Numerical Linear Algebra and Optimization

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. and 8 can be used as the text for an upper \ -