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Computational Matrix Analysis

Computational Matrix Analysis


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About the Book

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.


    Table of Contents:
    • Preface
    • Chapter 1: Preliminaries and Notation
    • Chapter 2: Introduction to Finite Arithmetic
    • Chapter 3: Conditioning and Numerical Stability
    • Chapter 4: Introduction to Rounding Analysis
    • Chapter 5: Numerical Matrix Algebra
    • Chapter 6: Gaussian Elimination
    • Chapter 7: Solving Linear Systems
    • Chapter 8: Linear Least Squares Problems
    • Chapter 9: Computing Eigenvalues and Eigenvectors
    • Chapter 10: Other QR-Type Algorithms
    • Chapter 11: Applications
    • Bibliography
    • Index.


      About the Author :
      Alan J. Laub is a Distinguished Professor in the Departments of Mathematics and Electrical Engineering at the University of California, Los Angeles. He has served on the editorial boards of numerous leading journals and is a member of SIAM, IEEE and ACM. He has authored or co-authored over 200 technical papers on his research interests in numerical linear algebra, scientific computation and computer-aided control system design. He is the author of Matrix Analysis for Scientists and Engineers (2005).


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      Product Details
      • ISBN-13: 9781611972207
      • Publisher: Society for Industrial & Applied Mathematics,U.S.
      • Publisher Imprint: Society for Industrial & Applied Mathematics,U.S.
      • Height: 229 mm
      • No of Pages: 167
      • Spine Width: 4 mm
      • Width: 152 mm
      • ISBN-10: 1611972205
      • Publisher Date: 30 Apr 2012
      • Binding: Paperback
      • Language: English
      • Returnable: N
      • Weight: 370 gr


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