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

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