linear algebra

Table of Contents 1. Motivation 2. Properties of the Legendre polynomials 3. Numerical integration via Gaussian Quadrature 4. Conclusion 5. References All the code used to generate the animations in this article is available at the following public repository: Auxiliary repository 1. Motivation There are many scenarios in which we need to compute the integral of a function over a given interval. For instance, in physics, we may want to calculate the work done by a force over a certain distance....

Table of Contents 1. Motivation 2. Orthogonalization via Gram-Schmidt 3. Legendre Polynomials 4. Conclusion 5. References All the code used to generate the animations in this article is available at the following public repository: Auxiliary repository 1. Motivation Orthogonal bases are a powerful tool in linear algebra. They allow us to decompose vectors into simpler components, and they are at the core of many numerical algorithms. For instance, imagine we are given an arbitrary function....