Prerequisite: Calculus, linear algebra, some programming experience in FORTRAN, C, Matlab or a similar language.
Text: Numerical Linear algebra, by L.N. Trefethen and D. Bau, SIAM 1997 (referred by TB)
Other reference : Fundamentals of Matrix Computations, by D.S. Watkins, Wiley-Interscience, 2010.
Instructor: Dr. Yulong Xing Email: xingy (at) math.utk.edu
Office: 214 Ayres Hall Office
Hours: 10:30-11:20pm T, TH
Office Tel: (865) 974-4314
Class Meeting Times: T, Th 12:40 - 1:55 PM, Ayres Hall 111
| Week |
M |
T |
W |
R |
F |
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01, Aug. 19. |
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First class Lecture 1 of TB, Matrix-Vector multiplication |
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02, Aug. 26. |
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Lecture 2 of TB, Orthogonal vectors and matrices. |
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Lecture 3 of TB, Norms. |
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03, Sep. 02. |
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Lecture 3 and 4, norms, SVD |
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Lecture 4 and 5, SVD |
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04, Sep. 09. |
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Lecture 6, projector |
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Lecture 6 and 7, QR algorithm |
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05, Sep. 16. |
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Lecture 7 and 8, QR and Gram-Schmidt orthogonalization |
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Lecture 8, Gram-Schmidt orthogonalization |
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06, Sep. 23. |
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Lecture 10, Househoulder triangulation |
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Lecture 10 and 11, Househoulder and least square problem |
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07, Sep. 30. |
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Lecture 11, Least square problem |
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Lecture 12, Condition number |
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08, Oct. 07. |
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Midterm |
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Fall break |
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09, Oct. 14. |
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Lecture 12 and 13, Condition number and floating point arithmetic |
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Lecture 13 and 14, Stability |
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10, Oct. 21. |
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Lecture 16,17,18,19, Stability |
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Lecture 20, Gaussian elimination | |
11, Oct. 28. |
Lecture 21, 23, Pivoting and Cholesky factorization |
Lecture 22 Stability of LU, Iterative methods | |||
12, Nov. 04. |
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Jacobi, Gauss-Seidal, SOR methods and their convergence |
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Convergence, Descent method |
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13, Nov. 11. |
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Steepest descent method, CG method |
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CG method, eigenvalue problems |
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14, Nov. 18. |
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Lecture 24, 25, 26, 27 Eigenvalue problems |
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Thanksgiving holiday |
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15, Nov. 25. |
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Lecture 27, 28, 29 Rayleigh quotient, power, inverse iteration, QR algorithm |
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Nonlinear problem HW13 Quiz4 |
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16, Dec. 02. |
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Last class |
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17, Dec. 09. |
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Final Exam |
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