Math 391 Numerical Linear Algebra


Lecture Notes

The lecture notes are written in Matlab script format. You may download them to your computer and then publish them using Matlab.

  • Lecture 6: IEEE Floating Point Standard
  • Lecture 7: Avoiding overflow, catastrophic cancellation, rearranging the recurrence
  • Lecture 8: Efficiency and Stability of an Algorithm
  • Lecture 9: Conditioning of a problem and condition numbers
  • Lecture 10: Condition number of a matrix and perturbation analysis of the linear system
  • Lecture 11: Gaussian Elimination
  • Lecture 12: Gaussian Elimination with Partial Pivoting
  • Lecture 13: Cholesky Factorizatin for Positive Definite Matrices
  • Lecture 14: Linear System with Special Matrices, Inverses, Determinants
  • Lecture 15: QR Factorization and Householder Triangularization
  • Lecture 16: Givens Rotation and QR Factorization
  • Lecture 17: Singular Value Decomposition and Its Properties
  • Lecture 18: Least Squares Problem
  • Lecture 19: Minimum-Norm Least Squares Solution
  • Lecture 20: Eigenvalue Problems
  • Lecture 21: Rayleigh Quotient, Power Iteration, Rayleigh Quotient Iteration
  • lecture22: QR Algorithm for Eigenvalue Problems and SVD

  • Matlab Code

  • Gaussian Elimination A=LU
  • Back Substitution for solving Rx=b
  • Gaussian Elimination with Partial Pivoting PA=LU
  • Cholesky Factorization
  • A=LU for Hessenberg Matrices
  • A=LU for Tridiagonal Matrices
  • Householder Reflection for QR Factorization
  • Form Q explicitly for A=QR
  • Multiply Q with a given vector implicitly
  • Multiply Q^T with a given vector implicitly
  • Solve Ax=b using QR factorization
  • Compute the (minimum-norm) (least squares) solution to Ax=b using SVD
  • Power Iteration
  • Inverse Iteration
  • Rayleigh Quotient Iteration
  • Testing Rayleigh Quotient Iteration

  • Solution to quiz 3
  • Solution to problem 2 of quiz 5