This text aims to give undergraduate students a grasp of the basic concepts of round-off errors, stability, conditioning, and accuracy as well as an appreciation of the core numerical linear algebra algorithms, their basic properties and implementations. The author draws heavily on applications from electrical, mechanical, and chemical engineering; physics and chemistry; statistics; control theory; and signal and image processing. The two most fundamental concepts of numerical linear algebra (the conditioning of the problem and the stability of an algorithm via backward round-off error analysis) are introduced early in the text with simple, motivating examples.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
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Maße
Höhe: 248 mm
Breite: 171 mm
Gewicht
ISBN-13
978-0-534-17466-8 (9780534174668)
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Schweitzer Klassifikation
1. A Review of Some Required Concepts from Core Linear Algebra. 2. Floating Point Numbers and Errors in Computations. 3. Stability of Algorithms and Conditioning of Problems. 4. Numerically Effective Algorithms and Mathematical Software. 5. Some Useful Transformations in Numerical Linear Algebra and Their Applications. 6. Numerical Solutions of Linear Systems. 7. Least Squares Solutions to Linear Systems. 8. Numerical Matrix Eigenvalue Problems. 9. The Generalized Eigenvalue Problem. 10. The Singular Value Decomposition (SVD). 11. A Taste of Round-Off Error Analysis. Appendix A: A Brief Introduction to MATLAB. Appendix B: MATLAB and Selected MATLAB Programs.
