Computational Matrix Analysis

Using an approach that author Alan Laub calls “matrix analysis for grown-ups”, this textbook introduces fundamental concepts of numerical linear algebra and their application to solving certain numerical problems arising in state-space control and systems theory. It is written for advanced undergraduate and beginning graduate students and can be used as a follow-up to Matrix Analysis for Scientists and Engineers (SIAM, 2005), a compact single-semester introduction to matrix analysis for engineers and computational scientists by the same author.

Computational Matrix Analysis provides readers with:

• A one-semester introduction to numerical linear algebra.
• An introduction to statistical condition estimation in book form for the first time.
• An overview of certain computational problems in control and systems theory.

>The book features a number of elements designed to help students learn to use numerical linear algebra in day-to-day computing or research, including:

• A brief review of matrix analysis, including notation, and an introduction to finite (IEEE) arithmetic.
• Discussion and examples of conditioning, stability, and rounding analysis.
• An introduction to mathematical software topics related to numerical linear algebra.
• A thorough introduction to Gaussian elimination, along with condition estimation techniques.
• Coverage of linear least squares, with orthogonal reduction and QR factorization.
• Variants of the QR algorithm.
• Applications of the discussed algorithms.