Computational Matrix Analysis

ยท Other Titles in Applied Mathematics ืกืคืจ 123 ยท SIAM
ืกืคืจ ื“ื™ื’ื™ื˜ืœื™
167
ื“ืคื™ื
ื›ืฉื™ืจ

ืžื™ื“ืข ืขืœ ื”ืกืคืจ ื”ื“ื™ื’ื™ื˜ืœื™ ื”ื–ื”

Using an approach that author Alan Laub calls "matrix analysis for grown-ups," this new 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; and 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; and applications of the discussed algorithms.
Using an approach that author Alan Laub calls "matrix analysis for grown-ups," this new 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 un...

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