Computational Matrix Analysis
ΡΠ°Π½. 2012β―Π³. Β· Other Titles in Applied Mathematics ΠΠ½ΠΈΠ³Π° 123 Β· SIAM
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Π‘ΡΡΠ°Π½ΠΈΡΠΈ
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reportΠΡΠ΅Π½ΠΈΡΠ΅ ΠΈ ΡΠ΅ΡΠ΅Π½Π·ΠΈΠΈΡΠ΅ Π½Π΅ ΡΠ΅ ΠΏΠΎΡΠ²ΡΠ΄Π΅Π½ΠΈ Β ΠΠΎΠ·Π½Π°ΡΡΠ΅ ΠΏΠΎΠ²Π΅ΡΠ΅
ΠΠ° Π΅-ΠΊΠ½ΠΈΠ³Π°Π²Π°
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.
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ΠΠ° Π΄Π° ΡΠΈΡΠ°ΡΠ΅ Π½Π° ΡΡΠ΅Π΄ΠΈ ΡΠΎ Π΅-ΠΌΠ°ΡΡΠΈΠ»ΠΎ, ΠΊΠ°ΠΊΠΎ ΡΡΠΎ ΡΠ΅ Π΅-ΡΠΈΡΠ°ΡΠΈΡΠ΅ Kobo, ΡΠ΅ ΡΡΠ΅Π±Π° Π΄Π° ΠΏΡΠ΅Π·Π΅ΠΌΠ΅ΡΠ΅ Π΄Π°ΡΠΎΡΠ΅ΠΊΠ° ΠΈ Π΄Π° ΡΠ° ΠΏΡΠ΅ΡΡΠ»ΠΈΡΠ΅ Π½Π° ΡΡΠ΅Π΄ΠΎΡ. Π‘Π»Π΅Π΄Π΅ΡΠ΅ Π³ΠΈ Π΄Π΅ΡΠ°Π»Π½ΠΈΡΠ΅ ΡΠΏΠ°ΡΡΡΠ²Π° Π²ΠΎ Π¦Π΅Π½ΡΠ°ΡΠΎΡ Π·Π° ΠΏΠΎΠΌΠΎΡ Π·Π° ΠΏΡΠ΅ΡΡΠ»Π°ΡΠ΅ Π½Π° Π΄Π°ΡΠΎΡΠ΅ΠΊΠΈΡΠ΅ Π½Π° ΠΏΠΎΠ΄Π΄ΡΠΆΠ°Π½ΠΈ Π΅-ΡΠΈΡΠ°ΡΠΈ.
