| 1 |
Introduction, Examples, Matrix-Vector and Matrix-Matrix Products |
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| 2 |
Orthogonal Matrices, Norms of Matrices |
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| 3 |
The Singular Value Decomposition |
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| 4 |
QR Factorization |
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| 5 |
Givens Rotations and Householder Reflections |
Homework 1 due |
| 6 |
Least Squares Problems |
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| 7 |
Floating Point Arithmetic |
Homework 2 due |
| 8 |
Conditioning and Stability |
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| 9 |
Stability of Givens Rotations and Backward Substitution |
Homework 3 due |
| 10 |
Stability of Least Squares Problems |
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| 11 |
Gaussian Elimination |
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| 12 |
Cholesky Factorization |
Homework 4 due |
| 13 |
Eigenvalue Problems |
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| 14 |
Hessenberg Reduction |
Homework 5 due |
| 15 |
QR Algorithm |
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| 16 |
Midterm |
Homework 6 due |
| 17 |
Stability of the QR Algorithm; Jacobi |
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| 18 |
Bisection, Divide and Conquer |
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| 19 |
SVD Algorithms |
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| 20 |
Iterative Algorithms, Arnoldi |
Homework 7 due |
| 21 |
Lanczos, GMRES |
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| 22 |
Conjugate Gradients |
Homework 8 due |
| 23 |
Solutions to Ordinary Differential Equations |
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| 24 |
Runge Kutta Methods |
Homework 9 due |
| 25 |
Solutions to Stiff ODEs - I |
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| 26 |
Solutions to Stiff ODEs - II |
Homework 10 due |
