| Lecture | Date | Topic | Reading | Assigned | Due |
|---|---|---|---|---|---|
| / | Matrix-vector multiplication, column space, rank, matrix-matrix multiplication, outer product matrix |
Strang I.1 - I.2
Lecture 1 notes |
HW1 | ||
| / | four subspaces of a matrix, column space, nullspace, rank(AB), rank(A+B)
A singular, nonsingular, Ax = b, existence and uniqueness, A = LU, PA = LU |
Strang I.3-I.4
Lecture 2 notes Lecture 3 notes |
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| / | HW2 | HW1 | |||
| / | Orthogonality, orthogonal vectors, orthogonal subspaces, orthogonal matrix, projector
Eigenvalues, eigenvectors, shifts, similarity |
Strang I.5-I.6
Lecture 4 notes Lecture 5 notes |
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| / | HW3 | HW2 | |||
| / | Symmetric positive definite matrices, Cholesky factorization, SVD |
Strang I.7-I.8
Lecture 6 notes Lecture 7 notes |
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| / | HW4 | HW3 | |||
| / | SVD, fundamental subspaces of A, pseudoinverse, vector and matrix norms |
Strang I.8, Strang I.11, (Strang II.2, Pseudoinverse subsection)
Lecture 8 notes Lecture 9 notes Example (run at https://octave-online.net) | |||
| / | HW5 | HW4 | |||
| / | QR decomposition, Gram-Schmidt, Householder
Review session |
Strang II.2 (pp. 128-131 (QR by Gram-Schmidt and Householder))
Lecture 10 notes (substitute lecturer: Craig Schroeder) Sample Midterm (shortened) (Solutions ) |
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| - | / | HW5 | |||
| / | Least squares, normal equations, least squares by pseudoinverse (minimum norm solution)
THURSDAY - MIDTERM - IN CLASS |
Strang II.2
Lecture 11 notes Midterm study guide (lectures 1-9) |
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| - | / | HW6 | |||
| / | Least squares by QR, Tikhonov regulariation of LS, weighted LS, condition number, matrix condition number (Ax =b)
Iterative methods, splitting, Jacobi, Gauss-Seidel, convergence rate, power iteration, inverse iteration, rayleigh quotient iteration, QR algorithm |
Strang II.2, Strang II.1
Lecture 12 notes Lecture 13 notes |
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| / | HW7 | HW6 | |||
| / | QR iteration, shifted QR, reduction to upper Hessenberg, Krylov vectors, Krylov subspace, Arnoldi iteration, eigenvalues from Arnoldi, symmetric matrcies and Lanczos
residual, GMRES, conjugate gradients |
Strang II.1, Shewchuk
Lecture 14 notes Lecture 15 notes |
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| / | HW8 | HW7 | |||
| / | line search, steepest descent method, conjugate gradients methods, preconditioning
THURSDAY - HOLIDAY - NO CLASS |
Strang II.1, Shewchuk
Lecture 16 notes |
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| - | / | ||||
| / | Nonlinear equations, root-finding, fixed-point iteration, convergence of fixed point iteration, Newton's method (root finding), unconstrained optimization, optimality conditions, Newton's method (optimization)
Review session |
Lecture 17 notes
Sample Final (shortened) (Solutions) |
HW8 | ||
| - | / | HW9 | |||
| - | 12/11 | FINAL: 8am - 11am in BOYHL 1471 | Final study guide (lectures 10-17) |