Introduction to Splitting Algorithms in Scientific Computing

Solving large-scale optimization problems and complex differential equations can be computationally overwhelming. Splitting algorithms solve this by breaking massive mathematical challenges down into simpler, manageable subproblems. This text-only course guides you through the core concepts, mathematical foundations, and practical implementations of these powerful numerical methods. By completing this course, you will understand how to analyze, select, and apply splitting techniques to solve real-world computational problems. You will develop a strong intuitive and mathematical grasp of how these algorithms function and how to translate them into clean, efficient code. What you'll learn: - Understand the foundational theory of operator splitting and its mathematical principles - Apply classical splitting techniques, including Lie-Trotter and Strang splitting, to differential equations - Explore modern optimization splitting methods such as proximal splitting and ADMM - Analyze the stability, convergence rates, and error bounds of different splitting schemes - Practice implementing splitting algorithms step-by-step using Python-based logic - Compare the computational efficiency and accuracy of various splitting approaches Our curriculum starts with essential mathematical definitions and core concepts before transitioning into classical differential equation solvers and modern optimization techniques. You will progress systematically from basic theoretical formulations to practical algorithmic application. This course is designed for beginners in numerical analysis, scientific computing, or data science. A basic familiarity with algebra and introductory programming concepts is recommended, but no prior experience with advanced numerical methods is required. Start reading today to master the logic of splitting algorithms and elevate your computational problem-solving skills.