Linear Algebra and Computing: Behind the Scenes

From vectors and matrices to eigenvalues and eigenvectors, linear algebra forms the foundation of many large-scale computing applications. In this talk, we introduce numerical linear algebra by exploring questions about solving linear systems Ax=b. How does a computer solve a very large system of linear equations? It isn’t by using the Gauss-Jordan elimination you learned in pre-calculus! Does a computer always have enough memory to store every number in a matrix? Learn beginning concepts of sparsity and data compression. Do computers always calculate exact answers? Discover the perils of unstable algorithms and ill-conditioned problems. This presentation introduces linear algebra and computing at a student-friendly level. Participants who are familiar with solving small linear systems by hand should find the basic talk accessible. The material can be adapted to incorporate advanced applications for students taking undergraduate or graduate-level courses in linear algebra.