This text provides an introduction to numerical linear algebra together with its application to solving problems arising in state-space control and systems theory. The book provides a number of elements designed to help the reader learn to use numerical linear algebra in day-to-day computing or research, including a brief review of matrix analysis and an introduction to finite (IEEE) arithmetic, alongside discussion of mathematical software topics. In addition to the fundamental concepts, the text covers statistical condition estimation and gives an overview of certain computational problems in control and systems theory. Engineers and scientists will find this text valuable as a theoretical resource to complement their work in algorithms. For graduate students beginning their study, or advanced undergraduates, this text is ideal as a one-semester course in numerical linear algebra and is a natural follow-on to the author's previous book, Matrix Analysis for Scientists and Engineers.
Alan J. Laub is a Distinguished Professor in the Departments of Mathematics and Electrical Engineering at the University of California, Los Angeles. He has served on the editorial boards of numerous leading journals and is a member of SIAM, IEEE and ACM. He has authored or co-authored over 200 technical papers on his research interests in numerical linear algebra, scientific computation and computer-aided control system design. He is the author of Matrix Analysis for Scientists and Engineers (2005).
Preface; 1. Preliminaries and notation; 2. Introduction to finite arithmetic; 3. Conditioning and numerical stability; 4. Introduction to rounding analysis; 5. Numerical matrix algebra; 6. Gaussian elimination; 7. Solving linear systems; 8. Linear least squares problems; 9. Computing eigenvalues and eigenvectors; 10. Other QR-type algorithms; 11. Applications; Bibliography; Index.