MATH 126: Numerical Linear Algebra

Many problems in the natural sciences, social sciences, and engineering are modeled using systems of linear equations, matrix factorizations, and eigenvalue problems. In practice, solving such problems requires numerical algorithms that operate in finite precision arithmetic. Numerical Linear Algebra studies how linear algebraic problems can be efficiently and accurately solved on computers, taking into account rounding errors, stability, and computational complexity. This course focuses on the development, analysis, and implementation of numerical algorithms for linear algebraic problems. We begin by examining how computers represent numbers and perform arithmetic, and how these issues affect numerical computations. We then study core algorithms for solving linear systems, least-squares problems, and eigenvalue problems, with an emphasis on stability, conditioning, and error analysis. A mathematical software package will be used to implement and experiment with numerical linear algebra algorithms. Applications arising from scientific computing and data analysis will be used to illustrate the theory and methods developed in the course.