Math 456

Calendar

Week 1 (1/18 - 1/22)

Monday	Wednesday	Friday
Martin Luther King, Jr. Day	The Least Squares Problem Backup Link	Orthogonal Matrices Backup Link

Week 2 (1/25 - 1/29)

Monday	Wednesday	Friday
Rotators and Reflectors Backup Link	Solving the Least Squares Problem Backup Link	Solving the Least Squares Problem in Python Backup Link

Week 3 (2/1 - 2/5)

Monday	Wednesday	Friday
Geometric Approach to Least Squares Backup Link	Intro to the SVD Backup Link	More on the SVD Backup Link

Week 4 (2/8 - 2/12)

Monday	Wednesday	Friday
The SVD and the Least Squares Problem Backup Link	Sensitivity of the Least Squares Problem Backup Link	Sensitivity of the Least Squares Problem in Python

Week 5 (2/15 - 2/19)

Monday	Wednesday	Friday
Exam 1	Intro to Eigenvalues and Eigenvectors Backup Link	More on Eigenvalues and Eigenvectors Backup Link

Week 6 (2/22 - 2/26)

Monday	Wednesday	Friday
The Power Method Backup Link	Shift and Invert Backup Link	Rayleigh Quotient Iteration in Python

Week 7 (3/1 - 3/5)

Monday	Wednesday	Friday
Similarity Transformations Backup Link	Reducation to Hessenberg form Backup Link	Francis Iteration of Degree One Backup Link

Week 8 (3/8 - 3/12)

Monday	Wednesday	Friday
Francis Iteration of Degree Two Backup Link	Convergence of Francis Iteration Backup Link	Francis Iteration in Python

Week 9 (3/15 - 3/19)

Monday	Wednesday	Friday
Eigenvectors with Francis Iteration Backup Link	The SVD Revisited Backup Link	Eigenvalue and SVD Computations in Python

Week 10 (3/22 - 3/26)

Monday	Wednesday	Friday
Exam 2	Systems of Differential Equations Backup Link	More on Systems of Differential Equations Backup Link

Week 11 (3/29 - 4/2)

Monday	Wednesday	Friday
The Determinant Backup Link	Principal Component Analysis Backup Link	Applications of Eigenvalues in Python I

Week 12 (4/5 - 4/9)

Monday	Wednesday	Friday
Markov Chains Backup Link	Wellness Day	More on Markov Chains Backup Link

Week 13 (4/12 - 4/16)

Monday	Wednesday	Friday
Page Rank Backup Link	Eigenvalue Applications in Python II	The Graph Laplacian Backup Link

Week 14 (4/19 - 4/23)

Monday	Wednesday	Friday
Algebraic Connectivity	Graph Clustering	Eigenvalue Appications in Python III

Week 15 (4/26 - 4/30)

Monday	Wednesday	Friday
Exam 3	Final Review I	Final Review II

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Intro. Numerical Analysis II

About

In this course, we will discuss one of the most important algorithms of the 20th century: Francis's Implicitly Shifted QR Algorithm. This algorithm changed the eigenvalue problem from difficult to routine in the early 1960s. It was later ranked as one of the top ten algorithms of the 20th century by Jack Dongarra and Francis Sullivan in the January/February 2000 issue of Computing in Science and Engineering. Armed with a reliable eigenvalue solver, we will be able to tackle other problems such as the singular value decomposition, least squares problem, and systems of differential equations. Applications include, but are not limited to, linear regression, roots of polynomials, principal component analysis, page rank, and graph clustering.