Computational Methods of Linear Algebra: A Practical Textbook with FORTRAN and MATLAB Codes by Granville Sewell

Introduction

Computational Methods of Linear Algebra: 3rd Edition by Granville Sewell is a comprehensive and practical guide for students, researchers, and professionals who need to solve real-world linear algebra problems using computational techniques. Published by World Scientific Publishing Company, this hardcover edition is an essential resource for anyone studying or working in science, mathematics, engineering, or data science. The book bridges the gap between theoretical linear algebra and its practical implementation, making it a valuable addition to any library in India.

Book Overview

This third edition builds on the strengths of its predecessors by presenting clear, efficient methods for solving fundamental linear algebra problems: linear systems, least squares problems, eigenvalue problems, and linear programming. It also includes a dedicated chapter on the fast Fourier transform and a practical introduction to solving linear algebra problems on modern supercomputers. The book is written in a straightforward style, emphasising both the underlying theory and the practical aspects of implementing these methods. Students using this book will have the opportunity to write and run their own programs, gaining hands-on experience that is crucial for academic and professional growth.

Key Highlights

• Practical Focus: The book provides highly readable FORTRAN and MATLAB codes that solve all major problems discussed, allowing readers to see theory in action.
• Updated Content: The third edition includes new material and revisions that reflect the latest developments in computational linear algebra.
• Supercomputing Insights: A unique chapter on solving linear algebra problems on modern supercomputers prepares students for high-performance computing environments.
• Comprehensive Coverage: From linear systems to the fast Fourier transform, the book covers a wide range of topics essential for scientific computing.
• Indian Relevance: The methods and codes are platform-independent and can be used with widely available software, making it ideal for Indian universities and research institutions.

Inside the Book

The book is structured to guide readers from foundational concepts to advanced applications. Each chapter begins with the necessary mathematical theory, followed by detailed algorithms and their implementation. The included FORTRAN and MATLAB codes are fully functional and can be adapted for various projects. The chapter on linear programming is particularly useful for operations research and economics students, while the fast Fourier transform section is invaluable for signal processing and data analysis. The supercomputing chapter addresses the challenges of parallel computing, a topic of growing importance in India's expanding computational research landscape.

Key Topics

• Linear Systems: Direct and iterative methods for solving systems of linear equations.
• Least Squares Problems: Techniques for overdetermined systems and data fitting.
• Eigenvalue Problems: Algorithms for computing eigenvalues and eigenvectors.
• Linear Programming: Methods for optimisation under linear constraints.
• Fast Fourier Transform: Efficient computation of discrete Fourier transforms.
• Supercomputing: Strategies for parallel and vector processing in linear algebra.

Reader Benefits

• Hands-On Learning: Write and run your own programs using the provided codes, reinforcing theoretical knowledge.
• Career Advancement: Gain skills that are directly applicable in industries like finance, engineering, data science, and academia.
• Time-Saving: Ready-to-use algorithms reduce the need to develop code from scratch.
• Deep Understanding: The blend of theory and practice ensures you grasp why methods work, not just how to use them.
• Exam Preparation: Ideal for Indian students preparing for competitive exams or advanced coursework in computational mathematics.

Learning Outcomes

After studying this book, readers will be able to: implement efficient algorithms for solving linear systems and eigenvalue problems; apply least squares methods to real-world data; solve linear programming problems using computational techniques; use the fast Fourier transform in signal and image processing; and write parallel code for supercomputers. These skills are highly sought after in research and industry, making this book a smart investment for your career.

Who Should Read

This book is perfect for undergraduate and postgraduate students in mathematics, physics, engineering, computer science, and related fields. It is also an excellent reference for researchers, data scientists, and professionals who need to solve linear algebra problems computationally. Indian students preparing for GATE, NET, or other competitive exams will find the practical examples and codes particularly helpful. The book assumes a basic understanding of linear algebra and programming, making it accessible to motivated learners.

About the Author

Granville Sewell is a renowned mathematician and educator with decades of experience in computational science. He has taught at several universities and is known for his clear, practical approach to complex topics. His expertise in numerical methods and linear algebra is evident in this well-structured book, which has been adopted by institutions worldwide. Sewell's writing style makes even challenging concepts understandable, a quality that Indian students and faculty will greatly appreciate.

About the Publisher

World Scientific Publishing Company is a leading academic publisher based in Singapore, with a strong presence in India. Known for its high-quality textbooks and research monographs, World Scientific focuses on science, technology, engineering, and mathematics. This hardcover edition is printed on durable paper and bound to withstand years of use, making it a reliable resource for students and professionals alike. The publisher's commitment to academic excellence ensures that every title meets rigorous standards.

Conclusion

Computational Methods of Linear Algebra: 3rd Edition is an indispensable guide for anyone serious about mastering the computational side of linear algebra. With its practical codes, clear explanations, and up-to-date content, it stands out as a top-tier textbook for Indian readers. Whether you are a student, researcher, or professional, this book will equip you with the tools to solve complex problems efficiently. Order your copy from Bookshops.in today and take a decisive step towards computational proficiency.