Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a graduate course on numerical linear algebra and numerous applications to engineering and science used in industry. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. It provides necessary mathematical background information for those who want to learn to solve linear algebra problems using MATLAB, and offers a thorough explanation of the issues and methods for practical computation, avoiding an extensive theorem-proof type of exposition for practical use.--
مندرجات
1. Matrices -- 2. Linear equations -- 3. Subspaces -- 4. Determinants -- 5. Eigenvalues and eigenvectors -- 6. Orthogonal vectors and matrices -- 7. Vector and matrix norms -- 8. Floating point arithmetic -- 9. Algorithms -- 10. Conditioning of problems and stability of algorithms -- 11. Gaussian elimination and the LU decomposition -- 12. Linear system applications -- 13. Important special systems -- 14. Gram-Schmidt orthonormalization -- 15. The singular value decomposition -- 16. Least-square problems -- 17. Implementing the QR decomposition -- 18. The algebraic eigenvalue problem -- 19. The symmetric eigenvalue problem -- 20. Basic iterative methods -- 21. Krylov subspace methods -- 22. Large sparse eigenvalue problems -- 23. Computing the singular value decomposition -- A. Complex numbers -- B. Mathematical induction -- C. Chebyshev polynominals
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