Numerical Methods in Matrix Computations

1. Front Matter

   Pages i-xvi

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2. Direct Methods for Linear Systems

   • Åke Björck

   Pages 1-209

3. Linear Least Squares Problems

   • Åke Björck

   Pages 211-430

4. Matrix Eigenvalue Problems

   • Åke Björck

   Pages 431-612

5. Iterative Methods

   • Åke Björck

   Pages 613-781

6. Back Matter

   Pages 783-800

   PDF

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given.

Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

• Discrete Inverse Problems
• Graph Models
• Partial Least Squares
• Recursive Algorithms
• Rounding Error Analysis
• Sparse Matrix Factorizations

“NMMC contains, of course, all expected classical topics and results on matrix computations, but it also contains very recent material … . this is a very well written excellent book, which I strongly recommend to anybody interested in matrix computations and in computational mathematics in general. … should be very useful for a wide audience, ranging from graduate students to specialists in matrix computations, as well as researchers in other areas that use matrix computations.” (Froilán M. Dopico, SIAM Review, Vol. 58 (2), June, 2016)

“This remarkable book aims at providing an up-to-date treatment of methods and algorithms within the context of matrix computations and really hits the target. … the interested reader can find a large, comprehensive and up-to-date list of references at the end of each chapter, together with some critical notes. ... this book is to be highly recommended to anybody with a serious interest in using matrix computations.” (Raffaella Pavani, Mathematical Reviews, March, 2016)

“This is a fundamental work giving the basic ideas and methods in modern computational linear algebra. … many ideas are mentioned and many references are given. Therefore, it will be an excellent reference work, parts can be used to teach a course on the subject, or it can be used by an independent reader to get a grasp on the topic, i.e., to learn something of the background, not just a practical hands-on programming course.” (Adhemar Bultheel, euro-math-soc.au, December, 2014)

• Department of Mathematics, Linköping University, Linköping, Sweden

  Åke Björck

Åke Björck is professor emeritus at Linköping University Sweden. He is the coauthor of several textbooks on numerical methods and a monograph and several papers on least squares methods. He has been visiting professor at Stanford University and University of Southern California.

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