Introduction to Numerical Linear Algebra

Introduction to Numerical Linear Algebra, Volume 1, provides a comprehensive foundation in numerical methods for linear algebra problems. Written by Christoph Borgers and published by the Society for Industrial and Applied Mathematics, this mathematics textbook is designed for undergraduate and beginning graduate students. The text assumes prior knowledge of linear algebra but includes necessary background reviews to ensure clarity. It serves as an effective resource for flipped classroom models, offering detailed explanations that support independent study.

This volume covers specialized topics often omitted from standard introductory texts, such as diffusion, computed tomography models, and global positioning systems. Students explore the use of eigenvalues for analyzing equilibrium stability, the QR method for eigenvalues, and multigrid methods. The book also examines the application of the SVD for assigning grades. It is a valuable resource for courses in advanced numerical analysis, data science, numerical optimization, and approximation theory.