Numerical Linear Algebra and Matrix Factorizations

Mastering the material in this book should enable a student to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and develop his or her own algorithms for solving them. Such problems can be large and difficult to handle so that much can be gained by understanding and taking advantage of special structures. For this we need a good understanding of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra for it allows one to tackle large problems through solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, assuming only first year calculus, an introductory course in linear algebra, and some experience in solving mathematical problems on a computer. A special feature of this book is that it provides detailed proofs of practically all results. Parts of the book can be studied independently making it suitable for self-study. A list of the exercises with page references can be found at the end of the volume. The book is consisting of 15 chapters which naturally disaggregate into five thematically related parts. The chapters are designed to be suitable for a one week per chapter one semester course. To ease out self-study, an introductory chapter contains a review of linear algebra, and provides the reader with convenient occasional reference.