Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra.
The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation.
The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts.
The MATLAB toolkit available online, 'MATCOM', contains implementations of the major algorithms in the book and will enable students to study different algorithms for the same problem, comparing efficiency, stability, and accuracy.
This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.
Exercise. Consider the linear system of equations Ax = b for the matrix A = 1 v u I ∈ K m×m . • Permute the rows and columns of A in such a way that the storage cost for the factors of an LU decomposition grows just ...
30 (1998) 107–117. T.H. Wei, The Algebraic Foundations of Ranking Theory, Cambridge University Press, University of Cambridge, 1952. Matrix Analysis, University Press, New York, 2013. 16. 15. second ed., Cambridge N.J. Higham, ...
This well-organized text provides a clear analysis of the fundamental concepts of numerical linear algebra.
Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations.
Problems involving linear algebra arise in many contexts of scientific computation, either directly or through the replacement of continuous systems by discrete approximations. This introduction covers the practice of matrix...