Matrix Computations with Python: A Practical Course for Physical and Data Sciences

G.R. Liu

Author

Dr. G.R. (Guirong) Liu is an expert in computational mechanics and numerical methods, currently serving as a Professor of Aerospace Engineering and Engineering Mechanics at the University of Cincinnati. A prolific researcher and educator, Dr. Liu is recognized for pioneering meshfree methods, smoothed finite element methods (S-FEM), and smoothed particle hydrodynamics (SPH). These innovations have significantly advanced simulation techniques in both solid and fluid mechanics. In recent years, Dr. Liu has authored several textbooks and reference works for courses and research in areas such as artificial intelligence, machine learning, mathematics, computational methods, mechanics of materials, solid mechanics, engineering mechanics, applied mechanics, and fluid dynamics.

Synopsis

Modern science and engineering rely on solving large-scale linear systems, eigenvalue problems, and singular value decompositions efficiently. This book provides a practical, code-driven guide to modern numerical algorithms for tackle these high-dimensional matrix problems, with a strong focus on iterative methods, Krylov subspace projections, and randomized techniques. What You Will Learn: Linear Systems: Core iterative solvers including Conjugate Gradient (CG) and GMRES,paired with preconditioning strategies. Eigenvalue Problems: Essential algorithms spanning Power Iteration, QR, Lanczos,and Divide-and-Conquer approaches. Singular Value Decomposition: High-impact SVD techniques, including Golub–KahanBidiagonalization, Randomized SVD, and the Randomized Nyström Method. An Interactive, Hands-On Approach: Designed for interactive learning, this text seamlessly bridges theory, mathematical formulation, and executable Python code within a Jupyter Notebook framework. Readers can directly execute code, tweak parameters, and analyze convergence through worked-out examples and real-world computational case studies. Who This Book Is For: An ideal resource for undergraduate and graduate students, researchers, and practicing engineers in scientific computing, computational engineering, applied mathematics, and data science seeking to master modern large-scale matrix solvers.

Matrix Computations with Python