Synopsis
This classic volume covers the fundamentals of two closely related topics: linear systems (linear equations and least\-squares) and linear programming (optimizing a linear function subject to linear constraints). For each problem class, stable and efficient numerical algorithms intended for a finite\-precision environment are derived and analyzed. While linear algebra and optimization have made huge advances since this book first appeared in 1991, the fundamental principles have not changed. \n\nThese topics were rarely taught with a unified perspective, and, somewhat surprisingly, this remains true 30 years later. As a result, some of the material in this book can be difficult to find elsewhere―in particular, techniques for updating the LU factorization, descriptions of the simplex method applied to all\-inequality form, and the analysis of what happens when using an approximate inverse to solve Ax=b. \n\nNumerical Linear Algebra and Optimization is primarily a reference for students who want to learn about numerical techniques for solving linear systems and\/or linear programming using the simplex method; however, Chapters 6, 7, and 8 can be used as the text for an upper\-division course on linear least squares and linear programming. Understanding is enhanced by numerous exercises.
About the Author
Philip E. Gill is Distinguished Professor of Mathematics at the University of California, San Diego (UCSD). He received his Ph.D. from Imperial College London in 1974. Before joining UCSD, he was a researcher at the National Physical Laboratory in the United Kingdom and the Systems Optimization Laboratory at Stanford. His research areas include scientific computation and numerical optimization. He was elected Fellow of the Society of Industrial and Applied Mathematics (SIAM) in 2014.^Walter Murray has been a professor at Stanford University since 1979. He is the director of the Systems Optimization Laboratory and was a previous director of the SCCM program and of ICME. He received his Ph.D. from the University of London in 1969 when working at the National Physical Laboratory. He has been principal advisor to 40 doctoral students from 19 countries and five continents who have graduated from a variety of universities (Stanford, London, Oxford, Royal Institute of Technology in Stockholm, South Australia).^Margaret H. Wright is Silver Professor at the Courant Institute of Mathematical Sciences, New York University. She received her Ph.D. in computer science from Stanford University. Before joining NYU, she was a researcher in the Systems Optimization Laboratory at Stanford and the Computing Science Research Center at Bell Laboratories. Her interests include numerical optimization and scientific computing. She is a member of the National Academy of Sciences, the American Academy of Arts and Sciences, and the National Academy of Engineering. She was elected Fellow of the Society of Industrial and Applied Mathematics (SIAM) in 2009.
"About this title" may belong to another edition of this title.
