Lagrange Interpolation for Data Science and Numerical Analysis

In data science, engineering, and scientific computing, we often encounter gaps in our data or need to approximate complex functions. Lagrange interpolation provides a elegant, direct mathematical method to find a polynomial that passes exactly through a given set of discrete points. This text-based course guides you from the foundational algebraic concepts to practical algorithmic implementation. You will start by learning the core terminology and mathematical definitions of interpolation, contrasting it with regression techniques. From there, you will explore how to construct Lagrange basis polynomials and assemble the final interpolating polynomial. To ensure your skills are relevant for today's technical workflows, you will also learn how to implement these mathematical models in Python using modern vectorization techniques with NumPy, and analyze potential pitfalls like Runge's phenomenon. What you'll learn: - Understand the fundamental differences between interpolation and curve fitting - Construct Lagrange basis polynomials step-by-step from discrete data points - Formulate the complete Lagrange interpolating polynomial for any given data set - Implement interpolation algorithms efficiently using modern Python code and NumPy arrays - Analyze error bounds and understand the limitations of high-degree polynomial interpolation - Apply interpolation techniques to solve practical estimation problems in data analysis This course begins with essential mathematical definitions before moving on to step-by-step manual calculations and modern programmatic implementations. It is designed for beginners, data analysts, and software developers who want to strengthen their mathematical foundations, requiring only basic algebra and introductory Python knowledge. Discover how to reconstruct missing data points and enhance your analytical toolkit today.