Exploration of eigenvalue and singular value decompositions (SVD) for dimension reduction. Guide to Getting Started
Differential equations model how physical systems change over time. Numerical solvers step through time to trace out these paths. Initial Value Problems (IVPs) and an initial state , we compute future states: . Simple, but highly unstable for larger step sizes.
. It is the most robust method for analyzing rank-deficient, highly ill-conditioned linear least squares problems and forms the mathematical basis for Principal Component Analysis (PCA). 5. Nonlinear Equations and Optimization Unlike linear equations, nonlinear equations rarely have exact analytical solutions. Root-Finding Algorithms
An open method that converges quadratically but requires the evaluation of the function's derivative
Solving Initial Value Problems (IVPs) using Euler's method and Runge-Kutta methods.
: Understanding the pitfalls of high-degree polynomials, such as Runge's phenomenon.
