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Date |
Lecture |
Reading |
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Wednesday 09/04 |
Lecture 1: Introduction
Lecture notes: slides |
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Tuesday 09/16 |
Lecture 2: Fundamentals Vector space, subspace, linear independence vector norm Lecture notes: slides |
Chapter 1-3 of Trefethen and Bau Chapter 2 of Golub and Van Loan Chapter 3 of Harville Chapter 2 of Luenberger Chapter 2 of Tomasi’s lecture notes on Mathematical Modeling of Continuous Systems |
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Wednesday 09/18 |
Lecture 3: Fundamentals and singular value decomposition Matrix norm, rank, null space, orthogonality, singular value decomposition Lecture notes: slides |
Chapter 2 of Golub and Van Loan Chapter 5 of Meyer Chapter 2 of Luenberger Chapter 3 and Chapter 4 of Harville |
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Monday 09/23 |
Lecture 4: Orthogonal projection, orthogonality, matrix inverse, singular value decomposition (SVD) Lecture notes: slides |
Chapter 4 of Trefethen and Bau Chapter 2 and Chapter 3 of Golub and Van Loan Chapter 3 of Tomai’s lecture notes on Mathematical Modeling of Continuous Systems |
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Monday 09/23 |
Lecture 5: Singular value decomposition, geometric interpretation of SVD, applications Lecture notes: slides |
Chapter 5 of Trefethen and Bau Chapter 3 of Golub and Van Loan Chapter 3 of Tomasi’s lecture notes Chapter 5 of Meyer Thomas Hofmann’s tutorial on Matrix Decomposition Techniques in Machine Learning and Information Retrieval |
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Wednesday 09/25 |
Lecture 6: Orthogonal projection and SVD, distance between subspaces, principal component analysis (PCA) Lecture notes: slides |
Chapter 6 of Trefethen and Bau Chapter 2 of Golub and Van Loan Chapter 5 of Meyer |
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Monday 09/30 |
Lecture 7: PCA,
Karhunen-Loeve transform, Multivariate Gaussian, applications Lecture notes: slides |
Chapter 6 of Trefethen and Bau Chapter 2 of Golub and Van Loan Chapter 5 of Meyer |
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Monday 09/30 |
Lecture 8:
Probabilistic PCA and factor analysis Lecture notes: slides |
Chapter 7 and Chapter 9 of Jolliffe |
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Wednesday 10/02 |
Lecture 9: Matrix
derivative, least squares minimization, regression, regularization Lecture notes: slides |
Chapter 11 of Trefethen and Bau Stephen Boyd’s EE 264 lecture 5 and lecture 6 |
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Monday 10/07 |
Lecture 10: Gaussian
elimination, LU decomposition, Cholesky decomposition Lecture notes: slides |
Chapter 20, 21, 23 of Trefethen and Bau Chapter 3-4 of Golub and Van Loan |
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Monday 10/07 |
Lecture 11: Gram-Schmidt
process, QR decomposition, Gram-Schmidt triangular orthogonalization Lecture notes: slides |
Chapter 7-8 of Trefethen and Bau Chapter 5 of Golub and Van Loan |
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Wednesday 10/09 |
Lecture 12: Matrix
decomposition QR decomposition,
eigendecomposition, Householder transformation, Givens rotation Lecture notes: slides |
Chapter 10 of Trefethen and Bau Chapter 5 of Golub and Van Loan |
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Monday 10/14 |
Lecture 13:
Eigenvalues and eigenvectors Unsymmetric
eigenvalue problems, Schur decomposition Lecture notes: slides |
Chapter 24 of Trefethen and Bau Chapter 7 of Golub and Van Loan |
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Monday 10/14 |
Lecture 14: Direct
methods for eigenvalue problems, Hessenberg form, power method Lecture notes: slides |
Chapter 25-27 of Trefethen and Bau Chapter 7 of Golub and Van Loan |
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Wednesday 10/16 |
Midterm presentation |
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Monday 10/21 |
Lecture 15:
Inverse iteration, Rayleigh quotient iteration, Conditioning and stability Lecture notes: slides |
Chapter 27, 17 of Trefethen and Bau Chapter 7 of Golub and Van Loan |
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Monday 10/21 |
Lecture 16:
Conditioning and stability Condition of
matrix-vector multiplication, condition number of a matrix, condition of a
system of equations Lecture notes: slides |
Chapter 18 of Trefethen and Bau Chapter 2 of Golub and Van Loan |
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Wednesday 10/23 |
Lecture 17:
Solving eigenvalue problems QR algorithm with
shifts, simultaneous iteration Wilkinson shits Lecture notes: slides |
Chapter 28-29 of Trefethen and Bau Chapter 8 of Golub and Van Loan |
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Monday 10/28 |
Lecture 18:
Iterative methods for eigenvalue problems Arnoldi method, Krylov
subspaces Lecture notes: slides |
Chapter 32-34 of Trefethen and Bau Chapter 9-10 of Golub and Van Loan |
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Monday 10/28 |
Lecture 20:
Iterative methods for eigenvalue problems Steepest descent,
conjugate gradients Lecture notes: slides |
Chapter 35-36 of Trefethen and Bau Chapter 10 of Golub and Van Loan An
Introduction to the Conjugate Gradient Method Without the Agonizing Pain |
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Wednesday 10/30 |
Lecture 20:
Iterative methods for eigenvalue problems Steepest descent, conjugate
gradients Lecture notes: slides |
Chapter 35-36 of Trefethen and Bau Chapter 10 of Golub and Van Loan An
Introduction to the Conjugate Gradient Method Without the Agonizing Pain |
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Monday 11/11 |
Lecture 21:
Iterative methods for eigenvalue problems Conjugate gradient
descent, preconditioning Lecture notes: slides |
Chapter 39-40 of Trefethen and Bau Chapter 10 of Golub and Van Loan |
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Monday 11/11 |
Lecture 22: Sparse
matrix approximation Lecture notes: slides |
Spielman’s lecture notes |
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Wednesday 11/13 |
Lecture 23: Matrix
algebra and machine learning Lecture notes: slides |
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Monday 11/18 |
Lecture 24: Norm
minimization Lecture notes: slides |
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Monday 11/18 |
Lecture 25: Sparse
representation Lecture notes: slides |
Atomic Decomposition by Basis Pursuit K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation |
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Wednesday 11/20 |
Lecture 26:
Compressive sensing Lecture notes: slides |
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Monday 12/09 |
Term project
presentation |
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