Description: Barycentric rational interpolation is a numerical method used to approximate functions using rational functions. This approach is based on the idea of representing a function as a combination of fractions, allowing for greater flexibility and accuracy in interpolation, especially compared to traditional polynomial methods. Barycentric interpolation is characterized by its ability to efficiently handle oscillation problems that can arise in polynomial interpolation, particularly over wide intervals or with poorly distributed interpolation points. This method constructs an interpolation polynomial expressed as a weighted sum of rational terms, enabling fast and stable evaluation of the interpolated function. Additionally, barycentric interpolation is particularly useful in the context of scientific computing, where precision and efficiency are crucial. In many programming environments, libraries have implemented barycentric interpolation algorithms, facilitating their use in data analysis and numerical modeling applications. In summary, barycentric rational interpolation is a powerful and versatile technique that enhances the quality of interpolation in various numerical applications.
