerical analysis, polynomial-based methods are employed for interpolation, approximation, and root-finding. For instance, polynomial interpolation
In computer science, polynomial-based algorithms are fundamental in areas such as cryptography, error correction, and computational
Polynomial-based methods also play a critical role in optimization and control theory. Polynomial approximations, such as
Despite their advantages, polynomial-based approaches have limitations. Polynomials can exhibit instability or poor performance when extrapolating