<p>Designed for first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommending which algorithms to use in various practical situations. Algorithms are derived in a mathematically illuminating way, including condition numbers and error bounds. Direct and iterative algorithms, suitable for dense and sparse matrices, are discussed. Algorithm design for modern computer architectures, where moving data is often more expensive than arithmetic operations, is discussed in detail, using LAPACK as an illustration. There are many numerical examples throughout the text and in the problems at the ends of chapters, most of which are written in MATLAB and are freely available on the Web.</p>

Applied Numerical Linear Algebra

Science & Math

Demmel, James W.

Mathematics

SIAM

ScaLAPACK user's guide (Software, environments, tools)

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Finite Difference Methods For Ordinary And Partial Differential Equations

Randall J. LeVeque

Iterative Methods For Sparse Linear Systems

Yousef Saad

Optimization And Nonsmooth Analysis

Frank H. Clarke

Optimal Control Of Viscous Flow

S. S. Sritharan

Numerically Solving Polynomial Systems With Bertini

Andrew J. Sommese

Daniel J. Bates

Jonathan D. Hauenstein

Charles W. Wampler

Mathematical Optimization and Economic Theory provides a self-contained introduction to and survey of mathematical programming and control techniques and their applications to static and dynamic problems in economics, respectively. It is distinctive in showing the unity of the various approaches to solving problems of constrained optimization that all stem back directly or indirectly to the method of Lagrange multipliers. It also covers in-depth both static programming problems and dynamic control problems of optimization and the techniques of their solution. It also clearly presents many applications of these techniques to economics, and shows why optimization is important for economics. Many challenging problems for both students and researchers are included.

Mathematical Optimization and Economic Theory

Michael D. Intriligator

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