# Reading¶

As described in the syllabus, you are required to read each section prior to each class.

- The reading assignments are listed below, and must be read prior to class on the date indicated.

## Chapter 0 – Mathematical preliminaries¶

**Introduction to logic, sets, and proofs**: read Logic, Sets, and Proofs by D.A. Cox and C.C. McGeoch, due Jan 24

## Chapter 1 – Gaussian Elimination and Its Variants¶

**Section 1.1: Matrix Multiplication**, due Jan 24**Section 1.2: Systems of Linear Equations**, due Jan 24**Section 1.3: Triangular Systems**, due Jan 29**Section 1.4: Positive Definite Systems: Cholesky Decomposition**, due Jan 31**Section 1.5: Banded Positive Definite Systems**, due Feb 5**Section 1.6: Sparse Positive Definite Systems**, due Feb 7**Section 1.7: Gaussian Elimination and the LU Decomposition**, due Feb 12**Section 1.8: Gaussian Elimination with Pivoting**, due Feb 14**Section 1.9: Sparse Gaussian Elimination**, due Feb 14

## Chapter 2 – Sensitivity of Linear Systems¶

**Section 2.1: Vector and Matrix Norms**, due Feb 19**Section 2.2: Condition Numbers**, due Feb 19**Section 2.3: Perturbing the Coefficient Matrix**, due Feb 21**Section 2.4: A Posteriori Error Analysis Using the Residual**, due Feb 26**Section 2.5: Roundoff Errors: Backward Stability**, due Feb 26**Section 2.6: Propagation of Roundoff Errors**, due Mar 5**Section 2.7: Backward Error Analysis of Gaussian Elimination**, due Mar 7**Section 2.8: Scaling**, due Mar 7**Section 2.9: Componentwise Sensitivity Analysis**, due Mar 19

## Chapter 3 - The Least Squares Problem¶

**Section 3.1: The Discrete Least Squares Problem**, due Mar 21**Section 3.2: Orthogonal Matrices, Rotators, and Reflectors**, due Mar 21**Section 3.3: Solution of the Least Squares Problem**, due Mar 26**Section 3.4: The Gram-Schmidt Process**, due Mar 28

## Chapter 4 – The Singular Value Decomposition¶

**Section 4.1: Introduction**, due Apr 2**Section 4.2: Some Basic Applications of Singular Values**, due Apr 4**Section 4.3: The SVD and the Least Squares Problem**, due Apr 9

## Chapter 5 – Eigenvalues and Eigenvectors I¶

**Section 5.1: Systems of Differential Equations**, due Apr 9**Section 5.2: Basic Facts**, due Apr 16**Section 5.3: The Power Method and Some Simple Extensions**, due Apr 18**Section 5.4: Similarity Transforms**, due Apr 23**Section 5.5: Reduction to Hessenberg and Tridiagonal Forms**, due Apr 23**Section 5.6: Francis’s Algorithm**, due Apr 25**Section 5.7: Use of Francis’ Algorithm to Compute Eigenvectors**, due Apr 30**Section 5.8: The SVD Revisited**, due May 2