Explorations in Numerical Analysis and Machine Learning with Julia

The textbook is an expansion of Explorations in Numerical Analysis that includes new chapters covering topics from machine learning. It is intended for advanced undergraduate and early graduate students, with a focus on the connections between numerical analysis and machine learning.

Topics covered include computer arithmetic, error analysis, solution of systems of linear equations by direct and iterative methods, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, partial differential equations, machine learning, classification, regression, and neural networks.

Each problem is presented with derivations of solution techniques, analysis of their efficiency, accuracy and robustness, and detailed implementation using the Julia programming language. This book is suitable for a year-long course in numerical analysis, or for a one-semester course in numerical linear algebra (Part II) or machine learning (Part VI).

James V Lambers is an Applied Mathematics Researcher working with Peraton, Inc. and the US Naval Research Laboratory, an Affiliated Professor in the School of Mathematics and Natural Sciences at The University of Southern Mississippi, and an ACUE Distinguished Teaching Scholar. His research interests span numerical methods for partial differential equations and numerical linear algebra.

Amber Sumner Mooney is an Associate Professor of Mathematics at William Carey University and Research Associate at USDA-ARS. Her research interests include deep learning and numerical linear algebra.

Vivian A Montiforte is a Research Oceanographer at the US Naval Research Laboratory. Her research interests include data assimilation and ocean forecasting, with a background in numerical methods and data analysis.

James Quinlan is Chair of the Department of Computer Science at University of Southern Maine. His research interests include scientific computing, computational fluid dynamics, and next-generation arithmetic.