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Reading Assignments are in Lloyd Trefethen, and David Bau. Numerical Linear Algebra. SIAM, 1997. ISBN: 0898713617, unless otherwise indicated.
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WEEK # |
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TOPICS |
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READINGS |
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1 |
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Linear Algebra Basics. Norms. |
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1, 2, 3 |
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2 |
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The Singular Value Decomposition. |
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4, 5, 31 |
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3 |
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Projectors. QR Factorization: Classical and Modified Gram-Schmidt. |
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6, 7, 8 |
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4 |
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QR: Householder Triangularization and Givens Rotation. Least Squares. |
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10, 11 |
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5 |
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Floating Point Arithmetic. MATLAB® Demo. |
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9, 13 |
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6 |
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Conditioning and Stability; Stability of Householder Decomposition. |
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12, 14, 15, 16 |
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7 |
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LU Factorization. Pivoting. Cholesky Factorization. Stability Issues. Special Linear Systems. |
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20, 21, 22, 23 |
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8 |
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Eigenvalue Problems and Algorithms. Rayleigh Quotient; Power Method; Inverse Iteration. |
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24, 25, 27 |
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9 |
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MATLAB® Demo. Exam 1. |
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10 |
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Hessenberg Form. Orthogonal Iteration. QR Algorithm with and without Shifts. |
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26, 28, 29 |
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11 |
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Symmetric Eigenvalue Problems; Tridiagonal QR Algorithms; Rayleigh Quotient Iteration; Divide--and--Conquer; Bisection and Inverse Iteration; Algorithms for Computing the SVD. |
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30, 31 |
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12 |
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Iterative Methods for Linear Systems; Preconditioning; Jacobi, Gauss--Siedel, Successive Overrelaxation; Convergence Criteria for Jacobi, GS, SOR; Chebyshev Acceleration; SSOR. |
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Demmel: 6.1-6.5 |
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13 |
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Arnoldi Iteration and Krylov Methods; Conjugate Gradient Method; GMRES; Fast Fourier Transform. MATLAB® Demo. |
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32, 33, 34, 35 |
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14 |
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Iterative Methods for Eigenvalue Problems; Rayleigh-Ritz Method; Lanczos Algorithm; Low Order Finite Element Methods. |
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36, 37, 38, 39, 40 |
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15 |
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Domain Decomposition Methods and Preconditioners; Additive and Multiplicative Schwarz Preconditioners; Overlapping and Nonoverlapping Methods; Coarse Spaces. Exam 2. |
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