Foundational Numerical Methods: SVD and Iterative Solvers

Uncover the power of numerical methods to solve challenging mathematical problems. This course provides a clear, conceptual introduction to Singular Value Decomposition and iterative techniques for linear systems. By the end of this course, you will be equipped with the theoretical knowledge and practical understanding to approach problems involving high-dimensional data analysis, system modeling, and efficient solution of vast linear equations, forming a solid base for further study or application. What you'll learn: * Understand the core concepts and applications of Singular Value Decomposition (SVD). * Learn how SVD is used for dimensionality reduction, data compression, and noise reduction. * Explore the principles behind various iterative methods for solving large linear equations. * Apply iterative techniques like Jacobi, Gauss-Seidel, and Conjugate Gradient to practical scenarios. * Grasp the concepts of convergence criteria, computational cost, and error analysis in numerical solutions. * Recognize the role of these methods in modern data science, scientific computing, and engineering challenges. The course begins with the foundational theory and practical applications of SVD, then transitions to the principles of iterative solvers, explaining their mechanics, convergence properties, and comparative advantages. This course is designed for absolute beginners with no prior experience in numerical methods or advanced linear algebra, providing all necessary foundational concepts. Embark on your journey to master essential numerical problem-solving techniques.