# Readings

When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more. |

This section contains documents that could not be made accessible to screen reader software. A "#" symbol is used to denote such documents.

The required textbook for this class is:

Trefethen and Bau. *Numerical Linear Algebra*. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1997, ISBN: 0898713617. (Abbreviated "NLA")

Other readings include:

Bai, et al. *Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide**.* Philadelphia, PA: Society for Industrial and Applied Mathematics, 2000. ISBN: 0898714710. (Abbreviated "Eig")

Barrett, et al. *Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods*. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1993. ISBN: 0898713285. (Abbreviated "It")

Shewchuk, Jonathan R. "An Introduction to the Conjugate Gradient Method Without the Agonizing Pain." Carnegie Mellon University (August 1994). (Abbreviated "CG") (PDF)^{#}

Goldberg, David. What Every Computer Scientist Should Know About Floating Point Arithmetic. *ACM Computing Surveys* 23, no. 1 (March 1991): 5-48. (Abbreviated "FP")

LEC # | TOPICS | READINGS |
---|---|---|

1 | Introduction, Basic Linear Algebra | NLA 1 |

2 | Orthogonal Vectors and Matrices, Norms | NLA 2 and 3 |

3 | The Singular Value Decomposition | NLA 4 and 5 |

4 | The QR Factorization | NLA 6 and 7 |

5 | Gram-Schmidt Orthogonalization | NLA 8 |

6 | Householder Reflectors and Givens Rotations | NLA 10 |

7 | Least Squares Problems | NLA 11 |

8 | Floating Point Arithmetic, The IEEE Standard | NLA 13, FP |

9 | Conditioning and Stability I | NLA 12, 14, and 15 |

10 | Conditioning and Stability II | NLA 16 and 17 |

11 | Gaussian Elimination, The LU Factorization | NLA 20 and 21 |

12 | Stability of LU, Cholesky Factorization | NLA 22 and 23 |

13 | Eigenvalue Problems | NLA 24 and 25 |

14 | Hessenberg / Tridiagonal Reduction | NLA 26 |

15 | The QR Algorithm I | NLA 27 and 28 |

16 | The QR Algorithm II | NLA 29 |

17 | Other Eigenvalue Algorithms | NLA 30 |

18 | The Classical Iterative Methods | It 2.2 |

19 | The Conjugate Gradients Algorithm I | NLA 38, CG |

20 | The Conjugate Gradients Algorithm II | NLA 38, CG |

21 | Sparse Matrix Algorithms | It 4.3, Eig |

22 | Preconditioning, Incomplete Factorizations | NLA 40, It 3 |

23 | Arnoldi / Lanczos Iterations | NLA 33 and 36 |

24 | GMRES, Other Krylov Subspace Methods | NLA 35 and 39, It 2.3 |

25 | Linear Algebra Software | Eig |