Computational Matrix Analysis

von Alan J Laub

170 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.