Numerical Linear Algebra with Applications

Chapter 12

Linear System Applications

Abstract

This chapter presents four applications involving the solution to linear systems. The first of these is Fourier series that introduce the concept of an infinite-dimensional vector space with a basis of orthonormal functions. In this case, the functions are sines and cosines. The Fourier series for a periodic square wave is computed and convergence of its partial sums to the square wave is demonstrated by a graph. The second example is the use of finite differences to approximate the solution of the heat equation in time and one space variable. A tridiagonal system of equations must be solved for every time step, the right-hand side of which is determined by the initial and boundary conditions. ...