LUP Decomposition, Matrix Inversion & Least Squares in Algorithms | Chapter 28 in Introduction to Algorithms
LUP Decomposition, Matrix Inversion & Least Squares in Algorithms | Chapter 28 in Introduction to Algorithms Chapter 28 of Introduction to Algorithms offers a deep dive into efficient techniques for solving systems of linear equations, computing matrix inverses, and applying least-squares methods using LU and LUP decomposition. These methods are central to numerical algorithms, especially in scientific computing, computer graphics, and machine learning. Watch the video above for a clear walkthrough, or continue reading for a detailed breakdown of the chapter's most important concepts and algorithms. Don’t forget to subscribe to Last Minute Lecture for more chapter-based study guides! Solving Linear Systems with LU and LUP Decomposition At the heart of this chapter is the equation Ax = b , a foundational form in linear algebra where the goal is to solve for x . While the theoretical solution x = A⁻¹b may seem straightforward, computing the inverse directly is ofte...