Course Program:
I Fundamentals
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Matrix-Vector Multiplication
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Orthogonal Vectors and Matrices
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Vector and Matrix Norms
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Singular Value Decomposition
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Application: Document Retrieval, Latent Semantic indexing, Procrustes analysis
II QR Factorization
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Projectors
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Gram-Schmidt Orthogonalization, QR Factorization
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MATLAB
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Householder Triangularization
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Least Square Problems
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Application: Polynomial and Basis Regression
III Conditioning and Stability
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Conditioning and Condition numbers
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Floating Point Arithmetic
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Stability
V Eigenvalues
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Eigenvalue Problems
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Overview of Eigenvalue Algorithms
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Reduction to Hessenberg or Tridiagonal form
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Rayleight Quotient, Inverse Iteration
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QR algorithm without/with shifts
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Computing the SVD
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Application: Spectral Clustering, Image segmentation
Textbook:
Reference Books:
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Golub, Gene H.; van Loan, Charles F. (1996), Matrix Computations, 3rd edition, Johns Hopkins University Press, ISBN 978-0-8018-5414-9
Grading:
Attendance and Participation in the lectures | %20 |
Midterm | %20 |
Final | %30 |
3 Projects | %30 |
Notes:
This course is dedicated to the memory of our collegue and friend Ismail Ari (1983-2013).